Understanding the universe   an introduction to astronomy
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The book is designed to provide a nontechnical description of modern astronomy, including the structure and evolution of planets, stars, galaxies, and the Universe as a whole. The book contains a ...

The book is designed to provide a nontechnical description of modern astronomy, including the structure and evolution of planets, stars, galaxies, and the Universe as a whole. The book contains a large number of images, diagrams, and animations. The vigor is probably at the level of non-science college major or advance high school level.

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Understanding the universe   an introduction to astronomy Understanding the universe an introduction to astronomy Document Transcript

  • “Pure intellectual stimulation that can be popped into the [audio or video player] anytime.” —Harvard Magazine “Passionate, erudite, living legend lecturers. Academia’s best lecturers are being captured on tape.” —The Los Angeles Times “A serious force in American education.” —The Wall Street Journal THE GREAT COURSES® Corporate Headquarters 4840 Westfields Boulevard, Suite 500 Chantilly, VA 20151-2299 USA Phone: 1-800-832-2412 www.thegreatcourses.com Course No. 1810 © 2007 The Teaching Company. Cover Image: © NASA. PB1810A Professor Alex Filippenko is currently the Richard and Rhoda Goldman Distinguished Professor in the Physical Sciences at the University of California, Berkeley. He is among the most highly cited astronomers in the world. His extensive career has brought him scores of awards and accolades, including election to the National Academy of Sciences, the highest honor given to an American scientist, and UC Berkeley’s Distinguished Teaching Award. Professor Alex Filippenko University of California, Berkeley Course Guidebook Understanding the Universe: An Introduction to Astronomy, 2nd Edition Science & Mathematics Topic Astronomy Subtopic AnIntroductiontoAstronomyGuidebook
  • PUBLISHED BY: THE GREAT COURSES Corporate Headquarters 4840 Westfields Boulevard, Suite 500 Chantilly, Virginia 20151-2299 Phone: 1-800-832-2412 Fax: 703-378-3819 www.thegreatcourses.com Copyright © The Teaching Company, 2007 Printed in the United States of America This book is in copyright. All rights reserved. Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of The Teaching Company.
  • P rofessor Alex Filippenko received his bachelor’s degree in physics (1979) from the University of California, Santa Barbara, and his doctorate in astronomy (1984) from the California Institute of Technology. He subsequently became a Miller Postdoctoral Fellow for Basic Research in Science at the University of California, Berkeley. In 1986, he joined the faculty at UC Berkeley, where he has remained through the present time. A member of the International Astronomical Union, Dr. Filippenko has served as president of the Astronomical Society of the Paci c and as councilor of the American Astronomical Society. An observational astronomer who makes frequent use of the Hubble Space Telescope and the Keck 10-meter telescopes, Dr. Filippenko’s primary areas of research are exploding stars (supernovae), active galaxies, black holes, gamma-ray bursts, and cosmology. He and his collaborators recognized a new class of exploding star, obtained some of the best evidence for the existence of small black holes in our Milky Way Galaxy, and found that other galaxies commonly show vigorous activity in their centers that suggests the presence of supermassive black holes. His robotic telescope at Lick Observatory in California is the world’s most successful search engine for relatively nearby supernovae, having discovered more than 800 of them since 1998. Dr. Filippenko also made major contributions to the discovery that the expansion rate of the universe is speeding up with time (the accelerating universe), driven by a mysterious form of dark energy—the top “Science Breakthrough of 1998,” according to the editors of Science magazine. Dr. Filippenko’s research ndings are documented in more than 600 published papers, and he is one of the world’s most highly cited astronomers. He has been recognized with several major awards, including the Newton Lacy Pierce Prize of the American Astronomical Society (1992), the Robert M. Petrie Prize of the Canadian Astronomical Society (1997), and the Richtmyer ii Alex Filippenko, Ph.D. Professor of Astronomy University of California, Berkeley
  • ii Memorial Award of the American Association of Physics Teachers (2007). A Fellow of the California Academy of Sciences, and an elected member of the National Academy of Sciences. Dr. Filippenko has also been a Guggenheim Foundation Fellow (2001) and a Phi Beta Kappa Visiting Scholar (2002). He has held distinguished visiting positions at numerous colleges and universities, including the Marlar Lecturer at Rice University and both the Spitzer Lecturer and Farnum Lecturer at Princeton University. At the UC Berkeley campus, Dr. Filippenko has won the coveted Distinguished Teaching Award (1991) and the Donald S. Noyce Prize for Excellence in Undergraduate Teaching in the Physical Sciences (1991), each of which is generally given at most once per career. He was voted the “Best Professor” on campus seven times in student polls. Also, in 2002, he received the Distinguished Research Mentoring of Undergraduates Award, given by UC Berkeley. Dr. Filippenko has delivered hundreds of public lectures on astronomy and has played a prominent role in science newscasts and television documentaries, such as “Mysteries of Deep Space,” “Stephen Hawking’s Universe,” “Runaway Universe,” and more than 20 episodes of “The Universe” on The History Channel. With Jay M. Pasachoff, Dr. Filippenko coauthored an introductory astronomy textbook, The Cosmos: Astronomy in the New Millennium, now in its 3rd edition, which won the 2001 Texty Excellence Award of the Text and Academic Authors Association for the best new textbook in the physical sciences. This 2006 edition of Understanding the Universe combines and updates Dr. Filippenko’s previous introduction to astronomy courses, recorded for The Teaching Company in 1998 and 2003. He also recorded Black Holes Explained in 2009. Dr. Filippenko was the recipient of the 2004 Carl Sagan Prize for Science Popularization from the Trustees of Wonderfest, the San Francisco Bay Area Festival of Science. The Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education honored him as the “Outstanding Doctoral and Research Universities Professor of the Year” in 2006. In 2010, he won the Astronomical Society of the Paci c’s Richard H. Emmons award for undergraduate teaching.
  • iii Table of Contents LECTURE GUIDES INTRODUCTION LECTURE GUIDESLECTURE GUIDES INTRODUCTIONINTRODUCTION LECTURE 1 A Grand Tour of the Cosmos ..............................................................5 LECTURE 2 The Rainbow Connection .................................................................10 LECTURE 3 Sunrise, Sunset ................................................................................15 LECTURE 4 Bright Objects in the Night Sky.........................................................21 LECTURE 5 Fainter Phenomena in the Night Sky................................................26 LECTURE 6 Our Sky through Binoculars and Telescopes....................................31 LECTURE 7 The Celestial Sphere........................................................................36 LECTURE 8 The Reason for the Seasons............................................................41 LECTURE 9 Lunar Phases and Eerie Lunar Eclipses ..........................................45 LECTURE 10 Glorious Total Solar Eclipses............................................................50 Professor Biography............................................................................i Course Scope.....................................................................................1
  • Table of Contents iv LECTURE 11 More Eclipse Tales ...........................................................................56 LECTURE 12 Early Studies of the Solar System....................................................60 LECTURE 13 The Geocentric Universe..................................................................66 LECTURE 14 Galileo and the Copernican Revolution............................................71 LECTURE 15 Re nements to the Heliocentric Model.............................................76 LECTURE 16 On the Shoulders of Giants ..............................................................81 LECTURE 17 Surveying Space and Time...............................................................86 LECTURE 18 Scale Models of the Universe...........................................................91 LECTURE 19 Light—The Supreme Informant ........................................................96 LECTURE 20 The Wave-Particle Duality of Light .................................................101 LECTURE 21 The Colors of Stars.........................................................................107 LECTURE 22 The Fingerprints of Atoms .............................................................. 111 LECTURE 23 Modern Telescopes ........................................................................116
  • Table of Contents v LECTURE 24 A Better Set of Eyes .......................................................................121 LECTURE 25 Our Sun, the Nearest Star..............................................................127 LECTURE 26 The Earth, Third Rock from the Sun...............................................132 LECTURE 27 Our Moon, Earth’s Nearest Neighbor .............................................137 LECTURE 28 Mercury and Venus.........................................................................142 LECTURE 29 Of Mars and Martians.....................................................................147 LECTURE 30 Jupiter and Its Amazing Moons ......................................................152 LECTURE 31 Magni cent Saturn..........................................................................157 LECTURE 32 Uranus and Neptune, the Small Giants..........................................162 LECTURE 33 Pluto and Its Cousins......................................................................167 LECTURE 34 Asteroids and Dwarf Planets ..........................................................172 LECTURE 35 Comets—Gorgeous Primordial Snowballs .....................................177 LECTURE 36 Catastrophic Collisions...................................................................181
  • Table of Contents vi LECTURE 37 The Formation of Planetary Systems .............................................186 LECTURE 38 The Quest for Other Planetary Systems.........................................192 LECTURE 39 Extra-Solar Planets Galore!............................................................197 LECTURE 40 Life Beyond the Earth.....................................................................202 LECTURE 41 The Search for Extraterrestrials......................................................207 LECTURE 42 Special Relativity and Interstellar Travel.........................................212 LECTURE 43 Stars—Distant Suns .......................................................................218 LECTURE 44 The Intrinsic Brightnesses of Stars.................................................223 LECTURE 45 The Diverse Sizes of Stars.............................................................228 LECTURE 46 Binary Stars and Stellar Masses ....................................................234 LECTURE 47 Star Clusters, Ages, and Remote Distances ..................................239 LECTURE 48 How Stars Shine—Nature’s Nuclear Reactors...............................244 LECTURE 49 Solar Neutrinos—Probes of the Sun’s Core...................................249
  • Table of Contents vii LECTURE 50 Brown Dwarfs and Free-Floating Planets.......................................254 LECTURE 51 Our Sun’s Brilliant Future ...............................................................259 LECTURE 52 White Dwarfs and Nova Eruptions..................................................263 LECTURE 53 Exploding Stars—Celestial Fireworks! ...........................................268 LECTURE 54 White Dwarf Supernovae—Stealing to Explode.............................272 LECTURE 55 Core-Collapse Supernovae—Gravity Wins ....................................277 LECTURE 56 The Brightest Supernova in Nearly 400 Years................................281 LECTURE 57 The Corpses of Massive Stars .......................................................286 LECTURE 58 Einstein’s General Theory of Relativity...........................................291 LECTURE 59 Warping of Space and Time ...........................................................294 LECTURE 60 Black Holes—Abandon Hope, Ye Who Enter.................................299 LECTURE 61 The Quest for Black Holes..............................................................304 LECTURE 62 Imagining the Journey to a Black Hole...........................................308
  • Table of Contents viii LECTURE 63 Wormholes—Gateways to Other Universes?.................................313 LECTURE 64 Quantum Physics and Black-Hole Evaporation..............................318 LECTURE 65 Enigmatic Gamma-Ray Bursts .......................................................323 LECTURE 66 Birth Cries of Black Holes...............................................................327 LECTURE 67 Our Home—The Milky Way Galaxy................................................332 LECTURE 68 Structure of the Milky Way Galaxy .................................................336 LECTURE 69 Other Galaxies—“Island Universes”...............................................342 LECTURE 70 The Dark Side of Matter .................................................................347 LECTURE 71 Cosmology—The Really Big Picture ..............................................352 LECTURE 72 Expansion of the Universe and the Big Bang.................................357 LECTURE 73 Searching for Distant Galaxies.......................................................363 LECTURE 74 The Evolution of Galaxies...............................................................368 LECTURE 75 Active Galaxies and Quasars .........................................................373
  • Table of Contents ix LECTURE 76 Cosmic Powerhouses of the Distant Past ......................................377 LECTURE 77 Supermassive Black Holes.............................................................383 LECTURE 78 Feeding the Monster.......................................................................388 LECTURE 79 The Paradox of the Dark Night Sky................................................393 LECTURE 80 The Age of the Universe.................................................................398 LECTURE 81 When Geometry Is Destiny.............................................................404 LECTURE 82 The Mass Density of the Universe..................................................409 LECTURE 83 Einstein’s Biggest Blunder?............................................................414 LECTURE 84 The Afterglow of the Big Bang........................................................419 LECTURE 85 Ripples in the Cosmic Background Radiation ................................425 LECTURE 86 The Stuff of the Cosmos.................................................................431 LECTURE 87 Dark Energy—Quantum Fluctuations?...........................................437 LECTURE 88 Dark Energy—Quintessence?........................................................443
  • Table of Contents x LECTURE 89 Grand Uni cation & Theories of Everything ...................................448 LECTURE 90 Searching for Hidden Dimensions..................................................454 LECTURE 91 The Shape, Size, and Fate of the Universe....................................459 LECTURE 92 In the Beginning..............................................................................465 LECTURE 93 The In ationary Universe................................................................470 LECTURE 94 The Ultimate Free Lunch?..............................................................475 LECTURE 95 A Universe of Universes .................................................................480 LECTURE 96 Re ections on Life and the Cosmos...............................................486 SUPPLEMENTAL MATERIAL Useful Symbols...............................................................................491 Universe Timeline...........................................................................492 Solar System Timeline....................................................................494 Glossary .........................................................................................495 Biographical Notes .........................................................................517 Bibliography....................................................................................522
  • Scope: 1 Understanding the Universe: An Introduction to Astronomy, 2nd Edition T his visually rich course is designed to provide a nontechnical description of modern astronomy, including the structure and evolution of planets, stars, galaxies, and the Universe as a whole. It includes almost all of the material in my rst two astronomy courses for The Teaching Company, produced in 1998 and 2003, but with a large number of new images, diagrams, and animations. The discoveries reported in the 2003 course are integrated throughout these new lectures, and more recent ndings (through mid-2006) are included, as well. Much has happened in astronomy during the past few years; we will discuss the most exciting and important advances. Astronomical objects have been explored with breathtaking data obtained by the Hubble Space Telescope, the Chandra X-Ray Observatory, the Keck 10-meter telescopes, planetary probes, and other modern instruments. We will explore amazing phenomena, such as quasars, exploding stars, neutron stars, and black holes, and we will see how they increase our understanding of the physical principles of nature. We will also investigate recent newsworthy topics, such as the Cassini mission to Saturn, evidence for liquid water on ancient Mars, the discovery of many small bodies beyond Neptune in our Solar System, the detection of numerous planets around other stars, the nonzero mass of ghostly neutrinos, enormously powerful gamma-ray bursts, the conclusive evidence for a supermassive black hole in the center of our Milky Way Galaxy, the determination of the age of the Universe, the discovery of a long-range repulsive effect accelerating the expansion of the Universe, and progress in the uni cation of nature’s fundamental forces. Scienti cally reasonable speculations regarding the birth of the Universe, the possibility of multiple universes, and the probability of extraterrestrial life are also included.
  • Scope 2 This course concentrates on the most exciting aspects of our fantastic Universe and on the methods astronomers have used to develop an understanding of it. The lectures present, in clear and simple terms, explanations of how the Universe “works,” as well as the interrelationships among its different components. Reliance on basic mathematics and physics is minimal but appropriate in some sections to deepen the interested viewer’s quantitative understanding of the material. The course is divided into three major sections, each of which consists of several units. (These major sections are called “parts” during the lectures, but they are not to be confused with the eight 12-lecture “parts” used in packaging the lectures.) There are 24 lectures in section 1, entitled “Observing the Heavens.” The rst unit, “Celestial Sights for Everyone,” describes simple daytime and nighttime observations that you can make to better appreciate the sky and what it contains. Various commonly observed phenomena, such as seasons, lunar phases, and eclipses, are also discussed. The second unit, “The Early History of Astronomy,” covers the study of astronomy from the ancient Greeks through Newton, including the transition from geocentric (Earth-centered) to heliocentric (Sun-centered) models of the Universe. In the third unit, “Basic Concepts and Tools,” we provide an overview of distance and time scales in the Universe to put our discussions in perspective. Because the study of light is of central importance to astronomy, we spend several lectures explaining its physical nature and utility. Modern telescopes, the main instruments used by astronomers, are also described. Section 2, “The Contents of the Universe,” consists of 46 lectures in 5 units. In the rst unit, “Our Solar System,” we discuss the major constituents of our own planetary system, including the Sun, planets and their moons, comets, asteroids, and Kuiper-belt objects. The discovery of a distant body larger than Pluto and the subsequent, highly controversial demotion of Pluto from planetary status have recently made worldwide headlines. The formation of other stars and planetary systems, as well as the discovery of such extrasolar planets, is the subject of the second unit, “Other Planetary Systems.” During the past decade, about 200 planets have been found orbiting other stars, making this one of the most exciting areas of modern astronomy. The search for extraterrestrial life is also described.
  • 3 In the third unit of section 2, “Stars and Their Lives,” we learn about the properties of other stars and the various observations needed to deduce them. Nuclear reactions, the source of energy from the stars, are described, as well. We examine how stars eventually become red giants, subsequently shedding their outer layers to end up as dense white dwarfs, retired stars. The explosive fates of some rare types of stars are the subject of the fourth unit, “Stellar Explosions and Black Holes,” and we explain how the heavy elements necessary for life are created. Bizarre stellar remnants include neutron stars and black holes, the realm of Einstein’s general theory of relativity. We continue our exploration of black holes with such phenomena as black-hole evaporation and powerful gamma-ray bursts, as well as speculations that black holes are gateways to other universes. In the fth unit, “The Milky Way and Other Galaxies,” we extend our explorations to the giant collections of stars called galaxies, along the way examining evidence for mysterious dark matter. Section 3, “Cosmology: The Universe as a Whole,” comprises the nal 26 lectures of the course in 3 units. The rst unit, “Cosmic Expansion and Distant Galaxies,” introduces the expansion of the Universe and shows how it is used to study the evolution of galaxies. We discuss active galaxies and quasars, in which matter is inferred to be falling into a central, supermassive black hole. In the second unit, “The Structure and Evolution of the Universe,” aspects of the Universe, such as its age, geometry, and possible fate, are considered. We examine evidence for the stunning conclusion that the expansion of the Universe is currently accelerating. We also describe the cosmic microwave background radiation—the generally uniform afterglow of the Big Bang—as well as the tiny irregularities that reveal the presence of early density variations from which all of the large-scale structure of the Universe subsequently formed. The nature of dark energy accelerating the Universe is explored in terms of modern attempts to unify forces, such as string theory. In the third and nal unit, “The Birth of the Cosmos, and Other Frontiers,” we examine the very early history of the Universe, showing how the lightest elements formed during a phase of primordial nucleosynthesis. The recognition of several troubling problems with the standard Big Bang theory led to a magni cent re nement—an in ationary epoch of expansion
  • Scope 4 that lasted only a tiny fraction of a second. The possible connection between in ation and the currently accelerating expansion of space is also discussed. We then consider very speculative ideas regarding the birth of the Universe and the hypothesis of multiple universes. We end, in the last lecture, on a philosophical note, with some re ections on intelligent life in the cosmos and of our place in the grand scheme of things. Overview of Course Organization Major Section Lectures Units Observing the Heavens 2–24 Celestial Sights for Everyone (2 11) The Early History of Astronomy (12 16) Basic Concepts and Tools (17 24) The Contents of the Universe 25–70 Our Solar System (25 36) Other Planetary Systems (37 42) Stars and Their Lives (43 52) Stellar Explosions and Black Holes (53 66) The Milky Way and Other Galaxies (67 70) Cosmology: The Universe as a Whole 71 96 Cosmic Expansion and Distant Galaxies (71 78) The Structure and Evolution of the Universe (79 90) The Birth of the Cosmos, and Other Frontiers (91 96)
  • 5 A Grand Tour of the Cosmos Lecture 1 “Get ready for a fantastic voyage through the Universe. We will explore just about all of the major topics in astronomy. I promise you a ride that you will never forget.” W e are in a golden age of astronomy. Amazing discoveries are being made at a rapid pace with powerful instruments, such as the Hubble Space Telescope. Hardly a week goes by without an astronomical news story, and major headlines appear almost monthly. I have a number of major goals in this course. The rst is simply to share with you the excitement and magni cence of the Universe: How does the Universe work? What are the most interesting new results? I’ll cover provocative, mind-boggling topics! Astronomical News Stories of the Past Decade • Spacecraft to various planets have revealed surprising new properties. • An object beyond the orbit of Pluto, and slightly larger than Pluto, has been found—the “10th planet,” according to some astronomers. • About 200 planets have been detected orbiting stars other than the Sun. • We understand the basic process by which stars are created from clouds of gas and dust. • The existence of black holes has been convincingly shown. • The birth and evolution of galaxies have been studied. • Tiny ripples in the distribution of material have been detected early in the history of the Universe; clusters of galaxies formed from these variations. • We have witnessed collisions between galaxies that induce giant bursts of star formation. • Colossal explosions have been seen billions of light years away. • The age of the Universe has been measured accurately. • The expansion rate of the Universe appears to be accelerating. • Most of the Universe consists of exotic dark matter and mysterious dark energy.
  • 6 Lecture1:AGrandTouroftheCosmos A second goal is to provide a survey of all of astronomy. This will give you a basic understanding of astronomy and, I hope, kindle your Socratic ame. Socrates said, “Education is the kindling of a ame, not the lling of a vessel.” My third goal is to show you that astronomy is a quest for our origins, our place in the cosmos. How did we get here, and where are we going? Most of us have gazed with wonder at the stars and asked some of these questions. This is part of what makes astronomy such a personal and popular science. Another goal is to give you some idea of how science is done and to convey the thrill of scienti c discovery. Science is a dynamic process: New ideas are developed and tested and modi ed when necessary. Scientists want to gure out how things work. Some of our views at the cutting edge of astronomy are changing yearly. What is said here re ects the state of knowledge in mid-2006, and part of it may be out of date shortly. But there are certain foundations that are unlikely to change and upon which we can build. I will try to indicate which parts of the course are the most speculative and uncertain. Course Contents Part 1: “Observing the Heavens” (Lectures 1–24) • Unit 1: Celestial Sights for Everyone • Unit 2: The Early History of Astronomy • Unit 3: Basic Concepts and Tools Part 2: “The Contents of the Universe” (Lectures 25–70) • Unit 1: Our Solar System • Unit 2: Other Planetary Systems • Unit 3: Stars and Their Lives • Unit 4: Stellar Explosions and Black Holes • Unit 5: The Milky Way and Other Galaxies Part 3: “Cosmology: The Universe as a Whole” (Lectures 71–96) • Unit 1: Cosmic Expansion and Distant Galaxies • Unit 2: The Structure and Evolution of the Universe • Unit 3: The Birth of the Cosmos and Other Frontiers
  • 7 Finally, I want to heighten your sense of awe and wonder about the cosmos and to increase your curiosity about the world around you. The course is mostly descriptive, non-technical, and non-mathematical. I will focus on concepts and qualitative explanations. Nevertheless, astronomy is a physical science, and many viewers do want a quantitative component. Hence, where appropriate, I will introduce simple mathematical and physical relationships, but their use will be minimal. Most of the quantitative parts will be easy to understand if you have a good knowledge of high-school algebra and geometry, as well as some high-school physics. However, if you don’t understand them, or are not in the mood for math and physics, you can largely ignore these interludes; you can get the main ideas without concentrating on the math. Some lectures are more technical than others, but at least a qualitative understanding should be accessible to most viewers. The primary textbook recommended as a supplement to these lectures is The Cosmos: Astronomy in the New Millennium (3rd edition, 2007; Thomson/ Brooks-Cole, available on amazon.com), by Jay M. Pasachoff and Alex Filippenko. It spans most, but not all, of the topics covered in this course, in roughly (but not exactly) the same order. It also includes many of the photographs and diagrams shown in the video lectures. “Cosmos” means “the Universe,”—but more speci cally, the Universe regarded as an orderly, harmonious whole. Pasachoff and I hope to have presented an orderly, harmonious overview of astronomy to the general reader. In the video ©iStockphoto/Thinkstock A spiral galaxy consisting of more than 100 billion stars.
  • 8 Lecture1:AGrandTouroftheCosmos lectures, I show an assortment of photographs and movies, covering some of the topics to be included in the course. You might want to leaf through the recommended textbook and look at many of the stunning photographs. black hole: A region of space-time in which the gravitational eld is so strong that nothing, not even light, can escape. Predicted by Einstein’s general theory of relativity. dark energy: Energy with negative pressure, causing the expansion of the Universe to accelerate. dark matter: Invisible matter that dominates the mass of the Universe. galaxy: A large (typically 5000 to 200,000 light years in diameter), gravitationally bound system of hundreds of millions (and up to a trillion) stars. light year: The distance light travels in one year—about 10 trillion kilometers, or 6 trillion miles. planet: A body that primarily orbits a star (so that moons don’t count), is large enough to be roughly spherical (typically, larger than about 600 km in diameter), gravitationally dominates its region of space (that is, has largely cleared away other debris), and has never undergone nuclear fusion. planetary system: A collection of planets and smaller bodies orbiting a star. quasar: A star-like, extremely luminous (powerful) object billions of light years away. star: A self-luminous, gravitationally bound ball of gas that shines (or used to shine) because of nuclear reactions in its core. The Sun is a typical star. Universe: “All that there is.” (Actually, there could be other, physically disjoint universes with which we have no direct interactions!) Important Terms
  • 9 The standard textbooks recommended to accompany these video lectures are as follows: Pasachoff and Filippenko. The Cosmos: Astronomy in the New Millennium, 3rd ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. (This is a longer but somewhat outdated version of The Cosmos, listed above.) Several monthly nontechnical magazines on astronomy should also be consulted; they have a wealth of useful information about new discoveries, current events in the sky, and so on. Among the best 3 are Sky and Telescope (www.skyandtelescope.com), Astronomy (www.astronomy.com), and Mercury (www.astrosociety.org). Viewers who want to explore much more mathematics and physics should consult the following textbooks: Carroll and Ostlie. An Introduction to Modern Astrophysics. Shu, The Physical Universe. The Astronomical Society of the Paci c (ASP) serves as a link among professional astronomers, amateur astronomers, teachers, and the general public. The society provides a wide variety of services, and I encourage you to join the ASP. See its Web site at www.astrosociety.org. 1. What do you hope to get out of this course? 2. In what ways do you think the study of astronomy is an investigation of our origins? 3. How is the pace of discovery in astronomy a sign of the eld’s health and intellectual vitality? 4. What are some of the most exciting astronomical discoveries of which you have heard during the past year or two? Suggested Reading Questions to Consider
  • 10 Lecture2:TheRainbowConnection The Rainbow Connection Lecture 2 “There are plenty of beautiful things to see in the daytime sky—full of color, full of wonderful geometry, all produced by the complex interaction of light waves with water in its liquid state and in the solid form of ice crystals.” T hough the night sky is full of light and color, the daytime sky also contains some intriguing natural sights. One such phenomenon is the rainbow. When sunlight enters a spherical raindrop, the light is refracted, or bent, by varying degrees, depending on its color. Violet light is bent the most, and red, the least. The light is then re ected, or bounced, off the back side of the raindrop and exits at the front at an angle relative to the incoming light ray. This re ected light forms the primary rainbow. Each color is re ected at a slightly different angle as measured from the center of the rainbow—the point opposite the Sun—to where the rays enter your eye. The radius of a primary rainbow is about 42°—more speci cally, 42° for red light and 40° for violet light. Depending on the angle of re ection, each raindrop produces a certain color. These colors will change depending on the angle at which you look at the rainbow. The rays you perceive as red come from a different set of drops than the rays you perceive as blue. Every drop along a light ray of a given color bends that same color to your eye. The very drop that re ects blue to your eyes can re ect another color to an observer elsewhere. Similarly, the angle of the Sun affects how much of a rainbow’s arc is visible. If the Sun is close to the horizon, you will see nearly a full semicircle. If the Sun is high, you will see a smaller arc closer to the ground. Full-circle rainbows are visible from an airplane. From the ground, you can see nearly a full circle when a rainbow appears over a canyon; part of the arc extends below the true horizon into the canyon. Why don’t the different colors of a rainbow mix together and become blurred? Light is re ected off a raindrop at different angles, depending on
  • 11 the angle at which the light entered the water droplet. However, there is an area where light enters the drop and exits at nearly the same angle. Because this exit angle changes minimally as a function of the entrance point, the rays bunch up at a certain angle, thus re ecting a speci c color. If sunlight is blocked, only a partial rainbow is visible. Rainbows appear to move as you move. If you change locations, the rainbow will be formed from a different set of raindrops. In strong sunlight, a secondary bow is sometimes visible at a radius of 51° from the point opposite the Sun. A secondary bow occurs when light enters the bottom of a raindrop and bounces twice within the raindrop to exit at a completely different angle compared with the light forming the primary bow. The colors of the secondary rainbow form opposite to the primary one. In a primary bow, blue appears on the inside, and red, on the outside. In a secondary bow, red is on the inside, and blue is on the outside. Next to the blue light of the primary rainbow, you can sometimes see faint bands, called supernumerary bows, produced by light waves interfering with each other. When two light waves are in phase, the result is constructive interference; when out of phase, destructive interference. Two rays can enter a raindrop at two different points yet have the same exit angle. But the two rays travel different paths inside the raindrop. Constructive interference creates a bright supernumerary bow; destructive interference creates a faint one. Solar halos are similar to rainbows in that they are created by refracted light, but in ice crystals, not raindrops. With a radius of 22°, solar halos—rings around the Sun—are created when light enters long and skinny hexagonal ice crystals. The ice crystals usually occur in high-altitude cirrus clouds, where the temperatures are very cold, regardless of Earth’s surface temperature. Sundogs, or mock suns, are phenomena related to solar halos and usually appear as a particularly bright part of the halo’s outer edge. They are produced by hexagonal ice crystals, just as halos are, but the crystals are at “You need raindrops in a particular direction of the sky, and you need them to be illuminated by sunlight. If there aren’t raindrops … you won’t see a rainbow.”
  • 12 Lecture2:TheRainbowConnection and plate-like. Sundogs can be so bright that you can often see them without seeing the rest of the halo. You can also see lunar halos, which are fainter than solar halos but easier to see because the Moon’s glare is far dimmer than that of the Sun. Additional and similar phenomena can occur in the atmosphere during the day, as well. Under exceptional conditions, a secondary halo—with a radius of 46°—appears around the Sun. Also, tangential arcs occur under very clear and cold conditions. Coronas are multicolored halo-like rings around the Sun or Moon, but they have much smaller angular radii than regular halos. Though called coronas, they have nothing to do with the outer atmosphere of the Sun, which is also called the corona. Coronas are formed by diffraction, when light is bent as it passes around a droplet of water, together with the wave interference of light, as in the supernumerary bows. You can see such a corona by looking Light refracted by ice crystals creates a solar halo. ©iStockphoto/Thinkstock
  • 13 at a bright headlight through fog; it is caused by this bending of light around droplets and the constructive and destructive interference of that light with itself. Another phenomenon, known as “the glory,” is still not fully understood. A ring of light appears around the shadow of an object cast on a cloud far from it. Here, light bends around and within water droplets and is re ected. Surface waves are also present, traveling through the raindrop. Sun pillars form a column of light above the Sun and are most easily visible just after sunset. Light re ects off at, hexagonal ice crystals in a way similar to sunlight re ecting off rippling water on the surface of a pond or lake. corona: The very hot, tenuous, outermost region of the Sun, seen during a total solar eclipse. diffraction: A phenomenon affecting light as it passes any obstacle, spreading it out. glory, the: A thin halo of light around the shadow of an object projected on a cloud; caused by the bending of light around and within water droplets. halo (solar or lunar): A circle of light around the Sun or Moon, having a radius of about 22 degrees, formed by light passing through hexagonal ice crystals. horizon: The great circle de ned by the intersection of the celestial sphere with the plane tangent to the Earth at the observer’s location; it is 90 degrees away from the zenith. interference: The property of radiation, explainable by the wave theory, in which waves in phase can add (constructive interference) and waves out of phase can subtract (destructive interference). Important Terms
  • 14 Lecture2:TheRainbowConnection sundog: A pair of bright spots on the outer edge of the solar halo at roughly the Sun’s altitude above the horizon. sun pillar: A faint pillar of light above the Sun in the sky, best visible after sunset. Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Parviainen, www.polarimage. (solar halos and other atmospheric phenomena). Light and Optics, ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/home.rxml (rainbows, solar halos, sundogs, and other atmospheric phenomena). 1. How could you determine the approximate location of raindrops that produce a rainbow? (Think about viewing the rainbow against a backdrop of objects that are at different distances from you.) 2. Under what conditions might you see a full 360-degree circle of a rainbow? 3. If you move toward the end of a rainbow, in search of the proverbial pot of gold, what will happen to the position of the rainbow? Will you ever reach the rainbow’s end? Suggested Reading Questions to Consider
  • 15 Sunrise, Sunset Lecture 3 “The Earth is shadowing part of the atmosphere. … As the sun dips farther below the horizon, the shadow grows more and more and looms above you; twilight starts when the whole shadow envelops you. At that point, the planets and stars begin to come out, and it’s time to start observing the night sky.” W hy is the sky blue? Blue light rays from the Sun are selectively scattered (re ected) by air molecules, producing the blue daytime sky away from the Sun’s direction. Violet light, having an even shorter wavelength than blue light, is scattered even more ef ciently than blue light, but there is not as much violet sunlight, and human eyes are not as sensitive to it. Green light, having a longer wavelength than blue light, is not scattered as ef ciently as blue light, so blue is the predominant color of the daytime sky. As the Sun sets, its color progresses through a range, from white to yellow, to orange, and nally, sometimes, to red. As the Sun rises in the sky in the morning, the color scheme is reversed. Closer to the horizon, sunlight travels through a longer atmospheric path, which causes more scattering of light out of your line of sight. Because yellow, orange, and red light are scattered out of your line of sight less than violet, blue, or green light, the yellow, orange, or red light is more likely to reach your eyes, making the Sun appear that color. Particulate matter, such as dust or smoke, in the atmosphere also affects the color of the setting and rising Sun. Violet and blue light are absorbed most easily by dust and smoke in the air, as is green light to a lesser extent. The more dust, smog, or other pollution in the air, the more absorption of violet, blue, and green Several atmospheric conditions contribute to the vivid colors that characterize both sunrises and sunsets, turning the Sun’s white light and the normal daytime blue sky into an artist’s palette.
  • 16 Lecture3:Sunrise,Sunset light there will be, producing a more orange or red sunset. Clouds also re ect the setting Sun’s rays, adding color to the sky. Light that reaches clouds and is re ected from them tends to be yellow, orange, or red, because the violet, blue, and green light has been scattered away by air or absorbed by particulate matter. The Moon can appear in different shades of yellow, orange, or red when it is rising or setting, for exactly the same reasons the Sun does. When the Moon and the Sun appear a little bit above the horizon upon setting or rising, they are actually just below the horizon. On entering the atmosphere, light is refracted, or bent, but our eyes don’t perceive this bending. They see only the direction from which the light was coming, which makes the Sun or the Moon appear to be higher than its true position. The magnitude of this effect is about one full Sun or Moon diameter. In other words, when the Moon or the Sun is just kissing the horizon, it is actually one whole diameter below the horizon. The green ash is a hard-to-see yet fascinating phenomenon that occurs just before the Sun fully sets or just as it begins to rise. To see the green ash, the skies must be clear and free of dust. You must have a clear view of the horizon, unobstructed by mountains or buildings. Lasting only a second or two, the ash is actually a green button-like spot of light visible at the top of the Sun just before it sets or rises. The ash is created, in part, because the Sun’s true position on the horizon is actually lower than it appears as a result of the bending of light. Violet and blue light rays, having short wavelengths, Sunrise in Kruger Park, South Africa. ©iStockphoto/Thinkstock
  • 17 are bent more than the longer-wavelength yellow, orange, and red light rays. Green rays are intermediate in wavelength and are bent at an intermediate angle. Thus, you see the green sunrays between red and blue, though in reality, these colors overlap quite a bit. Projected back onto the sky, the setting Sun seems to consist of several mostly overlapping disks of different colors; violet is highest and red is lowest, with green in the middle. Violet and blue light are scattered in the atmosphere and absorbed by dust; therefore, the violet and blue are not visible, which leaves green as the next shortest wavelength visible to our eyes. The red disk sets rst, followed by the orange, then the yellow. The green disk sets last, but because it overlaps the other disks, only the very top sliver is visible just before it sets, creating the green ash. An orange or red Sun indicates dust in the atmosphere, which lessens the chances of seeing the green ash. A more yellowish-white setting Sun offers a better chance. Mirages, which make the Sun appear as if a piece has been broken off, actually cause the green ash to be visible for a few seconds. A mirage occurs when the Sun’s rays are highly distorted, bending at different angles due to different layers in the atmosphere that have different temperatures and densities. Mirages come in two main types: An inferior mirage occurs when cool, dense air is above hot, less dense air. This typically occurs over a hot asphalt road or sand, when the shimmering heat waves appear just above the surface and look like water. The “water” actually consists of light rays from the blue sky. A superior mirage occurs when cold, dense air is below hot, less dense air. This typically occurs over a cold body of water, such as the ocean. Under inferior-mirage conditions, incoming light rays bend toward the denser, cooler air above, reaching the eye from a more horizontal angle and creating the “lake in the desert” effect. Under superior-mirage conditions, incoming light bends downward, reaching the eye at a steeper angle and making objects appear higher above the surface than they really are. The superior-mirage effect is strongest from the lowest points, which appear higher than other points that are actually physically higher on or above Earth’s surface. These mirages can also produce inverted images of objects. Ships sailing on the ocean, for example, can appear inverted.
  • 18 Lecture3:Sunrise,Sunset Applying the properties of mirages to the setting Sun, we see how they enhance the green ash. The Sun becomes distorted when it nears the horizon, causing a part of it to appear as if it’s hovering above the horizon as a result of the mirage effect. When the top piece of the Sun “breaks off,” the green button portion separates from the rest of the Sun, hovering above the horizon for an extra few seconds, allowing you to see the green ash. When looking at the Sun, even low on the horizon, avoid staring at it directly for more than a few seconds so as not to burn your eyes. Once desensitized from staring at the Sun, your eyes won’t perceive the green ash as easily. Other phenomena are visible as the Sun rises and sets. Buddha’s rays, or crepuscular rays, occur when sunlight lters through gaps in the clouds, forming rays of light with dark bands in between. Buddha’s rays appear to diverge, or fan out, from the Sun but are actually almost parallel. This perspective effect makes intrinsically parallel edges appear to converge as distance increases. For example, a railroad track appears to converge at its farthest visible point, the vanishing point, though the tracks are actually parallel. Although the rays are brightest in the general direction of the Sun, Buddha’s rays can sometimes appear directly opposite from where the Sun Just before sunset over the ocean. ©iStockphoto/Thinkstock
  • 19 is setting. These are called anti-solar crepuscular rays, or sometimes, anti- crepuscular rays. Another phenomenon that appears shortly before sunrise or after sunset is a dark blue band just above the horizon—Earth’s shadow. The setting Sun is still visible from the perspective of the higher, more brightly lit atmosphere; however, the Sun as seen from lower parts of the atmosphere has already set. As the Sun gets lower below the horizon, the dark part of the atmosphere climbs progressively higher, until essentially all of the visible atmosphere is in Earth’s shadow and there is no longer a clear demarcation. crepuscular rays: Beams of light shining through gaps in clouds, usually best seen near sunset or sunrise. green ash: A subtle green glow sometimes visible in very clear skies just as the last part of the Sun is setting (or the rst part is rising). mirage: An image of an object, often inverted, formed by light passing through layers of air having different temperatures. wavelength: The distance over which a wave goes through a complete oscillation; the distance between two consecutive crests or two consecutive troughs. Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Parviainen, www.polarimage. (green ash, mirages, and so on). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Young, mintaka.sdsu.edu/GF (green ash, mirages, and so on). Important Terms Suggested Reading
  • 20 Lecture3:Sunrise,Sunset 1. Suppose air molecules were to preferentially scatter red light instead of blue light. What would be the approximate color of the daytime sky, away from the Sun’s direction? 2. If you were to ignore the effects of Earth’s atmosphere on sunlight, and you calculated the total amount of time between sunrise and sunset, why would your answer be shorter than the actual time interval? 3. Why does the color of a sunset change with time, and why do different clouds sometimes have different colors at a given time? Questions to Consider
  • 21 Bright Objects in the Night Sky Lecture 4 “Now that the Sun has set, let’s start looking at the stars. There are 88 constellations in the sky, mostly of ancient Greek, Egyptian, and Chinese origin. These are familiar-looking patterns. Some are a bit hard to distinguish; others are quite easy.” W e have learned about some of the sky’s amazing natural shows during the day. Now we focus on the nighttime skies, beginning with a brief review of Earth’s rotation and an introduction to some of the more familiar constellations of the Northern Hemisphere. Earth rotates on its axis on a 24-hour cycle. As the axis spins from west to east, stars rise in the east and set in the west. As your perspective—your location on Earth—changes, what you see in the sky also changes. Earth orbits the Sun, which accounts for the change in seasons, as well as changes in what you see in the night sky. Constellations are groups or patterns of stars that are easily visible in the sky. The ancient Greeks, Egyptians, and Chinese named constellations after familiar-looking animals or people or in honor of them. Today, we have additional modern constellations, such as Telescopium, in honor of telescopes. Knowing some of the more prominent stars in the sky can help identify the constellations and vice versa. Well-known constellations include Leo (the Lion) and Ursa Major (the Great Bear). Generally, these and other constellations are named in honor of something, not because they explicitly resemble that object or entity. The Great Bear contains a more familiar asterism, a group of stars that is not itself a full constellation but, rather, part of one. This particular asterism is the Big Dipper, which forms part of the Great Bear. The two end stars of the bowl of the Big Dipper are known as the pointer stars because they roughly point toward the north celestial pole, very close to “A lot of people think that Polaris, the North Star, is the brightest star in the sky— far from true. It’s actually relatively faint.”
  • 22 Lecture4:BrightObjectsintheNightSky which is Polaris, the North Star. Polaris appears at the end of the tail of Ursa Minor, the Small Bear, which also has an asterism within it, the Little Dipper. Though a naked-eye star, Polaris is relatively faint. Like most other stars, it is actually a multiple-star system, not a single star. The two main components of Polaris are easily separated into Polaris A and Polaris B. Polaris A has a close companion that requires very sharp optics, such as those of the Hubble Space Telescope, to discern. Betelgeuse, in the left shoulder of Orion, is an enormous star, a supergiant. It is much bigger than the diameter of Earth’s orbit, which is 186 million miles—Jupiter is about 5 times farther from the Sun than Earth, and Betelgeuse is about the size of Jupiter’s orbit around our Sun. Betelgeuse will explode as a supernova later in its life. To the southeast of Orion’s belt is Sirius, the Dog Star, and the brightest in our sky. Sirius has a small, faint companion, known as a white dwarf, or a dead star that is roughly the same mass as the Sun and compressed into a volume about the size of Earth. A teaspoonful-size portion of a white dwarf would weigh several tons. Easily visible in the sky is Vega in the constellation Lyra the Harp, seen during summer in the Northern Hemisphere. A young star, Vega has a dusty disk of gas circling it. Deneb in Cygnus the Swan—often called the Northern Cross—is another bright star. Together with Altair in Aquila (the Eagle) and Vega, Deneb forms an easily recognizable star pattern called the Summer Triangle. Orion and Scorpius Orion is the brightest constellation in the sky and one of the most recognizable. Scorpius (the Scorpion) is another, but it is not quite as easy to nd because of its generally fainter stars. In Greek mythology, Orion is the great hunter, whose arrogance annoyed his friends. Scorpius, too, became annoyed with Orion, and the two battled until Scorpius stung Orion to death. Zeus took pity on Orion and put him up in the sky, but he put Scorpius on the opposite side of the sky so that the two would never again bother each other. As the Scorpion is rising, Orion is setting, and vice versa.
  • 23 Some of the stars you see in the sky are actually planets. How do we distinguish between a planet and a star? Unlike stars, planets change positions from night to night relative to the other stars. Although constellations rotate across the sky throughout the seasons, their stars don’t change position relative to one another. In general, planets twinkle less than stars. However, if it’s close to the horizon, a planet can twinkle just as much as a star straight overhead because of the greater amount of atmosphere through which one looks near the horizon. What causes twinkling, and how does the atmosphere affect it? The atmosphere is turbulent, with many layers of air at different temperatures and densities. As the light from a star passes through the atmosphere, it bends (refracts). Because the atmosphere changes constantly, the refraction of light also changes. The constant change in the refraction of light makes a star or planet appear to twinkle. The effect is similar to sunlight reaching the bottom of a swimming pool. Both bright and dark regions continually shift as the water concentrates the light rays in some areas and not in others. Apparent twinkling is also affected by your vantage point; when you look at a celestial object near the horizon, more layers of atmosphere cause more bending of light and, therefore, enhanced twinkling. Stars high in the sky twinkle less because there are fewer layers of atmosphere between you and the star. If you compare two star-like objects at the same altitude above the horizon and one is twinkling and the other is not, the latter is likely to be a planet. Why? Even through a telescope, stars look like points of light. Planets are physically much smaller than stars but a lot closer to Earth. Thus, through a telescope, you can see that a planet is more like a disk, with many points of light on its surface. Even though every point on the planet is twinkling, some points twinkle more brightly than others at any given moment. Many points across the planet’s disk, all twinkling at different light levels, will average out in brightness, merging in such a way that the source of light appears nearly constant in brightness. When Sirius, a very bright star, is close to the horizon, it sometimes twinkles in color, which changes rapidly. Like the Sun, a star near the horizon is actually lower than it appears because of the refraction of light. The different colors in the light are bent at different angles, making the colors
  • 24 Lecture4:BrightObjectsintheNightSky appear at different points in the sky. The star’s colors are displaced upward, each one ashing—twinkling—independently, sometimes faintly and sometimes brightly, so that at any given moment, one color is more visible than another. Other celestial objects and phenomena are easily visible in the night sky, including phases of the Moon and meteors. You can also see man-made satellites. Satellites, such as the International Space Station, occasionally move across the sky. The Iridium satellites consist of about 70 objects once used for communications. Their bright re ective panels sometimes re ect the Sun in ashes that last for a few seconds. Iridium ares are sometimes mistaken for bright meteors. Bright ashes seen near sunrise or sunset could be satellite re ections. However, if you see one during the middle of the night, at least a few hours after sunset or a few hours before sunrise, it is more likely to be a meteor. asterism: A grouping of stars that is not itself a full constellation but is part of a constellation. The Big Dipper is one example. constellation: One of 88 regions into which the celestial sphere is divided. The pattern of bright stars within a constellation is often named in honor of a god, person, or animal. meteor: The streak of light in the sky produced when an interplanetary rock enters Earth’s atmosphere and burns up as a result of friction. If the rock reaches Earth’s surface, it is called a meteorite. refraction: The bending of light as it passes from one medium to another having different properties. supergiant: The evolutionary phase following the main sequence of a massive star; the star becomes more luminous and larger. If its size increases by a very large factor, it becomes cool (red). Important Terms
  • 25 supernova: The violent explosion of a star at the end of its life. Hydrogen is present or absent in the spectra of Type II or Type I supernovae, respectively. white dwarf: The evolutionary endpoint of stars that have initial mass less than about 8 solar masses. All that remains is the degenerate core of He or C–O (in some cases, O Ne Mg). Dickinson, Nightwatch. Pasachoff, A Field Guide to Stars and Planets. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Why are arti cial satellites in low-Earth orbit visible only in twilight, shortly after sunset and before sunrise, whereas satellites far from Earth are also visible much later during the night? 2. Do you think the brightest stars in the sky are necessarily the intrinsically most powerful stars? Is some other variable also important? 3. If the stars seem to twinkle very little one night, but much more the next night, compare the properties of the atmosphere on the two nights. 4. If stars are physically much, much larger than planets but appear only as points of light even when viewed through a telescope, what can one say about the relative distances of stars and planets? Suggested Reading Questions to Consider
  • 26 Lecture5:FainterPhenomenaintheNightSky Fainter Phenomena in the Night Sky Lecture 5 “Faint stars are being washed out by the glow of the city. The bright stars are still visible, but the faint ones are not. … Bright city lights really hurt; so does bright moonlight. You don’t want to look for the Milky Way when there’s a really huge, full Moon out, illuminating the whole sky. It just washes these faint things out.” T hough the sky is full of phenomena that are easily visible, even from within a bright city, many spectacular sights require dark skies to see clearly. Such sights include the Milky Way, auroras, and the zodiacal lights. The band of light we call the Milky Way is formed by billions of stars in a galaxy shaped like a disc, about 100,000 light years across and 1000 light years thick. The Milky Way Galaxy (often simply called “the Galaxy”) bulges in the middle, with its nucleus in the very center. Our Sun is about two-thirds of the way out from the center to the edge, although there’s no well-de ned edge of the Galaxy. If you look along the plane of the Galaxy, a multitude of stars is visible in any direction. If you look perpendicular to the plane, you see relatively few stars because the whole plane is only about 1000 light years thick, much thinner than the extent of the disk in other directions. Because stars in the plane of the Galaxy surround the Sun, the Galaxy’s band of light forms a full circle around us. However, at most, half of the band is visible at any given time because the other half is below the horizon. The Milky Way has relatively dense clouds of gas and dust mixed with stars, which in some places are thick enough to actually block our view of more distant stars. The center of the Galaxy contains a supermassive black hole, nearly 4 million times the mass of the Sun. From the Southern Hemisphere, you can see the brightest part of the Milky Way nearly straight overhead. Also clearly visible from this vantage point is the Southern Cross constellation and the Magellanic Clouds—two satellite galaxies gravitationally bound to our Galaxy and orbiting it. The Large Magellanic Cloud is about 170,000 light years away and contains the Tarantula Nebula, a glowing cloud of gas with recently formed and
  • 27 newly forming stars. The Small Magellanic Cloud is about 210,000 light years away. Other phenomena are more easily viewed from the Southern Hemisphere, though some are also visible in the Northern Hemisphere. The nearest star to our Sun is Alpha Centauri, actually a double star system whose closest star to Earth is Proxima Centauri. Both stars are about 4.2 light years away. To the west of the Southern Cross is the diffuse Eta Carina Nebula, a glowing cloud of gas and dust. Eta Carina is a massive, erupting star in the nebula, perhaps 150 times the mass of our Sun, and incredibly unstable. This star will likely explode within the next few hundred thousand years. Sometimes, planets can affect the apparent shapes of constellations; for example, Jupiter can appear inside the constellation of Scorpius, making it look different than expected. From the Southern Hemisphere, Scorpius and Sagittarius, a constellation to the east of Scorpius, are relatively high in the sky, compared to their visibility from the Northern Hemisphere. The central part of our Galaxy is in the direction of the constellation Sagittarius. The zodiacal light is a conical, diffuse band of light sometimes visible when the sky is very dark but not too long after sunset or too long before sunrise. Its glow begins at the western horizon (after evening twilight has ended) or at the eastern horizon (before morning twilight begins), stretching upward in the sky. It consists of sunlight scattered by dust and gas in the plane of the Solar System. The scattering is most ef cient in the forward direction; thus, the zodiacal light is brightest in directions closest to the Sun. Because the plane of the Solar System forms its steepest angle relative to the horizon during February and March in the evening and during October and November in the morning, these are generally the best months for viewing the zodiacal light. Two other spectacular sights you can see with the naked eye at night are bright comets and auroras. Comets are concentrations of ice, dust, and rock from distant parts of the Solar System. As they approach the Sun, comets evaporate, freeing gases and dust particles that re ect sunlight to form the long, diffuse tail. Sunlight and charged particles from the Sun push the tail of the comet back, so the tail generally points away from the Sun.
  • 28 Lecture5:FainterPhenomenaintheNightSky Chargedparticlesemanatingfrom the Sun cause another beautiful phenomenon: the auroras, or the northern and southern lights. The auroras are bands of shimmering light in multiple colors of red, green, and sometimes, blue. They are created when charged particles, primarily electrons, from the Sun interact with atoms (and some molecules) in the atmosphere. The charged particles from the Sun interact with Earth’s magnetic eld, which we’ll discuss in another lecture. Charged particles have a hard time crossing magnetic eld lines, but can move along eld lines. The charged particles are trapped preferentially in certain bands where the magnetic eld is particularly strong; these are called the Van Allen belts. The trapped particles move along the magnetic eld lines toward Earth. Close to the poles, where the magnetic eld lines intersect Earth’s thin atmosphere (about 100 km thick), the trapped particles, especially electrons, interact with the atmospheric atoms (and some molecules). Electrons hitting the atoms and molecules kick the bound electrons to higher energy levels. Then, the electrons cascade down to lower levels, in the process emitting colorful light. The different colors are caused by emission of light from different kinds of atoms and molecules in Earth’s atmosphere, such as nitrogen and oxygen, excited to different electronic energy levels. The colors and light patterns of the auroras change quickly over time because the number “Auroras can also be seen from space. Space shuttle astronauts often see auroras looking down at the atmosphere of the Earth.” Active Aurora Borealis, also called the “Northern Lights.” ©iStockphoto/Thinkstock
  • 29 of electrons and the amount of interaction with the atmosphere changes. Typically, the auroras that are most visible are nearer to Earth’s poles. Occasionally, however, the magnetic elds allow charged particles to reach Earth’s surface relatively close to the equator. Auroras are especially prominent after major eruptions on the Sun’s surface, when unusually large numbers of energetic particles are ejected and subsequently reach Earth. By watching the Sun, astronomers can roughly predict when the next great auroral display will be visible. Auroras are visible from space and have been seen on other planets. aurora: The northern or southern lights, caused by energetic particles from the Sun interacting with atoms and molecules in Earth’s upper atmosphere, making them glow. comet: An interplanetary chunk of ice and rock, often in a very eccentric (elongated) orbit, that produces a diffuse patch of light in the sky when relatively near the Sun as a result of evaporation of the ice. electron: Low-mass, negatively charged fundamental particle that normally “orbits” an atomic nucleus. Large Magellanic Cloud: A dwarf companion galaxy of our Milky Way Galaxy, about 170,000 light years away; best seen from Earth’s southern hemisphere. Important Terms Did You Know? If Earth’s magnetic eld were stronger, the auroras would be con ned to even more northerly or more southerly latitudes because a stronger magnetic eld is more able to con ne the charged particles. If Earth’s magnetic eld were very weak, these charged particles would hit Earth in quite a few places and cause more mutations of cells. So, the risk of cancer would be greater if the Earth’s magnetic eld were considerably weaker.
  • 30 Lecture5:FainterPhenomenaintheNightSky Milky Way: The band of light across the sky coming from the stars and gas in the plane of the Milky Way Galaxy (our Galaxy). nebula: A region containing an above-average density of interstellar gas and dust. zodiac: The band of constellations through which the Sun moves during the course of a year. zodiacal light: A faint glow in the night sky around the ecliptic, stretching up from the horizon shortly after evening twilight and shortly before morning twilight, from sunlight re ected by interplanetary dust. Dickinson, Nightwatch. Parviainen, www.polarimage. (auroras, comets, and so on). Pasachoff, A Field Guide to Stars and Planets. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Suppose the average number of stars per unit area of the sky were essentially independent of direction in the sky. What might one conclude about the shape of our Galaxy or our location within it? 2. Why would you expect planets to occasionally appear in the same direction in the sky as the band of zodiacal light? 3. Why are auroras most easily visible from far northern or far southern latitudes on Earth? Suggested Reading Questions to Consider
  • 31 Our Sky through Binoculars and Telescopes Lecture 6 “Binoculars and telescopes collect more light, making objects brighter and allowing you to see fainter stars in the sky. They also magnify objects, making them look bigger or closer.” T elescopes and binoculars allow you to better view fainter and more distant celestial objects in the night sky. Let’s look at how they work and discuss the two main types of telescopes. Telescopes collect light, making objects appear brighter than your eye alone could detect. Telescopes also magnify objects, making them look bigger. In a previous lecture, we discussed how the rays of the Sun are nearly parallel when they reach Earth because of the Sun’s great distance from Earth. Because stars and most planets are even farther from Earth, their light is parallel to a very high degree of accuracy. Refracting telescopes use a primary lens to bring the incoming parallel light to a focus. In this type of telescope, light is collected and refracted (bent) by the lens. Rays at different distances from the center of the lens are bent at different angles, bringing them to the same focus. Rays that approach the lens from different directions (for example, from the top and bottom edges of a planet) are focused to different parts of the focal plane of the lens. From the focal plane in a refracting telescope, light travels to the eyepiece lens, which magni es the image of an object and allows your eye to see it. The focal length of a lens is the distance between the lens and the focal plane. The magni cation of the apparent size of an object can be determined by dividing the focal length of the primary lens by the focal length of the eyepiece lens. Because a bigger Astronomy in History Refracting telescopes were invented in Holland around the year 1600, and Galileo built his own soon thereafter, becoming the rst to systematically make and interpret astronomical observations using a telescope.
  • 32 Lecture6:OurSkythroughBinocularsandTelescopes primary lens captures more rays of light, objects look brighter when viewed with a lens that has a larger diameter. Refracting telescopes have a problem called chromatic aberration: Different colors of light are bent at different angles and, therefore, they do not have the same focal length. Specially designed refracting telescopes consisting of two primary lenses eliminate part of this problem, but such telescopes can be expensive. Re ecting telescopes, on the other hand, use mirrors to collect light and bring it to a common focus. All of the light rays, regardless of color, are brought to the same focus without chromatic aberration. Re ecting telescopes, invented by Isaac Newton around 1670, come in several styles. One style (known as the Cassegrain telescope) has a hole in the primary mirror. Incoming light rays bounce off the primary mirror, re ect back to a secondary mirror, bounce off that, then go through the hole in the primary mirror before arriving at the eyepiece lens. Instead of having a hole in the mirror, another style (the Newtonian telescope) uses a tilted secondary mirror to direct incoming light to the eyepiece, which is off to the side of the tube. This was the kind of telescope used by Newton. Each part of the primary mirror forms a complete image of the object. The larger the primary mirror, the brighter the object will appear. Binoculars are essentially two refracting telescopes joined together. What celestial objects can be easily seen with binoculars? With the naked eye, you can see the Summer Triangle, which consists of the stars Vega, Deneb, and Altair. Going from Vega and Deneb, look toward the constellationAndromeda to nd Messier 31 (M31), another galaxy, known as the Andromeda Galaxy; the nearest large collection to our own Galaxy, it is about 2.5 million light years away. You can also look for a pair of clusters known as the double cluster in Perseus. The Orion Nebula, in the constellation Orion (speci cally, in the sword of the great hunter), is a giant glowing cloud of gas and dust within which new stars are currently forming. The group of stars called the Pleiades, or the Seven Sisters, is visible with binoculars. You can also scan the Milky Way with binoculars to nd an array of nebulae (clouds of gas) and star clusters, particularly near the tail of Scorpius, visible in the Northern Hemisphere during summer.
  • 33 The Moon is also a fascinating object to view with the aid of binoculars, which accentuate its irregular surface of craters and lava plains. Known as the maria, these plains were once thought to be dried-up seas, but we now know that they are frozen, dead lava plains. Telescopes offer an even better view of celestial objects because, mounted on a tripod, they reduce the shakiness that comes with handheld binoculars. Telescopes also collect more light, magnify the images more, and create greater clarity. The Moon’s craters are most easily seen near the place where darkness begins on its surface—that is, where either sunrise or sunset is occurring and where the light comes in at a glancing angle to make long shadows. Through a telescope, concentrate your attention on this region, the terminator—the termination of the area where light shines on the Moon. This enhances the view of its ridges, mountain chains, valleys, and craters. Sometimes, you can see the Moon occulting, or covering up, one of the planets. Binoculars can be used to nd star clusters and nebulae. ©iStockphoto/Thinkstock
  • 34 Lecture6:OurSkythroughBinocularsandTelescopes Back at the Summer Triangle, locate Cygnus the Swan—the Northern Cross—and go down to the bottom of the cross to view a double star, Albireo ( Cygni). Near Vega is the constellation Hercules, within which is a cluster consisting of hundreds of thousands of stars, or perhaps a million, gravitationally bound together in a very tight group. Within Lyra the Harp, you can see the Ring Nebula, a cloud of gas ejected by a dying star. Near the end of the Big Dipper’s handle, you can view the Whirlpool Galaxy, M51. Although you won’t see much detail through a small telescope, it is a stunning spiral galaxy. Local amateur astronomy clubs, which often hold “star parties” (viewing sessions), provide opportunities for the public to view the night sky through a variety of telescopes, some quite powerful. Newton,Isaac(1642 1727):Englishmathematicianandphysicist;developed three laws of motion and the law of universal gravitation, all published in The Principia (1687). Invented the re ecting telescope, determined that white light consists of all colors of the rainbow, and invented calculus. At age 27, became Lucasian Professor of Mathematics at Cambridge University. Became Warden of the Mint in 1696; knighted in 1705. eyepiece: A small tube containing a lens (or combination of lenses) at the eye end of a telescope, used to examine the image. re ecting telescope: Telescope that uses a mirror instead of a lens to collect light; unlike the refracting telescope, it brings all colors into focus together. refracting telescope: Telescope that uses a lens to collect light and bring it to a focus. spiral galaxy: One of the two major classes of galaxies de ned by Edwin Hubble; made up of a roughly spherical central “bulge” containing older stars, surrounded by a thin disk in which spiral arms are present. Name to Know Important Terms
  • 35 star cluster: A gravitationally bound group of stars that formed from the same nebula. terminator: The line between night and day on a moon or planet; the edge of the part that is lighted by the Sun. Dickinson, Nightwatch. Kitchen and Forrest, Seeing Stars. Pasachoff, A Field Guide to Stars and Planets. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Does the hole in the center of the primary mirror in a Cassegrain telescope produce a hole in the object that is being viewed? What about the secondary mirror of a Newtonian telescope? 2. Telescopes are often advertised according to the amount by which they magnify the apparent size of an image. Do you think this magni cation is very relevant when looking at stars instead of planets? 3. Besides not suffering from chromatic aberration, can you think of some other advantages of re ecting telescopes over refracting telescopes? Suggested Reading Questions to Consider
  • 36 Lecture7:TheCelestialSphere The Celestial Sphere Lecture 7 “Go out, lie down in a sleeping bag, look at the sky, and watch over the course of hours the stately progression of the stars across the sky. ... Also, watch as the constellations that you can see change from season to season.” A stronomers have de ned 88 constellations in the heavens, all of which are seen against a backdrop called the celestial sphere. Each star is a member of one—and only one—constellation, though their boundaries are arbitrary. In most cases, these constellations consist of stars that are not physically bound to one another by gravity or any other force. Stars in any particular constellation weren’t formed in the same place; they just happen to be in approximately the same direction in space. An example is Cassiopeia, the Vain Queen, which looks like a W. Cassiopeia’s 5 main stars vary in distance from Earth, from 54 light years away ( Cassiopeia) to 613 light years away ( Cassiopeia).Alight year is the distance that light travels in 1 year, approximately 6 trillion miles, but fainter stars are not necessarily farther away than brighter stars. From our perspective on Earth, we can see only about half of the celestial sphere at any given moment. When you stand at a given location, your zenith is the point straight overhead. The horizon is 90 degrees away in all directions along lines tangent to Earth or a smooth surface in the absence of geographic features. To visualize your horizon, extend a plane tangent to the surface so that it intersects the celestial sphere. You can’t see objects that fall below that horizon. If the celestial sphere were close in, only stars along a limited arc would be visible. If the celestial sphere were farther away, you’d see a larger arc. Because the “The stars of the constellations have nothing to do with one another. They happen to be at approximately the same line of sight in the sky, but they were not physical groupings of stars.”
  • 37 celestial sphere is almost in nitely far away compared with Earth’s diameter, about half of the celestial sphere is above your horizon at any given time. Your position on Earth determines what part of the celestial sphere you can see. What’s visible from San Francisco, California (latitude roughly 40° north), largely differs from that seen in Quito, Ecuador (latitude roughly 0°), for example, but there is some overlap. At the poles (latitude 90° north or south), the observed part of the celestial sphere differs even more. In addition to the zenith and the horizon, we can de ne a few other interesting parts of the celestial sphere. The celestial equator is the projection of Earth’s equator onto the celestial sphere. It is a great circle—that is, a circle formed by the intersection of a sphere and a plane that passes through the center of the sphere. The meridian is another great circle, passing through the celestial poles and the zenith, as seen from a given location on Earth. A star crosses the meridian when it reaches its highest elevation above the horizon. Imagine extending the North and South Poles outward, along the axis of Earth’s rotation. The north celestial pole is the intersection of the North Pole’s extension with the celestial sphere, and the south celestial pole is the intersection of the South Pole’s extension with the celestial sphere. The apparent rotation of the celestial sphere is the result of Earth’s rotation on its own axis. Earth rotates in one direction, and the stars move across the sky in the opposite direction. As your position on Earth changes, so does the appearance of the celestial sphere. From the equator, Polaris—the north celestial pole star— appears on the horizon. At 20° north latitude, Polaris is 20 degrees above the horizon; at 40° north latitude, it’s 40 degrees up toward the zenith, and so on, until you reach the North Pole, where Polaris is right overhead at 90 degrees. As your position changes relative to the equator, for example, certain stars become visible, while others disappear below the horizon line. As Earth rotates, stars appear to move across the sky. The closer “Fainter stars are not necessarily farther away than the brighter stars. You could have a faint star that’s nearby, but it’s intrinsically not as powerful as another star that’s farther away—so it looks fainter.”
  • 38 Lecture7:TheCelestialSphere you look to the celestial poles, the less the stars appear to move. Similarly, stars farther from the celestial poles appear to move in great arcs across the sky throughout the night. Circumpolar stars are stars that never rise or set, as seen from a given location on Earth. They circle the pole, but don’t dip below the horizon. As seen from Earth’s North or South Pole, all of the visible stars are circumpolar. Each star circles around the sky at a constant elevation above the horizon. From the equator, stars appear to rise and set perpendicular to the horizon, arcing across the sky. There are no circumpolar stars.At intermediate latitudes, some stars (those close to the visible celestial pole) would be seen as circumpolar, while others would rise and set at an angle, slanted relative to the horizon. Because of Earth’s orbit around the Sun, the sky also changes over the course of the year. This orbiting accounts for the different positions and the appearance and reappearance of some constellations on an annual cycle. As seen from the equator in December, the constellation Orion begins to rise at sunset. By midnight, Orion is overhead, and at sunrise, Orion sets again. As seen from the equator, Orion is overhead at sunset in March and overhead at midnight in December. Sunset is roughly 6 hours earlier than midnight; thus, over the course of 3 months, Orion has risen 6 hours earlier. A constellation’s rising and setting changes at a rate of 4 minutes per day. Except for near the poles, the stars rise 4 minutes per day earlier with each successive night. (Near the poles, stars don’t rise or set at all; they just circle the poles, being circumpolar stars.) If Earth weren’t orbiting the Sun, then in one 24-hour day/night cycle, both the Sun and other stars would become aligned every 24 hours as a result of Earth’s own rotation. The changing perspective causes the solar day (the time interval been two consecutive meridian crossings of the Sun—or noon to noon) to be about 4 minutes longer than the sidereal day (the time interval between two consecutive meridian crossings of a given star). The Sun’s path in the sky is called the ecliptic. The constellations through which the Sun passes during its yearly journey across the sky are the zodiacal constellations. In September, if the Sun weren’t bright, you would see it projected against the stars of Virgo. In March, if you could see the stars during the day, you would see the Sun projected against Pisces. Planets
  • 39 also wander slowly among the zodiacal constellations. However, this planet wandering among the stars is not the same thing as the daily east-to-west rotation of the celestial sphere caused by Earth’s rotation. Given that constellations move around from season to season, how do you know where to look for them? Special star charts show constellation positions at different times of the year. Planispheres are another useful tool and have rotating circles you align appropriately, depending on the time of year and time of night. In addition, every star has a speci c set of coordinates, similar to longitude and latitude lines on Earth. A star’s latitude is called declination, which is a coordinate that de nes the number of degrees a star is above the celestial equator, up to 90°. A star’s longitude is called right ascension, which is a coordinate that de nes the number of hours a star is along the celestial equator, up to 24 hours. By knowing the declination and right ascension of a star, as well as the time of night, you can point a telescope to the proper location of the celestial sphere to see it. An equatorially mounted telescope is xed so that its axis is parallel to the axis of Earth’s rotation. Its other axis swings perpendicularly to this. The telescope can be rotated around the axis parallel to Earth’s axis of rotation to counter the rotational effect of Earth. If this weren’t possible, the position of the star would constantly move out of the telescope’s eld of view as Earth rotated. Some commercially available telescopes allow you to input the name of a star or planet, and the telescope’s computer points the telescope directly to that object. celestial equator: Projection of Earth’s equator onto the celestial sphere. celestial sphere: The enormous sphere, centered on the Earth, to which the stars appear to be xed. ecliptic: The path followed by the Sun across the celestial sphere in the course of a year. Important Terms
  • 40 Lecture7:TheCelestialSphere gravity: The weakest of nature’s fundamental forces but the dominant force over large distances because it is cumulative; all matter and energy contribute, regardless of charge. great circle: The intersection of a sphere with a plane passing through the center of the sphere. The meridian and the celestial equator are both great circles. meridian: A great circle passing through the celestial poles and the zenith; the highest point in the sky reached by a star during each day-night cycle. pole star: A star approximately at a celestial pole (Polaris, in the north). zenith: The point on the celestial sphere that is directly above the observer. Dickinson, Nightwatch. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tirion, The Cambridge Star Atlas. 1. As viewed from a given location on Earth, some stars never set (that is, they are circumpolar stars). Is it also the case that some stars never rise, if viewing them from the same location? 2. Given that the sky revolves once per day/night cycle, how many degrees does it appear to revolve in one hour? 3. As viewed from Earth’s equator over the course of a year, is the entire celestial sphere visible at some time during the night? In other words, can all stars in the celestial sphere be viewed from Earth’s equator? What if you are viewing from Earth’s North Pole or from Earth’s South Pole? Suggested Reading Questions to Consider
  • 41 The Reason for the Seasons Lecture 8 “The seasons are not caused by changes in the distance between Earth andtheSunoverthecourseofayear.Ifthiswereso,theseasonswouldn’t be opposite each other in the Northern and Southern Hemispheres.” T he celestial sphere and the relationship between the celestial equator and the ecliptic—the path of the Sun—play an important role in explaining the seasons. The most signi cant differences between seasons are the day’s length: how long the Sun remains above the horizon and how high it reaches before setting again. Earth rotates on its axis at a tilt of 23.5° relative to the axis of its orbit around the Sun. The orientation of Earth’s axis is xed—relative to the distant stars—as it orbits the Sun and spins. As a spinning object, Earth doesn’t change the absolute direction of its axis of spin, but its orientation relative to the Sun does change. In the Northern Hemisphere, June 22 (solstice) is the rst day of summer, when the hemisphere is most tilted toward the Sun. In the Southern Hemisphere, it is the rst day of winter, when that hemisphere is most tilted away from the Sun. The opposite occurs in each hemisphere on December 22 (solstice). During the Southern Hemisphere spring and summer, the South Pole experiences perpetual daytime for about 6 months. Much of the Northern Hemisphere has daytime skies, too, but the North Pole experiences perpetual nighttime for about 6 months. During winter in the Northern Hemisphere and summer in the Southern Hemisphere, mid-northern latitudes spend part of their time bathed in sunshine but a greater fraction of their time in darkness. Six months later, the situation is reversed. The equinox describes that time when Earth’s equator is most pointed toward the Sun. On approximately September 22 and March 22, the equator of Earth is pointed toward the Sun, and both poles experience an equal amount of light. During the equinox, equal days and nights occur everywhere on Earth, 12 hours each of day and night. The locations of sunrise and sunset change throughout the year, as does the Sun’s highest position in the sky as seen from any given location on Earth. As
  • 42 Lecture8:TheReasonfortheSeasons autumn commences, the Sun begins to rise to the south of due east. In winter, it rises south of east. In the summer, the Sun rises north of east. During the equinoxes, the Sun rises due east (and sets due west). When the Sun is high, as in the summer months, a cylindrical beam of light strikes a relatively small area on Earth, causing it to heat up more and creating hotter temperatures. When the Sun is low, as in the winter months, the light is spread out over a larger area, heating each unit of area less and causing cooler temperatures. Near the solstices, Earth’s tilt causes one hemisphere to be closer to the Sun during the day than the other hemisphere, but this effect is negligible because Earth’s radius is so small relative to its distance from the Sun. Instead, the Sun’s height above the horizon accounts for how much heat Earth receives at any given location. Earth’s orbit is elliptical, meaning that during certain points in its orbit around the Sun, it comes closer to the Sun but only by 3%. This small gure does not have much effect on temperatures. Earth is closest to the Sun during the Northern Hemisphere winter, in early January, creating some extra heat and slightly mitigating winter’s cold. Earth’s relative closeness to the Sun in January does not make Southern Hemisphere summers much hotter because most of the Southern Hemisphere has vast oceans, which take much more time to heat than land. The position of Earth in relation to the Sun throughout the year causes other interesting phenomena. As discussed in a previous lecture, the refraction—or bending—of the Sun’s rays as the Sun approaches the horizon makes the Sun appear higher above the horizon than it really is. Therefore, during the Northern Hemisphere summer, for example, the Sun appears above the horizon for a little longer than 6 continuous months as seen from the North Pole. At the Tropic of Cancer—23.5° north latitude—the Sun appears overhead on June 22. At the Tropic of Capricorn—23.5° south latitude—the Sun appears overhead on December 22. The analemma is a phenomenon that describes the position of the Sun at a given time of day over the course of the year. Taking photographs of the Sun’s position from a xed point at the same time every day over time will illustrate the Sun’s gure-8 pattern of changing position. The analemma is caused by Earth’s elliptical orbit around the Sun; Earth doesn’t travel at the same speed at all times. Another reason for the analemma is that the celestial equator and
  • 43 the ecliptic are tilted relative to each other. The analemma accounts for the fact that at noon, the Sun is not crossing the meridian (its highest point in the sky), as expected. Instead, depending on the season, the Sun is a bit to the east or to the west of the meridian. The difference between where the Sun should be, according to clock time, and where it actually is can be as much as about 15 minutes. This time varies by season and throws off sundials. Some natural phenomena occur oppositely in Earth’s two hemispheres. Because of Earth’s rotation, hurricanes rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. This is a consequence of the coriolis force, which affects the movement of air over great distances. The coriolis force does not, however, cause water to drain clockwise or counterclockwise depending on the hemisphere. This force affects only large-scale distances and has no bearing on such small-scale physical matters as draining water. Stars rise in the east and set in the west, which is clockwise around the south celestial pole as seen from the Southern Hemisphere and counterclockwise around the north celestial pole as seen from the Northern Hemisphere. The constellation Orion also looks different in the two hemispheres. In the north, it’s right side up; in the south, it’s upside down. Because of the gravitational in uence of the Moon and the Sun, Earth’s axis of rotation slowly changes orientation over the course of about 26,000 years. Earth behaves in a manner similar to that of a spinning gyroscope, which undergoes a conical motion called precession instead of being toppled by gravity. Earth’s axis precesses because its axis of rotation resists being changed by the gravitational forces of the Sun and the Moon. Gradually, over the course of about 13,000 years, precession will cause the seasons to reverse in their respective hemispheres, so that in the north, summer will begin on what we now call December 22. analemma: The apparent gure-8 path made by the Sun in the sky when photographs of the Sun’s position taken at a given time of day throughout the year are superimposed on each other. Important Terms
  • 44 Lecture8:TheReasonfortheSeasons equinox: One of two points of intersection between the ecliptic and the celestial equator, or the time of the year when the Sun is at this position. precession: A conical motion undergone by spinning objects pulled by an external force not directed along the axis. The Earth’s precession causes the direction of the north celestial pole to shift gradually with time. solstice: The northernmost or southernmost point on the celestial sphere that the Sun reaches, or the time of the year when the Sun reaches this point. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. ———, A Field Guide to Stars and Planets. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tirion, The Cambridge Star Atlas. 1. What would the seasons be like if: (a) Earth’s axis of rotation were parallel to the axis of Earth’s orbital plane, and (b) the axis of rotation were in the orbital plane? 2. Explain why, for an observer at the North Pole, the Sun changes its elevation (altitude) in the sky over the course of a year but the stars do not. 3. If someone were to tell you that Earth’s changing distance from the Sun causes the seasons, what arguments might you give to convince them otherwise? Suggested Reading Questions to Consider
  • 45 Lunar Phases and Eerie Lunar Eclipses Lecture 9 The Moon goes through a series of phases due to a changing geometrical relationship between the position of the Sun, the Earth, and the Moon. Also, the Moon can sometimes be eclipsed by the Earth’s shadow. T he Moon is perhaps the most commonly observed celestial object in the sky, characterized by its changing appearance—the lunar phases. The Moon has eight well-de ned phases over the course of its orbit, beginning with the new moon—which is dark—and proceeding through waxing crescent, rst quarter (or half moon), waxing gibbous, full moon, waning gibbous, third quarter (or half moon), waning crescent, and back to new moon again. The cycle from new moon to new moon, or full moon to full moon, takes about 1 month (roughly 29.5 days). It takes about 2 weeks for the Moon to go from new to full or full to new. Lunar phases are caused by the changing spatial relationship among the Sun, Earth, and the Moon. In other words, as the Moon orbits Earth, we see its lit face from a different perspective each night. At all times, the Sun illuminates the side of the Moon that faces the Sun, but as the Moon orbits Earth, varying portions of its lit side become visible from Earth. At new moon, the Moon is roughly between Earth and the Sun, so that the lit side of the Moon faces away from Earth; at full moon, Earth is roughly between the Sun and Moon, so that the lit side of the Moon faces Earth. The terminology describing phases of the Moon can be confusing. What we call the rst-quarter moon we actually see as half the Moon lit up. Though it is half lit, it’s only one-quarter of the way around Earth in its orbit, hence the name. In the same vein, the full moon is only halfway around its orbit, but we still call it a full moon. Not just a nighttime sight, the Moon is visible during the day. The times of day it is visible depend on its phase. The Moon rises and sets at different times depending on its phase. Though you can’t see the Moon during its new phase, it is aligned with the Sun; it rises at sunrise and sets at sunset. The full moon is in the opposite direction
  • 46 Lecture9:LunarPhasesandEerieLunarEclipses of the Sun, rising as the Sun sets and setting as the Sun rises. Lunar phases correspond to times at which they are visible. At 6:00 p.m., the rst-quarter moon is on or near the meridian. At 9:00 p.m., the rst-quarter moon is closer to the western horizon. At midnight, the rst-quarter moon is on the western horizon, setting. At 3:00 a.m., the rst-quarter moon has set and is not visible. (Occasionally, astronomers are asked to serve as expert witnesses in criminal trials to verify the position and phase of the Moon on the night a crime was committed.) Other interesting phenomena are associated with the Moon, including earthshine and optical illusions. Sometimes, the dark side of the Moon is faintly lit—from the Moon, Earth appears nearly fully lit. Earthshine is created when light is re ected from Earth to the Moon, then re ected back to Earth. It is less pronounced as the crescent moon grows, in part because the bright waxing crescent begins to outshine the faint light on the dark side of the Moon. A waxing crescent moon from Earth’s perspective corresponds to a waning gibbous Earth from the Moon’s perspective. The rising Moon near the horizon appears very large, but this is an optical illusion. When we see a rising Moon, especially a full or gibbous moon, it appears large to our eyes because we are comparing its size to that of much smaller objects in the foreground, such as buildings, trees, or people. Even when viewed over a clear horizon, such as an ocean—with nothing to compare with the Moon’s size—the Moon looks larger because our brains fool us into thinking so. Because the Moon’s orbit of Earth is elliptical, it actually is closer to Earth at certain times during its orbit. Yet this still doesn’t make it look bigger near the horizon on a given night because an elliptical orbit takes a full month and the Moon appears large near the horizon on most nights. Oddly, the true angular size of the rising Moon is actually smaller than the angular size of the Moon later that same night when it’s high up in the sky. Why? At midnight, the Moon is closer to Earth than it is when rising or setting; roughly one Earth radius closer, or about 1/60 of the distance (or roughly 2%) to the Moon. What happens during a lunar eclipse? If the Moon is between the Sun and Earth during a new moon and Earth is between the Moon and the Sun during a full moon, why don’t solar and lunar eclipses occur at every new and
  • 47 full moon, respectively? The plane of the Moon’s orbit around Earth is not exactly coincident with the plane of Earth’s orbit around the Sun. Because of the tilt between Earth’s orbital plane and that of the Moon, the Moon is either above or below Earth’s shadow most of the time when the Moon is full. Similarly, the Moon’s shadow usually misses Earth during a new moon. When the Moon does fall in Earth’s shadow, a lunar eclipse occurs. During the partial phases of a total lunar eclipse— when only part of the Moon falls in Earth’s shadow—it takes about an hour for the Moon to enter the shadow and another hour to exit the shadow. During a total lunar eclipse, the Moon remains in Earth’s shadow for about an hour, in addition to the 2 hours it takes to enter and exit Earth’s shadow. Earth’s shadow, cast into space, intersects the Moon only if the alignment is just right, which can occur during two so-called eclipse seasons per year. A total eclipse of the Moon is not completely dark. It appears more like a coppery red or orange, though colors vary. Some light from the Sun goes through Earth’s atmosphere, refracting (bending) toward the Moon and illuminating the Moon’s dark face. That light then re ects off the Moon back to Earth. During some eclipses, one part of the Moon can be illuminated more than another, creating a 3-dimensional effect. Yellow, orange, and red light are the predominant colors that illuminate the Moon. Violet, blue, and green colors are both scattered (re ected) by molecules of air and dust and absorbed by dust and smoke, diminishing these colors. A lot of dust in Earth’s atmosphere causes dark eclipses. Less dust makes for brighter eclipses because more light can reach the Moon. The part of the Moon that is closest to the edge of Earth’s shadow looks brighter because more light can lter into Earth’s shadow by bending through Earth’s atmosphere. “The rising Moon looks gargantuan compared to how it looks when it’s higher up in the sky. … It’s only its apparent size that looks large compared to familiar objects. The true angular size of the Moon when it’s rising is actually smaller than later that same night when it’s high up in the sky.”
  • 48 Lecture9:LunarPhasesandEerieLunarEclipses A total lunar eclipse is visible from the entire dark side of Earth. In other words, everywhere in this hemisphere, as long as you have good weather and the Moon isn’t blocked by objects, you will see the dark or partially illuminated Moon. Total lunar eclipses, although intrinsically rare, occur once every year or two and are visible from roughly half of Earth’s surface. earthshine: Sunlight illuminating the Moon after having been re ected from the Earth. eclipse: The passage of one celestial body into the shadow of another or the obscuration of one celestial body by another body passing in front of it. Harris and Talcott, Chasing the Shadow. Long, The Moon Book. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. In Lecture 8, we talked about the reversal of seasons between Earth’s two hemispheres, set to happen over the course of about 13,000 years. Given that this reversal is in part related to the Moon’s gravitational pull, will the Moon’s phases, as viewed from Earth, also be affected? 2. If tonight you see a rst-quarter moon, then 2 weeks from now, will you be able to see the Moon during the rst few hours of the night? Important Terms Suggested Reading Questions to Consider
  • 49 3. Describe the phases of Earth you would see over the course of a month if you were on the Moon. (Assume you are always on the side of the Moon facing Earth.) 4. In what way is the orange/red color of the fully eclipsed Moon related to the orange/red color of the setting Sun as seen from Earth?
  • 50 Lecture10:GloriousTotalSolarEclipses Glorious Total Solar Eclipses Lecture 10 “Any given location on Earth experiences a total solar eclipse roughly only once every 360 years, on average.” L ike the Moon, the Sun also has interesting features that can be viewed with the right equipment. The Sun is basically a featureless disk with a gaseous surface. The surface is called the photosphere and has a distinct boundary. On the photosphere are features called sunspots, which are dark and cooler areas near the Sun’s surface. Sunspots change quickly over time, so that if you photographed them each day, you would see changes in their size, shape, and location over time. Galileo was the rst to notice sunspots moving across the disk of the Sun and, therefore, inferred that the Sun rotated. While sunspots are interesting features to view, you should never look directly at the Sun with the naked eye, unless it is totally eclipsed by the Moon. Otherwise, you could cause serious damage to your eyes. To view sunspots, you need to use a proper lter. The best kind is shade 14 welder’s glass, which is thick enough to block out the damaging rays. You can also see a magni ed view of the Sun with a telescope that is properly out tted with lters. The telescope should be tted with a lter at the top end so that the sunlight is blocked before it enters the telescope. Again, never view the Sun directly through a telescope or binoculars without the proper lters. Without a lter, the large amount of light collected by the telescope or binoculars could crack the eyepiece and seriously damage your eyes. You can also look at sunspots with a device called a SunspotterTM or by projecting an image of the Sun through a telescope onto a sheet of paper. “[Galileo] also inferred that the Sun is not blemish-free. ... It isn’t the perfect celestial sphere that people in the Roman Catholic Church wanted it to be. That’s part of what put Galileo in trouble.”
  • 51 The Sun experiences both partial and total eclipses during certain times when the Moon is new, or dark. During the new moon phase, the Moon moves between the Sun and Earth. But in order for an eclipse to occur, the alignment has to be just right. How can such a small object as the Moon block the Sun as seen from Earth? The Sun is about 390 times physically larger than the Moon, and entirely by coincidence, the Sun is also farther away than the Moon by a factor of 390. Because of the Moon’s and Sun’s relative sizes and distances from Earth, they subtend, or cover, about the same angle in the sky—half a degree. Thus, when aligned just right, the Moon can block the Sun’s photosphere as viewed from Earth. Normally, the Moon does not obstruct the Sun’s photosphere, but when it does—if it blocks the entire photosphere—you see the faint, tenuous corona of the Sun. The Sun’s corona changes shape from one eclipse to another because it is structured by the shape of the magnetic elds emanating from the Sun, and these change with time. Inner corona of the Sun and the “diamond ring” effect. ©iStockphoto/Thinkstock
  • 52 Lecture10:GloriousTotalSolarEclipses Why don’t solar eclipses occur with each new moon? For the same reason lunar eclipses don’t occur during each new and full moon: The Moon’s orbit around Earth is not in the same plane as Earth’s orbit around the Sun—their orbits are tilted relative to each other by about 5°. Eclipses can occur only at certain times of the year. Most of the time, the shadow of the Moon does not hit Earth. Usually, a total eclipse occurs over a range of locations on Earth, but other spots don’t see the eclipse or, at least, not a total eclipse. The farther away you are from the path of totality (the point at which the Sun is completely covered), the less of the Sun is eclipsed from your perspective. Let’s explore how you can safely view a solar eclipse and what you might see. With a pinhole camera, you can examine the partial phases of an eclipse. You can make a pinhole camera using simple objects at home. Such a device is just an opaque screen with a hole in it through which the image is projected onto an opposing viewing screen. Simply puncture a hole through a piece of cardboard; shadow a viewing screen—a white piece of paper will do—with the cardboard to create a small image of the Sun on the screen. When the Sun is eclipsed, you will see a crescent shape or whatever the Sun’s shape happens to be at the time. Holes through leaves in trees also serve as pinhole cameras and produce a series of images on the ground surface below. You can also project the image of the Sun through a telescope to get a magni ed view or use a monocular or refracting telescope to project the Sun onto someone’s shadow. A pair of binoculars creates two images of the Sun. Just before totality, only a little bit of the Sun’s photosphere shows, creating a diamond-ring-like appearance where a small portion of the Sun’s light sparkles in one section along the edge of the Moon. If the sunlight passes through valleys on the Moon’s surface, you can sometimes see a series of sparkling, diamond-like lights called Baily’s beads. You can brie y (for a few seconds) view the diamond ring and Baily’s beads with the naked eye, but do not use binoculars or a telescope. During totality, many phenomena come into view. You can see a thin layer right above the photosphere called the chromosphere. It is somewhat hotter than the photosphere. You can also see the much more extensive, much hotter corona. You might also see protrusions from the Sun—called prominences— which are hot plumes of gas running along magnetic elds away from
  • 53 the Sun’s outer edges. The chromosphere, corona, and prominences are completely safe to view with the naked eye, through binoculars, or through a telescope. They are much fainter than the photosphere. As the Moon moves across the Sun and out of totality, another diamond-ring-like effect occurs and, perhaps, more of Baily’s beads. The totality portion of a solar eclipse typically lasts just 1 or 2 minutes. The maximum duration is only about 7.3 minutes, which is extremely rare. During totality, twilight sky colors appear all around the horizon. A small amount of light hitting the atmosphere is re ected toward you. Blues and greens are absorbed and scattered out of your line of sight, while the reds and oranges remain visible. Shadow bands can appear just before and just after totality. Shadow bands are a rippling effect of light on the ground caused by different layers of the atmosphere bending the sunlight in different ways as it hits the atmosphere and continues to Earth. Similar to the shimmering bands of light you see re ected in a swimming pool, shadow bands are created when the tiny bit of uneclipsed Sun twinkles alternately brighter and dimmer. Another phenomenon is the racing shadow of the Moon. You can sometimes see it approaching just before totality and racing away after totality. More easily viewed from above, the Moon’s shadow runs across the ground because the Moon is orbiting Earth during an eclipse. The shadow is projected to a progressively different location from west to east along the face of Earth. The projection of the shadow intersects Earth at different locations to produce a curved path on our spherical planet. Galileo Galilei (1564 1542): Italian mathematician, astronomer, and physicist; was the rst to systematically study the heavens with a telescope. Discovered the phases of Venus and the four bright moons of Jupiter, providing strong evidence against the geocentric model for the Solar System. After being sentenced by the Inquisition to perpetual house arrest, he published his earlier studies of the motions of falling bodies, laying the experimental groundwork for Newton’s laws of motion. Name to Know
  • 54 Lecture10:GloriousTotalSolarEclipses Baily’s Beads: During a solar eclipse, the effect of sparkling lights created by sunlight passing through valleys on the Moon’s surface. chromosphere: Hot, thin layer of gas just below the Sun’s corona and above the photosphere. pinhole camera: A hole in an opaque sheet used to project an image of the Sun. prominences: Hot plumes of gas streaming from the Sun’s photosphere along the lines of the Sun’s magnetic elds. sunspots: Cooler regions on the Sun’s photosphere that appear as dark blotches. Espenak, Fifty Year Canon of Solar Eclipses. Harris and Talcott, Chasing the Shadow. Littmann, Willcox, and Espenak, Totality. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. The image produced by a pinhole camera is inverted. Similarly, the lens of your eye produces an inverted image on the retina. Why, then, do you think we see people and other objects right side up? 2. During a total lunar eclipse, what would someone on the Moon see when looking toward the Sun? Important Terms Suggested Reading Questions to Consider
  • 55 3. Why can’t we observe the solar corona every day from Earth’s surface? 4. Why is a total solar eclipse visible from only a small fraction of Earth’s surface, whereas a total lunar eclipse is visible from about half of Earth’s surface?
  • 56 Lecture11:MoreEclipseTales More Eclipse Tales Lecture 11 “In a few hundred million years, most eclipses will be annular. … The reason for this is that the Moon is gradually receding away from the Earth … at a rate of about four centimeters per year. So, although right now the Moon is often big enough to cover the Sun’s photosphere, in a few hundred million years, usually it will be too small; and in half a billion years, it’ll always be too small to cover the Sun’s disk.” T hough scientists now know what causes solar eclipses, their occurrences throughout history have given rise to various interpretations. Ancient peoples interpreted solar eclipses in many interesting ways. Some cultures believed that a dragon was trying to devour the Sun; some believed that the Sun was ghting with its lover, the Moon, or that the two were making love discreetly in darkness; some thought that the Sun simply grew angry, sad, or ill, disappearing to recuperate. An annular eclipse occurs when the Moon is not quite at the right distance from Earth to completely cover the Sun’s photosphere. Annular refers to the annulus (ring) of the Sun that remains visible. The annulus is part of the bright photosphere; thus, you should always use eye protection when viewing an annular eclipse. Because the Moon’s orbit is elliptical, sometimes it’s farther from Earth than average and, at times, closer to Earth. When the Moon is farther than average from Earth, it is too small in angular size to cover the Sun, and an annulus of the Sun appears during what would otherwise be a total solar eclipse. Similarly, Earth’s orbit about the Sun is elliptical. Thus, when the Sun looks bigger than average, the Moon might not be large enough to cover the photosphere, causing an annular eclipse. During a hybrid solar eclipse, both an annular and a total eclipse occur but at different places on Earth; some places experience a total eclipse while others experience an annular eclipse. How? At those positions on Earth that are closest to the Moon, near the center of the eclipse path, the Moon’s angular size is just big enough to cover the Sun, creating a total solar eclipse. At those positions on Earth that are farther from the Moon, near the beginning
  • 57 and end of the eclipse path, the apparent size of the Moon is too small to cover the Sun, creating an annular eclipse. In a few hundred million years, the vast majority of eclipses will be annular because the Moon is gradually moving away from Earth. Conversely, more than a few hundred million years ago, the Moon was considerably closer to Earth, which made it completely cover the Sun’s photosphere during a total solar eclipse. Coronas, prominences, and the chromosphere weren’t as easily visible because the Moon fully or partially covered these phenomena. No other planet has moons of the right size and at the right distance to produce a total solar eclipse as dramatic as we experience on Earth. On the other hand, Jupiter occasionally experiences double eclipses. Astronomers can correctly predict when and where eclipses will occur. A number of eclipses have changed history. For example, in 585 B.C., an eclipse took place in what is now central Turkey, where the Medes and the Lydians were engaged in a 5-year battle. When the eclipse occurred, the armies took it as a sign to end their war. Scienti cally, the most famous eclipse was the one that provided the rst observational con rmation of a prediction from the general theory of relativity, which was conceived by Albert Einstein. The theory, published in 1916, postulates that mass warps space and time, producing the phenomenon of gravity. Particles follow their natural paths through curved space-time; indeed, this is why planets orbit the Sun. The theory predicts that light should also follow a curved path and, therefore, that light coming from a star—as viewed from Earth—actually does not come from the same direction as the star’s true location because of this bending. Einstein calculated how much the bending should be. This effect seems impossible to measure because stars are invisible during the day. During a total solar eclipse, however, bright stars are visible, and their apparent positions can be measured. These apparent positions can be compared with “The rst written record of a total solar eclipse was in the year 2134 B.C. in China. The two royal astrologers, Hsi and Ho, had apparently neglected to predict this event and were beheaded as a result.”
  • 58 Lecture11:MoreEclipseTales the “true” positions, as measured in a photograph taken during a time of year when those stars are visible at night, with no Sun along the line of sight. During a total solar eclipse in 1919, Arthur Eddington, a British astrophysicist, made measurements of the stars and found that, in accordance with Einstein’s predictions, their apparent positions were displaced outward from the Sun compared with their positions as measured in photographs taken at night. This displacement is greatest for stars whose light rays come closest to the edge of the Sun, smaller for stars that don’t quite graze the edge of the Sun, and smaller still for those stars whose light rays don’t come close to the Sun’s edge. In all cases, it is a very slight effect—so slight that, in retrospect, Eddington’s measurements were not compelling. Measurements during subsequent eclipses were used to con rm the predicted bending. News of the apparent con rmation made Einstein an instant celebrity among the lay public worldwide, and the New York Times ran a headline story about it. Eddington, Sir Arthur (1882–1944): British astrophysicist who studied the physical structure of stars and was an expert on Einstein’s general theory of relativity. Through his observations of a total solar eclipse in 1919, he helped to con rm this theory. Einstein, Albert (1879 1955): German-American physicist, the most important since Newton. Developed the special and general theories of relativity, proposed that light consists of photons, and worked out the theory of Brownian motion (the irregular, zigzag motion of particles suspended in a uid is due to collisions with molecules). Responsible for E = mc2 , the world’s most famous equation. general theory of relativity: Einstein’s comprehensive theory of mass (energy), space, and time; it states that mass and energy produce a curvature of space-time that we associate with the force of gravity. Names to Know Important Terms
  • 59 space-time: The four-dimensional fabric of the Universe whose points are events having speci c locations in space (three dimensions) and time (one dimension). Harris and Talcott, Chasing the Shadow: An Observer’s Guide to Solar Eclipses. Littmann, Willcox, and Espenak, Totality: Eclipses of the Sun. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Will, Was Einstein Right? Putting General Relativity to the Test. 1. If the Moon were placed at twice its current distance from Earth, physically how large would it have to be so that total solar eclipses could still occur? 2. Describe the conditions under which the thickest (widest) annulus is seen during an annular solar eclipse. Where should the Moon and Earth be in their respective elliptical orbits? 3. Is the bending of starlight by the Sun’s gravitational eld the same physical phenomenon as the bending of sunlight around Earth during a total lunar eclipse? Suggested Reading Questions to Consider
  • 60 Lecture12:EarlyStudiesoftheSolarSystem Early Studies of the Solar System Lecture 12 “The Sun, Moon, and planets were associated with gods, and people believed that human traits and lives were in uenced by the planets’ positions. Thus, astrology provided much of astronomy’s roots. As human consciousness evolved, celestial objects became the subject of wonder; the human relationship with the cosmos became a focus of study.” L eaving behind our observations of familiar celestial sights, we focus on the early history of astronomy, beginning with a brief look at the perspectives of the ancients. Astronomy had its roots in such ancient civilizations as Mesopotamia, Babylon, India, Egypt, and China. Early people looked at the heavens for practical purposes: They needed to know when to plant crops, when rivers might ood, and when other natural events might occur. Stars also helped them navigate. Some cultures left behind extensive documents, from which we’ve gained much knowledge. By studying ancient ruins, we can learn what people knew about the heavens. This link between archaeology and astronomy is called Stonehenge. CorelStockPhotoLibrary
  • 61 archaeoastronomy, the study of ancient structures and their astronomically signi cant alignments. Stonehenge in England is a famous example, with its giant standing stones forming a circle 100 feet wide. Stonehenge had signi cant social, political, and religious implications for the ancients, but archeoastronomers have also found astronomical alignments, indicating that the builders knew something of the stars. The most prominent alignment is with the Heel Stone, which is outside of the main circle. As viewed from the center of Stonehenge, the Sun rises along the Heel Stone at the moment of the summer solstice. The Egyptian pyramids also exhibit signi cant alignments, such as pointing toward certain stars. However, as with Stonehenge, some alignments may be purely coincidental, and scientists run the risk of mistaking coincidence for signi cance. About 1000 years ago, the Mayans had an advanced understanding of astronomy, as evidenced in numerous structures. From the Mayan-built Caracol in Chichen Itza, you can see the position of sunrise or sunset at the solstices and the equinoxes. The Mayans’ elaborate calendar involved Venus, the Moon, the Sun, and other celestial objects. Ancient Greek astronomy led to the greatest in uence on modern Western thought. Aristotle’s theories are particularly important. The ancient Greeks knew that Earth is roughly spherical, and Aristotle clearly articulated arguments to prove this. By observing Earth’s shadow, which always projected an arc on the Moon during a lunar eclipse, Aristotle deduced that Earth must be spherical. If Earth were a at, circular disk, then sometimes it would cast a circular shadow, and other times, an elliptical shadow. Also, phases of the Moon show that it is spherical, suggesting that Earth is, too. Astronomy in History Some people have suggested that Stonehenge was suf ciently complex and elaborate to even allow the prediction of eclipses: lunar and solar eclipses. That hypothesis has been discredited. There’s no real evidence that Stonehenge could do something as complicated as the prediction of solar eclipses.
  • 62 Lecture12:EarlyStudiesoftheSolarSystem Further, Aristotle used the different positions of the stars to argue that Earth is a sphere. Different stars are visible in the sky at different latitudes on Earth but at the same longitude and at the same time. From 20° north latitude, Polaris appears lower in the sky than at 40°. In addition, other stars shift their positions, which Aristotle argued could only indicate a round Earth. Later, more evidence surfaced: Ships approaching from far away come over a horizon. On a at, in nite Earth, they would grow dimmer and smaller as they sailed away, instead of sinking below the horizon. Aristarchus of Samos was another great astronomer. Although he underestimated the true distance of the Sun, Aristarchus correctly deduced that it was very large and distant. His calculations were based on the Moon’s phases. To see a precisely quarter moon—half of the visible face of the Moon, whether its rst or third quarter—the angle between Earth, Moon, and Sun must be precisely a right angle. Though Aristarchus made some incorrect assumptions, he measured this angle to roughly determine the relative distance of the Sun and how many times larger it was than the distance between Earth and the Moon. In practice, this measurement is dif cult to make because the Sun is so far away from us. The angle Aristarchus tried to measure is nearly 90°, regardless of how far away the Sun is. Indeed, Aristarchus measured this angle to be 87°. It’s also dif cult to measure the precise moment of the rst or third quarter moon. In performing his calculations, Aristarchus had to assume a circular and uniform orbit of Earth and Moon. (We now know that these orbits are elliptical and that the orbital speeds change.) Despite Aristarchus’s errors, his idea was correct and ingenious. From measurements,Aristarchus erroneously calculated that the Sun is 19 times more distant than the Moon—the true value is 390 times—but he correctly reasoned that the Sun was much larger than the Moon. Aristarchus argued that because the shadow of Earth was not much bigger than the Moon, Earth must be 2 to 3 times the size of the Moon. (Earth is actually 3.7 times bigger.) Thus, according to Aristarchus, if the Sun is 19 times bigger than the Moon, and Earth is 2 to 3 times the size of the Moon,
  • 63 then the Sun must be about 7 times bigger than Earth. In reality, the Sun is 109 times physically larger than Earth; again, Aristarchus was wrong, but his idea was correct. Finally, because the Sun is considerably larger than Earth and very distant, Aristarchus also reasoned that the Sun, not Earth, is the dominant object in the Universe. Eratosthenes determined Earth’s circumference. Eratosthenes noticed that a rod sticking up from the ground casts a shadow, even at noon, at many locations. But at some locations, Syene to be exact, at noon during the summer solstice, there was no shadow. On the same day in Alexandria, north of Syene but at the same longitude, the rod cast a short shadow. By knowing the length of the shadow and the length of the stick, the angle that the Sun makes relative to the stick can be calculated. Through a series of geometric calculations, Eratosthenes determined Earth’s circumference to within an error of about 1%. The next great astronomer to come along was Hipparchus, perhaps the greatest astronomer of pre-Christian antiquity. His studies were done c. 160–127 B.C. Hipparchus made the rst accurate catalog of about 850 stars, including their positions and their apparent brightness. He also re ned the method of Aristarchus of Samos and found that the Moon’s distance is about 59 Earth radii. The correct number is 60 Earth radii, meaning that the distance of the Moon from Earth is 60 times Earth’s radius. Hipparchus determined the length of the year to within 6 minutes. He also noticed that the direction of the north celestial pole changed slightly with time. It had changed over the 150 years or so during which accurate records had been kept. As mentioned in a previous lecture, because of the gravitational forces of the Moon and Sun on Earth, Earth’s tilted axis of rotation slowly undergoes a conical motion called precession. In about 13,000 years, summer and winter will be reversed in the two hemispheres from what they are now. Hipparchus noticed and measured the precessing motion of Earth.
  • 64 Lecture12:EarlyStudiesoftheSolarSystem Aristarchus of Samos (roughly 310 230 B.C.): Greek astronomer; measured the Sun-Earth distance relative to the Earth-Moon distance. Realized that the Sun is much larger than the Earth and reasoned that the Sun (rather than the Earth) is at the center of the Universe, predating Copernicus by 1800 years. Aristotle (384 322 B.C.): The most in uential early Greek philosopher. He lectured on a vast range of subjects; however, many or most of his beliefs in physics and astronomy turned out to be wrong. Developed a widely adopted geocentric (Earth-centered) model of the Universe consisting of 55 spheres. Correctly concluded that the Earth is spherical. Eratosthenes (276 194 B.C.): Greek geographer who estimated the circumference of the Earth to within 1% accuracy through measurements of the length of a stick’s shadow at different locations on Earth. Hipparchus (c. 160–c. 127 B.C.): Greek astronomer who made the rst accurate star catalogue. Re ned the methods of Aristarchus of Samos. Determined the length of the year to within six minutes and noticed that the direction of the north celestial pole changes with time. apparent brightness: The amount of energy received from an object per second, per square centimeter of collecting area. It is related to luminosity and distance through the equation b = L/(4 d2 ), the inverse-square law of light. archaeoastronomy: The study of the astronomical signi cance of ancient buildings and other structures. Important Terms Names to Know
  • 65 Fraknoi, Morrrison, and Wolff, Voyages through the Universe, 3rd ed. Hoskin, ed., The Cambridge Concise History of Astronomy. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pedersen, Early Physics and Astronomy: A Historical Introduction. 1. Had you been alive 2000 years ago, do you think you would have believed in a geocentric (Earth-centered) model of the Universe or a heliocentric (Sun-centered) model, as did Aristarchus? 2. Discuss the importance of assuming that the Sun is very distant if the method of Eratosthenes is used to determine the circumference of Earth. 3. How compelling do you nd Aristotle’s arguments for a spherical Earth? Suggested Reading Questions to Consider
  • 66 Lecture13:TheGeocentricUniverse The Geocentric Universe Lecture 13 “It’s reasonable to think that the Earth isn’t moving. If I jump up in the air, or if you do, the Earth doesn’t go sailing out from under me, right? So, if it were moving quickly around the Sun, the Earth should go sailing out from under us. We now know that it shouldn’t because of inertia.” E arly Greek astronomers had observed the movement of the planets from night to night slowly among the stars. This movement is unrelated to the general rising of stars in the east and setting in the west as a result of Earth’s axial rotation. The Greeks also noticed that, at times, the planets appeared to move backward among the stars. Normally, the planets move among the stars in a forward, or prograde, motion from west to east. But for a little while every year, each of the planets moves east to west in a retrograde, or backward, motion. The prograde-to-retrograde-to-prograde movement can form an S-shaped gure, or it can be a loop. It is not a straight line because the planes of the planets orbiting the Sun are slightly tilted relative to one another. Many hypotheses about the origin of the Star of Bethlehem have been proposed over the centuries. Some believe it was a comet; others, a nova or supernova. For various reasons, however, these ideas all fail. Astronomy in History Ahypothesis proposed by Michael Molnar states that the Magi actually practiced an obscure form of astrology and interpreted a particular planetary alignment to foretell the birth of Christ. Other astrologers might not have seen such an alignment as being particularly signi cant. The Star of Bethlehem may have been Jupiter moving through the constellation Aries the Ram near the time of its retrograde motion, along with other astrologically signi cant conditions, such as the presence of the Sun in Aries. Saturn was near this alignment as well, but Mars and Mercury (generally bad omens) were far away. Moreover, Jupiter and Aries were rising in the east, just ahead of the Sun, at this time. Molnar’s hypothesis is supported by a number of factors, including what we now know were these special planetary alignments 2000 years ago.
  • 67 The apparent motion of planets among the stars, including their retrograde motion, was important to Aristotle and Ptolemy in developing the Earth- centered model of the Universe. Most ancient Greek astronomers believed that the Earth was the center of the Universe and that it was stationary. The Earth couldn’t possibly rotate or orbit the Sun; if it did, people would y off. To the ancient Greeks, the stars appeared to be embedded in a celestial sphere that rotated around the Earth. The planets, Sun, and Moon were also embedded in their own spheres, which rotated around the Earth between Earth and the stars. Thus, Earth was the center of these spheres. Aristotle proposed such a geocentric, or Earth-centered, model, the key to which is a stationary Earth. If Earth were orbiting the Sun and if the celestial sphere were nearby, then at one position of the Earth’s orbit, Polaris would be along the line to the north celestial pole. But six months later, Polaris would be nowhere near the apparent extension of our Earth’s north pole. Of course, Polaris is more or less xed in the sky at any given latitude, which is what the Greeks observed. Moreover, constellations and asterisms would appear to change shape as viewed from Earth over the course of a year, but they don’t. Today, we know that the celestial sphere is much farther away than the Greeks thought, which was the aw in their reasoning. The Earth is moving, but they assumed that the celestial sphere was nearby and concluded that the Earth is not moving because of the apparent absence of changes in shape of the constellations. To account for the retrograde motion of planets, Aristotle proposed that the planetary spheres had to be rotating in a complex manner. In his system, there were 55 nested spheres in uencing one another’s motion. Ptolemy (2nd century A.D.), a great astrologer, produced a better system than Aristotle’s for predicting planetary positions as a function of time. Ptolemy suggested that Earth was slightly offset from the center of a deferent, or planetary sphere. Another point, called the equant, was the center, around which the deferent rotated at a uniform angular rate. To explain retrograde motion, Ptolemy theorized that planets moved along paths called epicycles that were centered on the deferent, the planetary sphere. Epicycles were essentially their own self-contained spheres, along which the planets moved. As a planet moved along its epicycle in the same direction as the deferent, it would be moving in a prograde fashion. If a planet moved in the opposite
  • 68 Lecture13:TheGeocentricUniverse direction in its epicycle around the deferent, that opposite motion could make the planet appear to move backward among the stars, or go retrograde. Ptolemy’s system was complicated, but it gave accurate results and was accepted for nearly 1500 years. Nonetheless, people still believed in a “perfect reality” represented by Aristotle’s nested spheres. The Polish astronomer Nicolaus Copernicus also focused on the retrograde motions of the planets to develop his heliocentric, or Sun-centered, theory of the Universe. Independently reviving the ancient hypothesis of Aristarchus, Copernicus developed a model of the Sun as the center of the Universe, with Earth and the other planets orbiting the Sun. This concept naturally explained how planets went into retrograde motion. Because each planet is a different distance from the Sun, each orbits the Sun at a different rate. Mars, for example, takes longer to orbit the Sun than Earth does. For a time, Mars appears to move backward because Earth actually passes by Mars in its own orbit of the Sun. Similarly, planets closer to the Sun than Earth is (Mercury, Venus) go through retrograde motion as they pass Earth in their orbits around the Sun. Copernicus did not place the Sun in the actual center of the Universe. The Sun had to be slightly off center for his theory to work because he assumed that planets had perfectly circular orbits. Circular orbits would not have allowed for the changing angular speed of a planet across the sky during different times of the year. Copernicus’s off-center circular orbits worked well because they mimicked an ellipse—especially a nearly circular ellipse—with the Sun at one focus. However, Copernicus still needed epicycles to account for the small difference in an observed position of a planet from its predicted position. Copernicus’s epicycles weren’t needed to explain the retrograde motion, but they were used to ne-tune his theory for agreement between observed planetary positions “Copernicus came along, and he presented an alternate hypothesis: the hypothesis of a Sun-centered Universe. He did not let this theory be published until the day of his death. He just was afraid of what might happen to him if he published such a heretical theory before he was already dead of natural causes.”
  • 69 and predicted positions. By using detailed observations and geometry, Copernicus was also able to determine the relative distances of planets from the Sun with remarkable accuracy. Copernicus, Nicolaus (1473 1543). Polish astronomer; proposed the heliocentric (Sun-centered) model of the planetary system. He showed how the retrograde motion of planets could be explained with this hypothesis. His book De Revolutionibus was published the year of his death. Ptolemy, Claudius (85 165). Greek astronomer who developed an elaborate model for planetary motions, based on Aristotle’s geocentric Universe, that endured for more than 1400 years. Compiled the Almagest, a set of 13 volumes that provides most of our knowledge of early Greek astronomy. ellipse: A set of points (curve) such that the sum of the distances to two given points (foci) is constant. nova: A star that suddenly brightens, then fades back to its original intensity; caused by the accretion of stellar matter from a companion star. supernova: The violent explosion of a star at the end of its life. Hydrogen is present or absent in the spectra of Type II or Type I supernovae, respectively. prograde motion: The apparent motion of the planets when they appear to gradually move from west to east among the stars; retrograde motion is the opposite direction. retrograde motion: The apparent backward (east-to-west) motion among the stars that planets undergo for a short time each year. Names to Know Important Terms
  • 70 Lecture13:TheGeocentricUniverse Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler. Gingerich and MacLachlan, Nicolaus Copernicus: Making the Earth a Planet. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Molnar, The Star of Bethlehem: The Legacy of the Magi. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Pedersen, Early Physics and Astronomy: A Historical Introduction. 1. Describe how you can tell when observing the sky whether a planet is in prograde or retrograde motion. 2. Describe the astronomical conditions that may explain the appearance of the Star of Bethlehem. 3. How did the heliocentric model of Copernicus explain the apparent retrograde motion of the planets? Consider planets both closer to the Sun and farther from the Sun than Earth is. Suggested Reading Questions to Consider
  • 71 Galileo and the Copernican Revolution Lecture 14 “How was the Copernican system proven to be correct? That task came to Galileo, whose telescopic observations in 1610, and in the years thereafter, con rmed that the heliocentric hypothesis was the correct one.” I n the 16th century, there were two competing hypotheses for the nature of the Universe. In Aristotle’s geocentric system, all celestial bodies rotated on spheres around a stationary, non-rotating Earth. Claudius Ptolemy had a detailed version of the geocentric model in which planets moved along epicycles, whose centers moved along a deferent around the Earth. The Ptolemaic system was particularly adept at accurately predicting the positions of planets. In particular, retrograde motion would occur when a planet was moving along its epicycle in a direction opposite to the motion of the deferent. In Nicolaus Copernicus’s heliocentric system, rst published upon his death in 1543, Earth and other planets orbit the Sun, which is at the center of the Universe. The planets more distant from the Sun have slower orbital speeds than the planets less distant from the Sun. Retrograde motion is a natural consequence of the changing perspective when Earth passes an outer planet in its orbit or when an inner planet passes Earth. A good analogy is found by considering a traf c circle with several different lanes and outer cars moving more slowly than inner cars. When an inner car is passing an outer car, the outer car appears to move backward (retrograde), whereas the rest of the time, it appears to move forward. Although no epicycles were needed to explain retrograde motion in Copernicus’s Sun-centered system, some epicycles were required to get better agreement between the observed and predicted positions of planets. Copernicus’s heliocentric model of the Universe was initially not widely accepted. One reason was that his system was no better at predicting the movements of planets than Ptolemy’s geocentric model. Further, to believe that the Sun—not Earth—was the center of the Universe was heretical.
  • 72 Lecture14:GalileoandtheCopernicanRevolution Galileo’s telescopic observations, beginning in 1610, con rmed that the planets orbit the Sun. Galileo Galilei found the Copernican system more philosophically attractive than Ptolemy’s model and set out to see whether it was true by conducting observations. He believed that observations should be used to determine the truth or falsity of hypotheses. He was also a faithful Catholic, but he questioned some of the teachings of the Church. Galileo improved on the design of early Dutch toy telescopes, allowing him to see considerable detail in the heavens. One of Galileo’s followers, Benedetto Castelli, encouraged Galileo to observe Venus, believing that if the Copernican system were correct, Venus should go through a complete set of phases, as the Moon does. After looking at Venus over the course of many months, Galileo indeed observed the planet go through a set of phases, from new to crescent, quarter, gibbous, full, and back through the phases to new again. Galileo made a number of otherimportantobservations. He observed that Jupiter itself rotates. From this, he hypothesized that perhaps the Earth rotates, as well. He found that Jupiter has moons orbiting it. They proved that objects can orbit other bodies, not just the Earth. The observations demonstrated that as Jupiter moves through the sky—with its moons following—the moons aren’t left behind. Thus, the Earth could orbit the Sun, and objects associated with Earth are not left behind. Galileo also found that our own Moon has craters, mountains, and valleys, like Earth, and realized that perhaps Earth isn’t unique. Galileo observed changing sunspots, noting that the Sun isn’t perfect, and found that the Sun rotates, as well. He saw that Saturn has what he described as “handles”; his telescope wasn’t good enough to show ©HemeraTechnologies/AbleStock.com/Thinkstock Astronomy in History How exactly do Galileo’s observations of Venus strike a blow to the Ptolemaic system? In the Ptolemaic model, Venus is between Earth and the Sun, and its epicycle does not cross the Sun’s orbit; therefore, Venus could exhibit only the new—or dark—and crescent phases. In the Copernican system, in which both Venus and Earth orbit the Sun, sometimes Venus is between the Earth and the Sun, in which case it appears new; at other times, it is on the other side of the Sun as viewed from Earth, allowing for a full phase.
  • 73 that these “handles” were actually Saturn’s rings. Finally, he found that the Milky Way consists of an almost countless number of stars, and he wondered whether there might be other planets—other worlds—orbiting them. However, Galileo suppressed at least one set of observations that did not directly support the heliocentric hypothesis. He noticed that some stars in the sky appeared double, but he didn’t know that they were physically bound together by gravity. He simply believed the fainter star to be more distant. If the fainter star was indeed more distant, then under the heliocentric hypothesis, the stars should appear in slightly different positions, depending on where the Earth is in its orbit. Yet when Galileo observed these double stars, he found no shift over the course of six months. He may have suppressed this observation because he realized that his crucial assumption—the fainter star being more distant than the bright one—might be wrong. Galileopublishedhis ndingsintwofamous works, which were not well received by the Roman Catholic Church. Galileo’s Sidereus Nuncius (Starry Messenger) was published in 1610. His Dialogue on the Two Great World Systems was published in 1629, which he intentionally wrote in popular, witty Italian so as to be accessible to everyone. The Catholic Church didn’t object to Galileo’s models explaining his observations, but they did object to the belief that these models represented truth. The Church and the Inquisition believed that his book was written to convince the public that the Copernican system was correct, which was an attack on the Bible. To avoid being imprisoned or killed, Galileo recanted his belief in the Copernican theory but spent the rest of his life under house arrest. He used that time to organize and publish his earlier observations and experiments, and perhaps, he redid a few of his experiments. “To avoid being locked up in a dungeon or killed, as Bruno was, [Galileo] recanted his belief in the Copernican theory. Though the legend goes that, as he knelt before the Inquisition, he said under his breath, ‘And yet it moves’ (referring to the Earth).”
  • 74 Lecture14:GalileoandtheCopernicanRevolution The most famous of his ndings was that a light object and a heavy object, both of the same size, hit the ground at the same time when dropped from a height, neglecting air resistance. With air resistance, objects of different sizes fall at different speeds. Galileo also found that an object accelerates as it falls. Thus, if an object travels 1 unit of distance in 1 second, after a total of 2 seconds, it travels 4 units of distance; after 3 seconds, 9 units; and after 4 seconds, a total of 16 units. This observation and Galileo’s other results were the basis for Newton’s subsequent development of the laws of motion. In 1992, Pope John Paul II of cially pardoned Galileo, stating that the Church had been overly harsh when it condemned Galileo in 1633. Drake, Galileo: A Very Short Introduction. Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler. Gingerich and MacLachlan, Nicolaus Copernicus: Making the Earth a Planet. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. MacLachlan, Galileo Galilei: First Physicist. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sobel, Galileo’s Daughter: A Historical Memoir of Science, Faith, and Love. 1. By including many additional smaller epicycles on the larger epicycles in the Ptolemaic model, do you think that the accuracy of the predicted planetary positions can be continually improved? 2. How did Galileo’s observations of Venus serve to disprove the Ptolemaic model of the Universe? Suggested Reading Questions to Consider
  • 75 3. Examining each of Galileo’s telescopic discoveries separately, do you think they tended to support, oppose, or be irrelevant to the heliocentric hypothesis? 4. If an apple and the Moon are the same distance from Earth, compare the acceleration of the apple toward the Earth with the acceleration of the Moon toward the Earth based on what you know from Galileo’s experiments on falling bodies.
  • 76 Lecture15:RenementstotheHeliocentricModel Re nements to the Heliocentric Model Lecture 15 “The rst law that [Kepler] gured out in the year 1604 is that the planetary orbits are ellipses, not circles. The Sun is not at the center of the ellipse, but rather is at one focus of the ellipse.” R oughly 70 years after the publication of Copernicus’s book Concerning the Revolutions, Galileo’s observations proved Ptolemy’s system wrong and the Copernican system as probably the correct description of physical reality. However, even before Galileo’s groundbreaking observations, other scientists had made some re nements to the Copernican model. One idea combined the features of both the heliocentric and the geocentric system, suggested by the Danish nobleman Tycho Brahe. Basically, Tycho thought that everything except the Moon orbits the Sun, and the Sun, along with its orbiting planets, orbits the Earth. At that time, no one really knew that the Earth was moving; that idea was just conjecture by Copernicus. However, neither the geocentric camp nor the heliocentric camp was particularly pleased with this combination of motions. At a young age, Tycho saw a partial solar eclipse and was impressed that astronomers had been able to predict it. He then dedicated his life to making ever more accurate observations of the Moon, Sun, and planets in order to enhance the predictive power of physics and these models. Tycho discovered a supernova, an exploding star, in 1572. He didn’t know the physical nature of the star—that it was a star at the cataclysmic end of its life, visible with the naked eye. Until then, people had thought that the heavens were immutable, and Tycho’s observation went a long way toward dispelling that belief. Tycho set up an observatory, where he made accurate observations of the planets. He had no telescope, but he had other instruments that measured the altitude of a planet above the horizon and its angular distance from stars. Before Tycho’s early death in 1601, he had hired a superb mathematician, Johannes Kepler, to analyze his data. Kepler re ned the Copernican model with three important empirical laws. Kepler’s laws were empirical because he had no physical explanation for them. He simply found that, quantitatively, they appeared to be true. Later, Newton demonstrated why.
  • 77 Kepler’s rst law states that planetary orbits are ellipses, not circles. The Sun is not at the center but at one focus of the ellipse, while nothing is at the other focus. An ellipse is de ned as a shape in which the sum of the distances from any two foci ( xed points), a + b, is a constant. In an ellipse, the long axis is called the major axis; the short axis is the minor axis. Half these lengths are the semimajor and semiminor axes, respectively. The semimajor axis is close to the average distance between a planet and the Sun. The eccentricity of an ellipse is the distance between the foci divided by its major axis. As the foci move farther apart, the ellipse becomes more highly eccentric, or more elongated. For nearly circular orbits, the semimajor axis is simply the orbital radius. Kepler’s second law states that a line between the Sun and a planet sweeps out in a pie shape in equal areas as long as the time intervals are equal. When a planet is close to the Sun, it moves faster than when it is far from the Sun. An extreme example of this is the highly eccentric orbits of many comets, which spend very little time near the Sun. Kepler’s third law states that the square of a planet’s orbital period is proportional to the cube of its semimajor axis, or average distance from the Sun. In mathematical form, this law is P2 = kR3 , in which P is the orbital period, R is the semimajor axis, and k is a constant (the same for all planets). The more distant a planet is from the Sun, the longer it takes to complete an orbit. Kepler called this third law the “harmonic law,” suggesting an almost musical relationship between orbital periods and sizes. Did You Know? When discussing planets in our Solar System, it is sometimes convenient to use units based on Earth’s orbit. We write Pp 2 = kRp 3 , in which the subscript p refers to a given planet. Similarly, we write PE 2 = kRE 3 , in which the subscript E refers to Earth. Dividing one equation by the other, the constant k cancels out: (Pp / PE )2 = (Rp / RE )3 . If we adopt units of years for Pp and AU (astronomical units) for RE , we have Pp 2 = Rp 3 because PE = 1 year and RE = 1 AU. If we know that the orbital period of Mars is 1.88 years (Pp = 1.88), then 1.882 = 3.53 = Rp 3 ; thus, the semimajor axis of Mars’s orbit is the cube root of 3.53, or 1.52 (Rp = 1.52 AU).
  • 78 Lecture15:RenementstotheHeliocentricModel Kepler’s third law also applies to objects orbiting the Earth—in particular, satellites. A satellite just above the Earth’s surface travels about 230 degrees in 1 hour—about two-thirds of a full circle—whereas the Earth itself rotates about 15 degrees per hour. A satellite orbit at 3.25 Earth radii from Earth’s center traverses 42 degrees in 1 hour. But if the satellite is at 6.5 Earth radii from Earth’s center, then it traverses 15 degrees in 1 hour; that is, it traverses the same angular distance as the Earth’s rotating surface. That means that this satellite will appear stationary above a particular point on the Earth’s surface. This is the idea behind geostationary orbits. Isaac Newton now enters the scene, a brilliant but eccentric English physicist who made many magni cent contributions to physics and astronomy. Newton developed calculus, a form of mathematics, as well as the laws of motion and the law of universal gravitation; he also invented a form of telescope, the Newtonian re ecting telescope. Newton’s rst law of motion states that a body continues to be at rest or in motion in a straight line with constant speed unless a force acts on it. We rarely see this in operation because frictional forces are almost always present, slowing a body down until it stops. This was a revolutionary idea; the medieval view held that a continuous force was needed to keep a body moving. In particular, a planet doesn’t need any force to keep it going. The second law is expressed algebraically as a = F/m (or, more commonly, F = ma), in which F is force, m is the mass of the particle on which the force is applied, and a is the particle’s acceleration. The term velocity refers to both speed and direction, and acceleration is the rate at which velocity changes speed or direction or both. Pulling on a planet from the side changes the direction of motion but not the speed. This is how the gravitational force of the Sun keeps a planet curving in its orbit. A large mass is accelerated less than a small mass for a given force. It turns out that most of the planets have orbits that are nearly circular; the ellipses have only a very small eccentricity. This is the reason that Copernicus’s system with circular orbits worked quite well.
  • 79 The third law states that for every action, there is an equal and opposite reaction. In other words, forces always come in pairs and act in opposite directions. When you jump off a chair and the Earth’s force of gravity brings you down again, you exert just as strong a force on the Earth as it does on you. It’s the mass dependence in the second law that makes the difference: That force accelerates the enormously massive Earth far less than it accelerates you. An orbital example would be the Earth and Moon exerting equal forces on each other, but the Moon gets much more acceleration because it is only 1/80th as massive as Earth. The Earth is accelerated, though, and it follows a little monthly orbit 1/80th as large as that of the Moon. Rocket propulsion also provides a familiar example. The force pushing gas out of a rocket is balanced by an oppositely directed force on the rocket, propelling it forward. Brahe, Tycho (1546 1601). Danish astronomer; measured the positions of planets with unprecedented accuracy, laying the foundations for Kepler’s work. Discovered and studied a bright supernova in 1572; thus, the “sphere of xed stars” is not immutable, in contradiction to Aristotelian and Christian dogma. Kepler, Johannes (1571 1630). German mathematician and astronomer; was Tycho Brahe’s assistant and gained access to Brahe’s data after his death. Developed three empirical laws of planetary motion that represent a signi cant revision of the Copernican model. Studied a very bright supernova in 1604. astronomical unit (AU): The average distance between the Sun and the Earth (1.5 108 km). eccentric: Deviating from a circle. Eccentricity is a measure of this. Names to Know Important Terms
  • 80 Lecture15:RenementstotheHeliocentricModel Kepler’s third law: If one object orbits another, the square of its period of revolution is proportional to the cube of the semimajor axis (half of the long axis) of the elliptical orbit. Christianson, Isaac Newton and the Scienti c Revolution. Ferguson, The Nobleman and His Housedog: Tycho and Kepler: The Unlikely Partnership That Forever Changed Our Understanding of the Heavens. Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler. Gleick, Isaac Newton. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thoren, The Lord of Uraniborg: A Biography of Tycho Brahe. 1. If planetary orbits can be reasonably approximated as circles centered on the Sun, can you use Kepler’s third law to derive an equation relating the orbital speeds and distances of planets? 2. Why does a satellite speed up as it spirals toward the Earth due to friction with the outer atmosphere? Naively, it seems that the friction should cause it to slow down. 3. What is the semimajor axis of a comet that orbits the Sun with an orbital period of 100 years? Compare this with the semimajor axis of Uranus, about 20 AU. 4. How might you demonstrate that Earth is orbiting the Sun, thus disproving Tycho Brahe’s model of the Universe? Suggested Reading Questions to Consider
  • 81 On the Shoulders of Giants Lecture 16 “The generalization of Kepler’s rst law, where Kepler said that the orbits are ellipses with the Sun at one focus—Newton was able to prove that, but he generalized it, and he said that really, the trajectories of particles are conic sections. That includes circles, ellipses, parabolas, and hyperbolas.” I saac Newton proposed the law of universal gravitation, a force acting between objects and tending to pull them together. Supposedly, an apple fell on or near Newton, and he guessed that qualitatively, the same force acts upon the Moon, making it fall toward the Earth. This is the Earth’s gravitational force. It was sensible to suppose that all bits of matter within an object contribute to the gravitational force exerted by the object. Thus, the Earth’s gravitational force is proportional to the total mass of Earth, and an apple’s pull toward Earth is proportional to the apple’s total mass. Given that Newton’s third law states that forces are equal and opposite—the force exerted by the apple is equal in magnitude to the force exerted by the Earth—the two forces must be proportional to the product of their masses. A gravitational force proportional to the product of the two masses, together with Newton’s second law (F = ma), is consistent with Galileo’s nding that two bodies of equal physical size but differing mass fall at the same rate. Newton theorized that gravity spreads out over a sphere, diminishing with distance—speci cally, the inverse square of distance. Newton’s formula describes the law of gravitation: 1 2 2 Gm m F d , in which F is the magnitude of the gravitational force between two objects, G is Newton’s gravitational constant, m1 is the mass of the rst object, m2 is the mass of the second object, and d is the distance between the two objects. The form of mathematics Newton invented to perform his calculations, called the calculus, showed that the gravitational force of the Earth acts as though all of the Earth’s mass were concentrated in its center.
  • 82 Lecture16:OntheShouldersofGiants The relevant distance between an apple and Earth is the distance between the center of the apple and the center of Earth. The relevant distance for the Moon is the distance between the center of the Moon and the center of Earth. Earth’s radius is roughly 6400 kilometers, the relevant distance for the case of the apple and the Earth attracting each other. The relevant distance for the Moon is about 384,000 kilometers from Earth, roughly 60 times Earth’s radius. If Newton is correct, the acceleration felt by the Moon should be 2 1 60 of that felt by the apple, and 2 1 60 is 1 3600 . At the Earth’s surface, the measured acceleration due to gravity is 980 centimeters per second, per second—980 cm/s2 —which is equal to 32 feet per second, per second. Thus, 1 3600 of that measurement is 0.27 centimeters per second, per second—the known acceleration of the Moon and that which it must maintain in order to orbit the Earth. Newton believed that the law of gravitation was universal and that Jupiter attracts its moons in the same way that Earth attracts its Moon. How does gravity produce an orbit and prevent the Moon from hitting Earth? According to Newton’s rst law, in zero gravity, an object launched perpendicular to the direction of Earth results in motion along a straight line at constant speed. According to Newton’s second law, releasing that object from rest with gravity causes it to accelerate toward Earth because of Newton is depicted contemplating gravity under the infamous apple tree. ©Photos.com/Thinkstock
  • 83 gravity’s force. Combining these two motions, we can examine them along small time steps. The Moon falls toward Earth during each moment it takes to travel a short distance perpendicular to Earth, but its new distance from the center of the Earth remains unchanged. During the next moment, the same thing happens, but now, the tangential motion (perpendicular to the direction of Earth) is in a slightly different direction because of the acceleration during the preceding moment. Again, the new distance remains unchanged. Thus, along numerous tiny steps of time, a smooth curved orbit is formed. In other words, the Moon really does fall toward Earth, but it never hits because the tangential motion keeps it away. It keeps missing the Earth, in a sense. If Earth’s gravity were eliminated, the Moon would continue to move with constant speed and direction along the tangent to the orbit at the instant gravity disappeared. Newton illustrated his point by demonstrating that as the speed at which an object is thrown or projected increases, the object travels a farther distance before falling to Earth because of gravity. For example, a cannonball red at great speed will eventually fall to the ground, but the distance will be greater than expected because the surface of the Earth partially curves away from the ball’s trajectory. Similarly, if an object were red suf ciently fast, it would follow a trajectory that matched the Earth’s curvature, never hitting the ground but, rather, orbiting the Earth. If an object travels fast enough, it can escape the Earth’s gravitational pull. This speed is known as the escape velocity. At Earth’s surface, the escape velocity is 11.1 kilometers per second. Newton could generalize Kepler’s laws and apply them to situations in which objects attracted each other by gravity. Newton proved Kepler’s rst law: that orbits are ellipses with the Sun at one focus. Furthering this, Newton stated that an object’s trajectory is really a section of a cone—a circle, ellipse, parabola, or hyperbola. If an object is gravitationally bound to another object, the orbit is generally an ellipse—the curve formed when a plane intersects a cone at an angle less steep than the cone’s side. Only if conditions are special does one get a perfectly circular orbit. If an object is unbound (that is, traveling at a speed greater than its escape velocity), the orbit is generally a hyperbola—the curve formed when a plane intersects a cone at an angle steeper than the side of the cone. If an object is just barely unbound (that is, traveling at its escape velocity), its orbit is a parabola—
  • 84 Lecture16:OntheShouldersofGiants the curve formed when a plane intersects a cone at an angle parallel to the cone’s side. Newton derived the constant of proportionality from Kepler’s third law: 2 2 3 1 2 4 P R G m m = kR3 , in which m1 and m2 are the masses of two bodies and G is Newton’s gravitational constant. For planetary orbits, let m1 be the Sun’s mass and m2 be the planet’s mass. The constant k in Kepler’s version depends on m2 ; thus, it’s really not a constant. However, because the mass of each planet is much smaller than the Sun’s mass, the combination 2 1 2 4 [ ( )]G m m is nearly constant for all planets. If the mass m2 is negligible relative to m1 , we can ignore m2 . Therefore, Newton’s version of Kepler’s third law becomes 2 2 3 1 4 ( ) P R Gm , in which m1 is the mass of the dominant object, that is, the Sun. If P and R of the small object are measured, we can solve for m1 , which allows us to determine the Sun’s mass. Assuming that Earth’s mass is negligible and using the known values of P (1 year) and R (1 AU) for Earth, we nd that the mass of the Sun is m1 = 2 1033 grams. This is indeed far larger than the mass of the Earth (m2 = 6 1027 grams), thereby proving that m2 is negligible in comparison. We can also use Newton’s version of Kepler’s third law to determine the orbital speeds of different planets. For any planet, 2 2 3 1 4 ( ) P R Gm . Call this equation (1). If the planet’s orbit is roughly circular,thenthecircumferenceoftheorbit(2 R)mustequaltheplanet’sspeed multiplied by the time period of the orbit: 2 R = vP. This is an application of distance = speed time, which is true for constant speed. Thus, 2 R P v . Substituting this into equation (1) and rearranging, we nd that 2 1 v R m G . Equivalently, 1 2 1Gm v R , so we see that 1 21 v R .
  • 85 Therefore, the speed of a planet is inversely proportional to the square root of its semimajor axis. In other words, distant planets move more slowly than those near the Sun. escape velocity: The minimum speed an object must have to escape the gravitational pull of another object. Christianson, Isaac Newton and the Scienti c Revolution. Cohen, The Newtonian Revolution. Gleick, Isaac Newton. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What is the speed of a planet orbiting 3 AU from a star that is three times as massive as the Sun? 2. If a hypothetical planet is four times farther from the Sun than Earth is, what is its orbital speed (not period) relative to Earth’s? 3. Which is greater: the Earth’s gravitational force on the Sun or the Sun’s gravitational force on the Earth? Explain. 4. Why was it important to verify Newton’s prediction that the “constant” in Kepler’s third law actually depends on the mass of the planet under consideration? Important Term Suggested Reading Questions to Consider
  • 86 Lecture17:SurveyingSpaceandTime Surveying Space and Time Lecture 17 “Thenearestbiggalaxytoourown,theAndromedaGalaxy,is2.4million light years away. … You can see it, and yet the light has been traveling to you for 2.4 million years—right around when early hominids were wandering around on Earth.” W e now come to the third unit in the rst major section of this course. In this unit, we will discuss some of the basic concepts and tools used by astronomers. We begin by getting some idea of the absolute size of the Solar System and of the rest of the Universe. Determining the absolute physical scale of the Solar System was a big problem in science up until the 18th century. A key to getting the distance scale was a transit of Venus across the face of the Sun, when Venus travels between Earth and the Sun, a rare event. Venus transited the Sun in 1761 and 1769, enabling astronomers to determine the physical length of the astronomical unit (AU), which is de ned as the average distance of the Sun from the Earth. Depending on the location on Earth from which you look, the exact position of Venus on the disk of the Sun will shift a bit. This is known as a parallax. By measuring the angle of the shift and knowing the length of the baseline over which the shift occurred, you can determine the size and shape of the unique triangle that de nes that parallax. Please Note In this lecture series, we often use the metric system. • The unit of length is the meter (m). • One meter is 39.37 inches, a bit larger than a yard. • One kilometer (km) = 1000 m, or about 0.62 mile. • One centimeter (cm) = 1/100 m, or about 0.39 inch. • The unit of mass is the gram (g). • There are 453.6 grams in 1 pound. • One kilogram (kg) = 1000 g, or about 2.2 pounds. • The unit of time is the second (s).
  • 87 The problem is that the shift for two observers separated by an Earth radius is only about one-third of the diameter of Venus—very small—and dif cult to determine for people in the mid-18th century. Instead of measuring the actual parallax shift, you can measure the time Venus takes to transit (go across) the face of the Sun. The transit as seen from point P on Earth takes some total time, T. And the transit as seen from point P (read “P prime”) on Earth takes some total time, T . The difference between those transit times is correlated with the angular parallax shift, (alpha). These measurements were made by a number of observers who developed a value for the AU, which is about 150 million kilometers—or 93 million miles—the average distance to the Sun from Earth. 150 million kilometers = 93 million miles = 1 AU. To avoid writing out many zeros, 150 million kilometers can be written as 1.5 108 kilometers (or 9.3 107 miles), the preferred scienti c notation. (Note that 1 mile 1.6 km.) Astronomers used this image of spiral galaxy NGC 4414 to calculate its distance from Earth (60 million light years). TheHubbleHeritageTeam(AURA/STScI/NASA)
  • 88 Lecture17:SurveyingSpaceandTime When dealing with stars or galaxies that are so far away, the AU is an inadequate unit. Instead, we talk about distances in terms of the time it takes light to travel in space from one place to another. The speed of light in a vacuum, 3 105 km/s (or 186,000 miles per second), is constant. It is the greatest possible speed with which information can travel through space. If speed is constant, then distance equals speed multiplied by time ( d vt ). Thus, solving for time, we get t = d/v, and for light, this becomes t = d/c. Light traveling from the Moon, 3.84 105 km away, takes t = (3.84 105 km)/(3 105 km/s) 1.3 seconds (s) to reach us. We say that the Moon is about 1.3 light seconds away. This led to the noticeable delay in the responses of lunar astronauts to questions from people on Earth, which were transmitted via radio signals traveling at the speed of light. Given that t = d/c = (1/c)d, the light travel time is proportional to distance, and (1/c) is the constant of proportionality. The Sun is 390 times farther from Earth than the Moon is. Hence, light from the Sun takes (1.3 s)(390) 500 seconds to reach us. This is about 8.3 minutes (1 minute = 60 seconds). We say that the Sun is 8.3 light minutes away. If the Sun were to abruptly stop shining, we wouldn’t know it for 8.3 minutes because the light just prior to that event is already on its way and will take 8.3 minutes to reach us. A light year is the distance light travels in 1 year: d = (3 105 km/s)(1 year). Converting 1 year into seconds: (1 year)(365.25 days/year)(24 hours/day) (60 minutes/hour)(60 seconds/minute) = 3.15 107 seconds; one can easily remember this as being roughly 107 s, in which is the irrational number 3.14159… Thus, d = 9.6 1012 km, about 10 trillion kilometers. The nearest star, Proxima Centauri (a companion of Alpha Centauri), is 4.2 light years away. Other stars visible in the night sky can be hundreds or thousands of light years away. Thus, different stars are seen at different times in the past. The nearest large collection of stars, the Andromeda Galaxy, is 2.4 million light years away. Galaxies are typically millions of light years apart. The faint light just now reaching us from distant galaxies many billions of light years away allows us to see them as they were billions of years ago. Hence, the nite speed of light gives us a kind of “fossil record” of the Universe’s history. If we assume that distant parts of the Universe are
  • fundamentally similar to nearby parts, we can gain insights into how our own cosmic environment may have evolved. Distance scales naturally bring us to time scales. Many events happened in the history of the Universe that were critical to the eventual emergence of human intelligence. Here, we highlight seven of them. The Universe was born about 13.7 billion years ago, give or take half a billion years; this is the measured time since the Big Bang. All the galaxies are moving away from each other. If we extrapolate backward in time, we nd that these galaxies (or at least the material of which they now consist) were all in the same place 13.7 billion years ago, at the birth of the Universe. Many galaxies, such as our own Milky Way Galaxy, formed about 13 billion years ago, within the rst billion years after the Big Bang. We know this by measuring the ages of the oldest stars, such as those in globular star clusters. The third major event was the formation of the Solar System about 4.6 billion years ago. We determine this by radioactive dating of meteorites and Moon rocks. Next, unicellular life emerged at least 3.5 billion years ago, as evidenced in the fossil records (seen in the form of stromatolites—giant colonies of cyanobacteria). There is indirect evidence for life 3.8 billion years ago. Then, around 550 million years ago, what’s referred to as the Cambrian explosion took place, a giant diversi cation of complex, hard-bodied animals, such as trilobites. Dinosaurs ruled for more than 150 million years, suddenly becoming extinct roughly 65 million years 89 A Second Glance To place astronomical time scales into perspective, let’s compress the 14-billion-year history of the Universe into one day, or 86,400 seconds. Thus, the Big Bang occurred at t = 0 and now is at 24 hours. Our Galaxy formed just a few hours after the Big Bang. Our Solar System formed at about 16 hours; in other words, two-thirds of the day had passed before the Solar System formed. Homo sapiens appeared about 1 second ago, and a long human lifetime of 100 years is 0.0006 seconds—less than 1/1000 of a second. Our lives are a blink of an eye in the history of the Universe, illustrating that astronomical time scales are very, very long.
  • 90 Lecture17:SurveyingSpaceandTime ago—the great Cretaceous/Tertiary extinction. Mammals then emerged, culminating with early hominids—about 4.5 million years ago—and, nally, Homo sapiens developed about 150,000 or 160,000 years ago. Big Bang: The birth of the Universe in a very hot, dense state 13.7 billion years ago, followed by the expansion of space. parallax: Apparent movement of an object due to a change in the position of the observer. The parallax of a star is de ned as the angular distance subtended by 1 AU, the distance between the Earth and the Sun, as seen from the star. Horwitz, Blue Latitudes: Boldly Going Where Captain Cook Has Gone Before. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Cosmos. 1. How would our view of the Universe differ if the speed of light were in nite? 2. Why is it useful to talk about distance in terms of light years? 3. Geologists study different strata to determine conditions on Earth long in the past. How is it that astronomers are able to see parts of the Universe appearing as they were in the past? Important Terms Suggested Reading Questions to Consider
  • 91 Scale Models of the Universe Lecture 18 “It’s interesting to ask yourself, what is emptier in the universe? Are atoms emptier than planetary systems?Are they emptier than galaxies? Is the universe as a whole the emptiest thing?” T he Universe has been in existence for about 14 billion years; thus, astronomical time scales are very long. Distance scales in the Universe are also hard to fathom, but scale models can help put these distances into perspective. Suppose that the Sun (1.4 106 km in diameter—109 times the diameter of the Earth) were only the size of the period at the end of this sentence (about 0.5 mm). The nearest star, 4.2 light years away, would be about 14 kilometers away on this scale. The Milky Way Galaxy, about 105 light years in diameter, would be 320,000 kilometers in size—not quite the distance to the Moon (384,000 km away). Astronomers must also consider objects on tiny scales, such as atoms and subatomic particles. Suppose one atom were the size of an apple, about 8 centimeters in diameter. On this scale, a human (20 billion times larger) would be 1.6 million kilometers high—more than four times the distance to the Moon. Nevertheless, the nucleus of the atom (a single proton, in the case of hydrogen) would be only 1.6 millionths of a meter (1.6 m) in diameter. Thus, hydrogen is 99.999999999999% empty! Other objects, though opaque, also consist almost entirely of empty space—99.99999999% empty. Electrons are in a cloud surrounding the nucleus of an atom and make up a much bigger volume (but the electrons themselves have essentially zero volume). The reason that atoms are so big lies in the study of quantum physics and can be explained by a combination of the Heisenberg uncertainty principle (which we’ll discuss in a subsequent lecture) and the Pauli exclusion principle, which prevents electrons from accumulating in the same regions of an atom. Even if we add more electrons, making bigger and bigger atoms, the electrons have to stay comfortably spaced from each other.
  • 92 Lecture18:ScaleModelsoftheUniverse Which structure is emptiest, an atom, the Solar System, our Galaxy, or the whole Universe? To gain a deeper perspective of size scales in the Universe, we compare how empty these different structures are. The ratio of the radius of the electron cloud to the radius of a proton in a hydrogen atom is about 5 × 104 , or 50,000. An example of a comparable ratio in our Galaxy is the distance to the nearest star, 4.2 light years, divided by the radius of the Sun. But 4.2 light years divided by 700,000 kilometers (the radius of the Sun) is a ratio of about 60 million, 6 × 107 —much bigger than the ratio of 50,000 (5 × 104 ) that we found for an atom. Thus, our Galaxy is much emptier than an atom. The analogous ratio in our Solar System might be the distance of the Earth to the Sun divided by the Sun’s radius: 1 AU 700,000 kilometers 200, which is far less than the ratio for an atom (50,000). By this calculation, an atom is far emptier than our Solar System. Considering the Universe as a whole, we take the ratio of the distance of a relatively nearby galaxy, such as the Andromeda Galaxy, to our own Milky Way Galaxy’s radius. Andromeda is about 2.5 million light years away, and our Galaxy’s radius is about 50,000 light years. That ratio, then, is about 48. But 48 is much less than 50,000. Thus, using the distance between galaxies relative to the radii of the individual galaxies as a measure of the emptiness of the Universe, an atom is much emptier. The Universe as a whole isn’t all that empty; much less empty than atoms or than stars within a galaxy. To appreciate these size scales, the distances between objects, and the fact that certain regions of the Universe are relatively empty while others are lled with activity, we view the Universe on progressively larger or smaller scales, each a factor of 10 larger or smaller than the preceding one. We start with a familiar scale, looking at the Very Large Array (a set of radio telescopes in New Mexico) as viewed from a height of 100 meters. If we steadily decrease the scale by a factor of 10, we get closer by a factor of 10, going from 100 The universe is much less empty than an atom. Despite the vast distances between galaxies, the ratio of the distances between galaxies to the radii of galaxies is smaller than the ratio of the radius of the electron cloud to the radius of a proton.
  • 93 meters to 10 meters, to 1 meter, to 1/10 meter, and so on. Our journey takes us to a kangaroo rat, and we peer into the nucleus of one of its kidney cells on a scale of 10–6 meter (1 micrometer), nally revealing the structure of DNA on a scale of 10–9 meter (1 nanometer). The outer shell of electrons in a carbon atom has a diameter of about 10–10 meter (0.1 nanometer, equivalent to 1 angstrom unit). The nucleus of the atom is much smaller, and we begin to see it clearly from a distance of 10–14 meter (10 femtometers). Between the electron shell and the nucleus is largely empty space. The quarks that make up protons and neutrons are visible on a scale of 10–16 meters. Going back to the familiar scale of the Very Large Array, we next increase our view by a factor of 10 with each step, going from 100 meters to 1000 meters (1 kilometer), to 10,000 meters, and so on. We see the entire state of New Mexico from a distance of 106 meters (1000 km). Going out another factor of 10, to a distance of 107 meters, much of North America comes into view. As we increase the scale, we see the entire Earth, then the inner part of the Solar System, and nally, the entire Solar System from a distance of 1013 meters (roughly 100 AU from the Earth). Moving out several factors of 10 in distance, we reach a scale of 1017 meters, or about 10 light years. The Sun appears very small from this distance, and we nally see a few other stars. From a distance of 1020 meters, about 10,000 light years from the Sun, we see a plethora of stars, including part of a spiral arm. Moving out to 1022 meters, a million light years from the Sun, the entire Milky Way Galaxy and its two main satellite galaxies, the Magellanic Clouds, can be seen. From a distance of 1024 meters, or 100 million light years, we see that our Galaxy is just one of tens of thousands of galaxies in a supercluster. Going to even larger scales, 1026 meters or 10 billion light One popular analogy is to compare the number of stars in the Milky Way Galaxy to that of the grains of sand on a beach. Depending on numerous factors, there may or may not be as many grains of sand on a beach as stars in our Galaxy. Either way, the numbers are fantastically large, and it is helpful to think of analogies to put some intuitive scale to the size of things.
  • 94 Lecture18:ScaleModelsoftheUniverse years, where distances up to 13.7 billion light years are visible, we are actually looking back in time 13.7 billion years. We see the small variations in density from which the large-scale structure of the Universe formed. Through 43 orders of magnitude—that is, powers of 10—starting from about 10 billion light years from the Milky Way Galaxy and ending on a scale of 10–16 meters, we have gone from the largest scales in the observable Universe to the inner world of atomic nuclei. We can use everyday analogies to illustrate powers of 10 to gain a more intuitive feeling for numbers spanning a vast range. For example, if $1.00 equals 1 meter, then 1 centimeter equals 1¢—1/100 of $1.00 is 1¢; 1/100 of a meter is 1 centimeter. The radius of an atom is 1 angstrom—a unit equivalent to 10–8 centimeters, or 1/100,000,000 of a cent. But no one talks about 1/100,000,000 of a cent; already, then, the money analogy isn’t working on a scale the size of an atom. On a large scale, one light year is 1013 kilometers, or 1016 meters (10 quadrillion meters)—$10 million billion. Again, the scale doesn’t work because our Galaxy is 100,000 times bigger than that, and the Universe is another factor of 100,000 larger. angstrom (Å): A unit of length commonly used for visible wavelengths of light; 1 Å = 10 8 cm. large-scale structure: The network of clusters, voids, and other shapes seen on the largest scales of the Universe. neutron: Massive, uncharged particle that is normally part of an atomic nucleus. Pauli exclusion principle: Wolfgang Pauli’s explanation for the arrangement of electrons in an atom. The quantum mechanical principle states that no two electrons can be in the same “quantum state” (same con guration) in an atom at the same time. Important Terms
  • 95 proton: Massive, positively charged particle that is normally part of an atomic nucleus. The number of protons in the nucleus determines the chemical element. quark: A fundamental particle with fractional charge; protons and neutrons consist of quarks. Davidson, Secret Worlds: The Universe Within, micro.magnet.fsu.edu/ primer/ java/scienceopticsu/powersof10/. Eames Of ce, Powers of 10, www.powersof10.com/. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Cosmos. 1. Construct a scale model of our Solar System by choosing a speci c object to represent the Sun or the Earth. Consult a standard textbook for a data table of sizes and distances. 2. Suppose the distance from the Sun to Pluto, 40 AU 6 109 km, were compressed to the size of a pen (15 cm). On this scale, what would be the distance from the Sun to Aldebaran, a bright star (the eye of Taurus the Bull) whose true distance is roughly 60 light years? 3. Estimate the number of atoms in a human, assuming an atom has a radius of 1 angstrom (10 8 cm), and compare this with the approximate number of stars in the Milky Way Galaxy (about 1011 ). Suggested Reading Questions to Consider
  • 96 Lecture19:Light—TheSupremeInformant Light—The Supreme Informant Lecture 19 “What is light? It seems like a simple question, but in fact it’s very complex, and it occupied physicists for hundreds of years.” A s we discussed, galaxies and stars are so far away that we measure their distance in light years—that is, the time it takes light to travel across space from point A to point B. With a few exceptions, most astronomical objects are studied through the light they emit. But what is light? This seems like a simple question, but in fact, de ning light is complex and has preoccupied physicists for hundreds of years. We can grasp the idea of light’s properties by passing what we call white light, sunlight, through a prism to produce a spectrum, or a rainbow. Isaac Newton was the rst to systematically decompose white light into its spectrum of colors with the use of a prism. He noticed that if any one color were isolated and sent through a prism, it remained the same color. This experiment suggests that glass somehow takes white light and spreads it out into its intrinsic component colors. Thus, Newton realized that white light is this spectrum of colors. He veri ed this idea by passing the light through two prisms with a lens in between. The lens bent the light beams back to parallel and sent the rainbow of colors through the second prism to get white light back out again. We can measure the amount of light at each color—red through violet—and plot the amount of light, its brightness or intensity, along a vertical axis; along the horizontal axis, we can plot each color band. This brightness versus color is what we call a spectrum, which in turn, offers quantitative information about the physical nature of the objects that we are studying. One way to remember the order of the light color spectrum is with the mnemonic device Roy G. Biv, or red, orange, yellow, green, blue, indigo, violet. Visible light is one form of electromagnetic radiation, produced as waves with different lengths and frequencies. A static electric eld exists around a stationary charge, such as an electron. A static magnetic eld exists around
  • 97 a stationary magnet. If a proton (positively charged ion) is placed next to another proton at rest, the rst proton will move away from the stationary one along radial lines. If an electron (negatively charged ion) is placed next to the stationary proton, the electron will be attracted along these radial lines, or lines of force. A magnet also has lines of force, but they run from a north pole to a south pole only; they do not radiate in all directions. If you break a magnet in half, each piece still has a north pole and a south pole. There is a deep connection between electric and magnetic elds. A current— which consists of electrons in motion through a wire—produces a magnetic eld, as in an electromagnet. Conversely, passing a loop of wire through a magnetic eld produces a current in the wire. As a magnetic eld moves, it changes in strength and direction, going from strong to weak and then back again (in the opposite direction) in a wave-like motion. This oscillation (sinusoidal change) of the magnetic eld produces an electric eld. The electric eld also oscillates in a wave-like motion, perpendicular to its associated magnetic eld, changing in strength and direction as it moves, just as the magnetic eld does. The two waves consist of self- propagating, oscillating electric and magnetic elds perpendicular to each other and perpendicular to their direction of motion. An oscillating electric eld produces an oscillating magnetic eld and vice versa. These propagate as electromagnetic waves. James Clerk Maxwell modi ed and combined four equations of electromagnetism that were known during his time to produce an equation that described this propagation of electric and magnetic elds: oscillating (vibrating), propagating, and self-generating. Maxwell calculated the speed of these waves, which turned out to be none other than the known speed of light. Thus, light is a vibration of electric and magnetic elds, an electromagnetic wave traveling at 300,000 kilometers per second. “Different kinds of electromagnetic radiation are fundamentally the same thing, but they have different wavelengths, different frequencies. They’re seen in different ways using different detectors, but they’re all fundamentally the same thing.”
  • 98 Lecture19:Light—TheSupremeInformant Let’s look at this wave and some of its properties. The wavelength, denoted by the Greek letter (lambda), is the distance from one wave crest to the next. This has units of length, such as centimeters. The frequency, denoted by the Greek letter (nu), is the number of times per second that a crest passes a xed point Q; the units are 1/seconds, or hertz (Hz). Hence, the period of the wave, P (in seconds), is simply 1/ . In general, the length per wave ( ) multiplied by the number of waves per second ( ) gives the length per second traversed by the wave. This is its speed, v: = v. In our case, v = c, the speed of light. Different colors of visible light correspond to electromagnetic waves having different wavelengths. The typical unit of wavelength of visible light is measured in angstroms (Å), which is 10–10 meters, or 0.1 nanometer (0.1 nm). Violet, blue, green, yellow, orange, and red light correspond to wavelengths of about 4000 Å, 4500 Å, 5000 Å, 5500 Å, 6000 Å, and 6500 Å, respectively. The spectrum of visible light extends beyond what we can see, including infrared, or beyond red, and ultraviolet, or beyond violet. Electromagnetic Radiation Spectrum The main types of electromagnetic radiation and their approximate numerical dividing lines are as follows: • Gamma rays have wavelengths shorter than about 0.1 Å. • X-rays have wavelengths roughly in the range 0.1 to 100 Å. • Ultraviolet (UV) light spans wavelengths of 100 to 4000 Å. • Visible (optical) light is in the range 4000 to 7000 Å. • Infrared (IR) radiation goes from 7000 Å to about 1 mm. • Radio waves are longer than 1 mm and often up to 10 km or more. Optical light Gamma rays X-rays UV rays IR rays Radio waves 0.1 Å 100 Å 1 mm 4000 Å 7000 Å violet redgreen 5000 Å 6000 Å
  • 99 There are no qualitative differences between the types of electromagnetic waves, but the instruments and techniques used to detect them are often very different. The human eye is sensitive to visible light (4000 to 7000 Å), only a minuscule fraction of the entire electromagnetic spectrum. All electromagnetic waves in a vacuum travel with the same speed, c, regardless of . The measured speed of light is independent of the relative speeds of the observer and the light source. This is admittedly counterintuitive, but it has been completely veri ed; indeed, it is one of the foundations of Einstein’s theory of relativity. Maxwell, James (1831 1879). Scottish physicist; showed that visible light is only one form of electromagnetic radiation, whose speed can be derived from a set of four equations that describe all of electricity and magnetism. Also investigated heat and the kinetic theory of gases. electromagnetic radiation: Self-propagating, oscillating electric and magnetic elds. From shortest to longest wavelengths: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio. spectrum: A plot of the brightness of electromagnetic radiation from an object as a function of wavelength or frequency. Bova, The Beauty of Light. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sobel, Light. Verschuur, Hidden Attraction: The History and Mystery of Magnetism. Name to Know Important Terms Suggested Reading
  • 100 Lecture19:Light—TheSupremeInformant 1. Why is electromagnetic radiation so important to astronomers? Why might it be useful to study objects over a broad range of wavelengths? 2. What are some examples in which you know that magnetic or electric elds play a prominent role? Is there evidence that one type of eld induces or interacts with the other? 3. Announcers at a certain radio station say that they are at “95 FM on your dial,” meaning that they transmit at a frequency of 95 MHz (95 megahertz, or 95 million cycles per second). What is the wavelength of the radio waves from this station? Questions to Consider
  • 101 The Wave-Particle Duality of Light Lecture 20 “The energy of a photon is Planck’s constant, h, multiplied by its frequency. It does not have a corresponding mass. A photon is a massless particle. If you stopped it, you would destroy it; it would no longer exist. It only has energy as it’s traveling. It has no mass if you stop it; it ceases to exist.” I n the previous lecture, we learned that light is a wave of electromagnetic radiation, changing electric and magnetic elds that reinforce, support, and create one another as they move and propagate through space. How do we know light is a wave? There’s abundant evidence in nature to demonstrate that light is a wave, including the phenomena of supernumerary bows on the inner part of rainbows and the corona-like light effect that sometimes occurs around the Sun and Moon when viewed through clouds or fog. To understand these phenomena, we have to look at how waves interfere with one another, both constructively and destructively. Where the crests of the two waves meet, they reinforce each other constructively. Where a crest and a trough meet, they combine destructively, effectively canceling each other out. Two light waves that are in phase—constructive interference— whose crests and troughs are lined up, add together to make bigger crests and troughs. This creates a higher amplitude for the wave, or brighter light. If the waves are out of phase—destructive interference—where a crest is lined up with another wave’s trough, no light is produced. Light waves bending around water droplets go through holes or spaces between these water droplets, like light streaming through fog. But they also bend around the individual droplets to create semicircular wavelets of light having different paths. The wavelets of light can both constructively and destructively interfere, depending on the difference in paths. This type of interference is what creates the corona effect of light around the Moon or the Sun, the soft glow of rings of light close to the Sun or Moon that you sometimes see through fog.
  • 102 Lecture20:TheWave-ParticleDualityofLight The patterns of light waves, whether constructively or destructively interfering, shift for different angles, different wavelengths, and different thicknesses of the objects they penetrate. For a good example of how light waves interact with each other to produce different light or colors, look at how light glints off a soap bubble and the patterns of colors it produces. In a supernumerary bow, two paths of two different rays penetrate a water droplet and emerge, having traversed slightly different path lengths. If they emerge out of phase, destructive interference occurs and creates a dark region in the bow. If they emerge in phase, constructive interference occurs and creates a brighter part of the bow. Light can also be a particle, forming little packets of energy called photons. A photon might be viewed as a package of energy with electromagnetic waves inside, each with a different color—that is, different wavelength and different frequency. White light consists of many photons with a range of wavelengths and frequencies; collectively, we say these photons produce white light. Experiments can distinguish the particle nature of light or the wave nature of light but never both simultaneously, which is explained in further detail below. A photon has no rest mass, but its energy, E, is given by the product of Planck’s constant, h, and its frequency : E = h . Planck’s constant is very small (6.627 10–27 erg seconds, in which an erg is a unit of energy); thus, the energy of any given photon is usually very small. Because a photon is a massless particle, if you stopped it, it would no longer exist. It has energy only as it travels. High-energy photons have higher frequencies but short wavelengths. Low- frequency photons have lower frequencies but longer wavelengths. Thus, red-light photons have longer wavelengths, and violet-light photons have shorter ones. The energy of a photon is directly proportional to its frequency or inversely proportional to its wavelength: E = h , which can also be written as E = hc/ , because = c. What prompted physicists to think that light could be quantized—that is, subdivided into small, measurable increments? Max Planck was the rst to deduce the relationship between energy and the frequency of radiation. Planck considered the energy in a hot oven, which according to the classical theory of waves, should have progressively more and more waves of shorter
  • 103 and shorter wavelength. This overabundance of short-wavelength waves, the energy in an oven, should technically be in nite—what’s called the ultraviolet catastrophe. However, an in nite amount of energy has not been spent heating up an oven, which would occur according to the wave theory. With the formula E = h , Planck quantized, or subdivided, the energy of light, thereby making the ultraviolet catastrophe problem disappear. Albert Einstein also quantized light and initially introduced the idea of photons when he considered a phenomenon called the photoelectric effect. Einstein noticed that when long-wavelength light, such as red light, is shone on a piece of metal, no electrons are ejected from the metal. Blue or violet light shone on the metal, however, produces electrons that pop off the metal’s surface. This indicates that light with longer wavelengths is not able to store enough energy to pop off an electron, but shorter-wavelength light is. Thus, Einstein proposed that photons hit the metal one at a time, and the blue and violet photons individually have enough energy to kick off an electron, but the green and red photons individually do not have enough energy to do so. Another indication of photons comes from the Compton effect. If you shine electromagnetic radiation at a stationary electron, the wave that bounces off the electron is longer than the wave that hits it. For example, a blue wave shone on the electron bounces off as a red wave, and the electron moves away in some diagonal direction. According to the wave theory, the electromagnetic wave interacting with the electron should cause it to oscillate (vibrate) at exactly the same frequency as the incoming wave; thus, the electron should emit a wave of exactly the same frequency—but it doesn’t. When a photon hits an electron, causing that electron to move, the photon loses energy, further evidence that light is also composed of photons, each with a certain amount of energy equal to Planck’s constant times the frequency. “I’ve just given you evidence that light is a particle. Yet … I said that it’s a wave, emphatically a wave. It shows all these interference effects. So, which is it? Is it a particle or a wave? It’s both. It’s really both at the same time, and this is the essence of quantum physics.”
  • 104 Lecture20:TheWave-ParticleDualityofLight Given the evidence, we can demonstrate that light is both a particle and a wave—a duality that is the essence of quantum physics. Collectively, many photons having the same energy produce an electromagnetic wave with the corresponding wavelength . Sunlight and the light from most light bulbs consists of photons having a broad range of energies or wavelengths. Individual photons also have wave-like properties. Constructive and destructive interference effects, such as those seen in waves owing through gaps in a breakwater, are produced even when photons are sent one at a time through holes in a screen. Thus, a photon must interfere with itself, and it can do this only by passing through all of the holes, behaving like a wave. If we determine which hole the photon went through, the interference (wave-like) effects disappear; the photon acts like a particle because the measurement “disturbs” the photon, destroying the wave. This is a consequence of the Heisenberg uncertainty principle, set forth by Werner Heisenberg. Therefore, either the wave-like or particle-like properties of light can be measured in a given experiment, but both cannot be measured simultaneously. This wave-particle duality of light is also a quantum aspect of normal matter, including that of which humans are made. For example, an electron can behave as a wave of wavelength = h/mv, in which m is its mass and v (not to be confused with frequency, ) is its speed relative to the observer. Electrons passing through holes in a screen produce interference effects, just as light does. The large masses of most particles imply that their wavelengths “Richard Feynman, one of the greatest, most intuitively thinking physicists ever to have lived, said this about quantum mechanics: ‘If you are not bothered and puzzled by it, you haven’t thought about it enough.’ ” Did You Know? What Einstein proposed was that light comes with these energy packages that he called photons. The photons hit the metal one at a time. The blue and violet photons individually have enough energy to kick off an electron, but the green and red photons individually do not. It is for this explanation that Einstein actually won the Nobel Prize, not for relativity.
  • 105 are exceedingly small, making it more dif cult to discern their wave-like nature than is the case for light. Many of the greatest minds of physics have struggled with this duality for a century, agreeing that it works but with no intuitive feeling for how. Heisenberg uncertainty principle: One form: In any measurement, the product of the uncertainties in energy and time is greater than or equal to Planck’s constant divided by 2 . Another form: In any measurement, the product of the uncertainties in position and momentum is greater than or equal to Planck’s constant divided by 2 . photon: A quantum, or package, of electromagnetic radiation that travels at the speed of light. From highest to lowest energies: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio. Planck’s constant: The fundamental constant of quantum physics, h; a very small quantity. rest mass: The mass of an object that is at rest with respect to the observer. The effective mass increases with speed. Gribbin, In Search of Schrodinger’s Cat: Quantum Physics and Reality. Hey and Walters, The Quantum Universe. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Wolf, Taking the Quantum Leap: The New Physics for Nonscientists. Important Terms Suggested Reading
  • 106 Lecture20:TheWave-ParticleDualityofLight 1. What do you think produces the rings of color seen when sunlight shines on a thin layer of oil? Why do the patterns change with viewing angle and other variables? 2. Describe the behavior of waves and how it differs from the behavior of particles. How can it be possible for light and matter to have both wave- like and particle-like properties? 3. If one photon has 10 times the frequency of another photon, which photon is the more energetic and by what factor? What if the rst photon has twice the wavelength of the second photon? Questions to Consider
  • 107 The Colors of Stars Lecture 21 “When things are glowing due to their own jiggly motions, hot is blue, and cold is red. Hot stars are blue; cold stars are red.” I n the last lecture, we learned that light is both a wave and a particle. Let’s look brie y at why stars emit different colors of light. Stars are huge, opaque, luminous balls of gas held together by the mutual gravitational attraction of their constituent particles. There are about 300 to 400 billion stars in a big galaxy like our own, each of which emits its own color. The hottest stars are bluish in color, and the coldest stars are reddish in color. Stars at intermediate temperatures appear white. Our Sun is a white star. The colors indicate the temperature of the star’s surface, or photosphere. How? In a gas, particles move around randomly; temperature is a measure of how much these particles move. As the particles bump into each other, they accelerate because they’re changing their speed and direction of motion. Accelerated charged particles—electrons and the nuclei of atoms— emit electromagnetic radiation. When this radiation escapes from a star’s photosphere, it is seen as a particular color. The higher the temperature, the more random motions of particles there are, and the emitted light tends to have shorter wavelengths. The lower the temperature, the smaller the motions, resulting in light having predominantly longer wavelengths. Stars emit thermal radiation because of the random motions of particles inside them. The higher the temperature, the more rapid the motions. Stars are nearly ideal radiators because they emit light in such a way that the mathematical shape of the spectrum—the precise shape of the brightness versus wavelength or color—is dictated only by its temperature, not by its chemical composition or any other of its physical properties. Ideal radiators don’t re ect light, nor do they transmit light like a window. They only generate light of their own; they are purely thermal emitters. They can also absorb light, thus becoming hotter and increasing the rate at which they emit thermal radiation. In the case of stars, the amount of radiation they absorb from the outside is usually negligible compared with the energy generated inside them.
  • 108 Lecture21:TheColorsofStars When we discuss the temperature of stars, we use the absolute or Kelvin scale, in which 0 is the lowest possible temperature. On this scale, water freezes at 273 degrees and boils at 373 degrees. If we plot an average star’s brightness against the wavelength of the radiation emitted, we don’t see much in the violet part of the spectrum—short wavelengths. The spectrum peaks at some given wavelength, then drops toward the red. The shape of this emitted spectrum is one of a purely thermal emitter. If we plot the spectra of objects having different temperatures, we can see their main characteristics. Spectra of the hotter objects peak more in the blue to violet range, while spectra of the cooler objects peak in the red to orange range. For any object of a given size, a hotter object emits more light at all wavelengths. The shapes of the plotted curves are all alike mathematically and are called Planck curves, after Max Planck, who rst derived the mathematical form of the curve. The product of the temperature (T) and the wavelength of the peak of the spectrum max is a constant: maxT = 2.9 107 Å K. This is known as Wien’s law, and it is consequence of the mathematical properties of Planck curves. People emit thermally at infrared wavelengths (about 105 Å, or 10 m , according to Wien’s law); thus, we can be seen with infrared detectors even at night. We are visible at optical wavelengths, however, only because of re ected light (such as sunlight or light from indoor bulbs), which has nothing to do with the thermal emission produced by our own bodies. At higher temperatures, the area under the Planck curve is much greater for a hot object than for a cold object, indicating that, per unit of emitting area, a hot object emits much more radiation than a cold object. This is known as the A Second Glance We know that when a stove or coals glow red, they are hot. But when a piece of metal glows blue, the temperature is even hotter. Given this example, we might think that ice should be hot because it’s bluish in color. However, ice’s blue color is not an effect of how much movement its particles are experiencing but, rather, an effect of the type of light waves it re ects. Ice re ects incoming white light in such a way that preferentially favors the blue over the red.
  • 109 Stefan-Boltzmann law, another consequence of Planck curves. According to the Stefan-Boltzmann law, the energy emitted per square centimeter per second is proportional to the fourth power of temperature. We can write E = T4 , in which E is the energy emitted per unit area (e.g., cm2 ) per second, T is the temperature, and is a constant of proportionality (known as the Stefan-Boltzmann constant). Thus, if two stars have the same surface area, but one is twice as hot as the other, the hotter star emits 24 , or 16 times, more energy per second than the colder star. It’s important to remember that re ected light differs from light seen as a result of thermal emission, though both can happen at the same time. Planets shine at visible wavelengths because they re ect sunlight (or the light of other stars, in the case of extrasolar planets). Planets also shine because of their own thermal radiation, glowing at infrared wavelengths (which are invisible) because of their warm temperatures. They are not hot, like optically visible stars. extrasolar planet: A planet orbiting a star other than the Sun; an exoplanet. Kelvin: The size of 1 degree on the Kelvin (absolute) temperature scale, in which absolute zero is 0 K, water freezes at 273 K, and water boils at 373 K. To convert from the Kelvin scale to the Celsius (centigrade, C) scale, subtract 273 from the Kelvin-scale value. Degrees Fahrenheit (F) = (9/5)C + 32. Planck curve: The mathematical formula describing the spectrum of light produced by a perfect thermal emitter. “We glow ourselves due to the jiggly motions, and that’s in the infrared, but we also re ect light. The appearance we have depends on whatever dyes we have, whatever colors happen to re ect best in our clothes.” Important Terms
  • 110 Lecture21:TheColorsofStars Stefan-Boltzmann law: Law stating that, per unit of surface area, an opaque object emits energy at a rate proportional to the fourth power of its surface temperature. Hey and Walters, The Quantum Universe. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What is the difference between light emitted thermally and re ected light? 2. In what ways are humans not a good approximation to ideal radiators? Why do astronomers and physicists use the concept of an ideal thermal radiator when, theoretically, such objects are almost nonexistent? 3. Why do we not see the thermal radiation of planets as we do with stars? 4. What is the surface temperature of a star whose spectrum peaks at a wavelength of about 6000 angstroms? If this star were hotter by a factor of 4, how much more energy would it emit per second? Suggested Reading Questions to Consider
  • 111 The Fingerprints of Atoms Lecture 22 “Each neutral element, and every ionization stage of any particular element has a unique ngerprint of patterns that appears in its spectrum.” S tars emit light through thermal radiation, the spectrum of which (the Planck curve) depends only on their surface temperature, not on their chemical makeup or other physical properties. However, because stars are not ideal radiators, their plotted curves deviate from a perfect Planck curve. This allows us to discover information on the stars’ chemical compositions, pressures, densities, and other aspects of their physical nature. In addition to a hot, opaque outer layer, stars also have a cooler, thinner atmosphere, where atoms interact with photons to produce deviations to the Planck curve. Typically, the deviations appear as absorption lines, parts of the spectrum where the light is less bright than in adjacent regions; in other words, there are fewer photons and, therefore, less energy in these regions, which appear as dark lines or depressions in the spectrum. Every element, and every neutral and ionized form of a given element, produces a unique ngerprint in its set of absorption lines (or emission lines; see below). Let’s look at atoms in general. Atoms have a nucleus consisting of protons and neutrons; a cloud of electrons surrounds the nucleus. The whole structure is about 1 angstrom in size (10–8 centimeters), although the nucleus is much smaller. Each individual proton and neutron is only about 10–13 centimeters. Neutrons are neutral, protons are positively charged, and electrons are negatively charged. The electrons and protons attract one another, making atoms stable.As a consequence of quantum physics, electrons occupy discrete sets of A model of an atom. ©ClarkDunbar/Corbis
  • 112 Lecture22:TheFingerprintsofAtoms energy levels, sometimes called orbits, though electrons do not really orbit the nucleus the way a planet orbits the Sun. A hydrogen atom in its neutral state has a lone proton in the nucleus and a single electron. That electron can be in its lowest energy level or higher energy levels. In general, the farther away an electron is from the nucleus, the greater its energy. What happens when a photon interacts with an electron? Photons can be absorbed by an electron, causing the electron to jump to a higher energy level. The photon is absorbed, or destroyed, in the process. The energy of the absorbed photon must be exactly equal to the difference between the two energy levels occupied by the electron. If a photon does not equal the energy difference between the two energy levels, it will just go right through the atom without being absorbed. The energy of the photon absorbed is equal to the difference in energy, E, between the fourth energy level, E4 (the higher level), and the second energy level, E2 (the lower level). E is equal to the energy of the photon, which in turn, must be Planck’s constant multiplied by the frequency of the photon, or Planck’s constant multiplied by the speed of light divided by the wavelength of the photon. Mathematically, this statement reads as follows: photon 4 2 photon /E E E E h hc . Thus, shining white light at a cloud of atoms (of a given element) causes their electrons to absorb or “ignore” the different-colored photons according to each photon’s energy and the atoms’ electronic energy levels. Once the electron is in an excited state, it generally jumps back to a lower energy level after a very short time interval, emitting a photon in any random direction and possibly re-emitting photons in a series of steps across energy levels. In a spectrum, absorbed photons create a de cit in their color range, known as an absorption line—also called Fraunhofer lines, after Josef Fraunhofer, who discovered them in the early 1800s. Atoms have many energy levels with many possible absorption lines. The spectrum of a gas cloud viewed without a star in the background can consist of many emission lines having different wavelengths. If you look through the cool cloud of gas at a bright continuum-emitting object, such as a hot star, absorption lines occur because some of the photons from the hot star were absorbed by the cloud of gas. Stars are more complicated than just clouds
  • 113 of cool gas because stars are opaque, hot, and have high densities, but many of the same physical principles are still relevant. A suf ciently energetic photon can completely dislodge an electron from an atom in a process called ionization. Knowing this also helps us to determine the elemental makeup of stars. Ionization can occur with any photon that has more energy than the minimum required energy to dislodge an electron. The resulting so-called free electron moves at random through the gas, no longer bound in a speci c energy level, until it comes close to a lone proton (or other atomic nucleus), latches onto it, and is re-bound to a speci c energy level. In so doing, it re-emits a photon because it must get rid of the energy that it previously absorbed. This process of recombining with a positively charged nucleus is called recombination. An atom can also be ionized if another atom or an energetic electron hits it, forcing the electron away and causing it to wander around through the gas in no speci c energy state. Each neutral element, and every ionization stage of any particular element, has a unique ngerprint of patterns that appears in its spectrum as absorption lines. Let’s consider the case of hydrogen, the simplest (and most common) element. Absorption lines in the ultraviolet range are called Lyman lines and have corresponding Greek designations: alpha ( ), beta ( ), gamma ( ), delta ( ), epsilon ( ), and so on, which refer to the electronic transitions. Absorption lines in the visible range of the spectrum are called Balmer lines, also with their associated Greek designations. Absorption lines in the infrared region of the spectrum are called Paschen lines, with their associated Greek designations. If you look at the spectrum of light going through hydrogen, for example, from the ultraviolet all the way to the infrared, you see a continuum. Superimposed on that continuum are these unique absorption lines. Thus, we can tell which element made them. If we obtain and analyze the spectra of stars—a process called spectroscopy— we can discern their patterns and know which elements produced them, thus giving us the chemical compositions of very distant stars. “When we look at stars and we examine their spectra, lo and behold, we see the patterns produced by hydrogen, and only by hydrogen. Therefore, we know that the hydrogen is present in the stars.”
  • 114 Lecture22:TheFingerprintsofAtoms absorption line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is less than it is at neighboring wavelengths. emission line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is more than it is at neighboring wavelengths. ionized: Having lost at least one electron. Atoms become ionized primarily by the absorption of energetic photons and by collisions with other particles. recombination: Process by which electrons combine with protons and other atomic nuclei to form neutral atoms; believed to have rst occurred about 380,000 years after the Big Bang. Bova, The Beauty of Light. Hearnshaw, The Analysis of Starlight: One Hundred and Fifty Years of Astronomical Spectroscopy. Hey and Walters, The Quantum Universe. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. If someone were to say that we cannot know the composition of distant stars because there is no way to perform experiments on them in terrestrial laboratories, how would you respond? 2. What determines the various absorption lines (e.g., Lyman, Balmer, Paschen in the case of hydrogen) created by white light that is shining through a cloud of gas? Important Terms Suggested Reading Questions to Consider
  • 115 3. An electron of an atom of an imaginary element has three energy levels: 0E , E = 3, and E = 9. Suppose you know that the transition from the highest energy level to the middle energy level emits a photon with wavelength = 3000 angstroms. What is the wavelength of a photon emitted in the transition from the middle energy level to the lowest energy level?
  • 116 Lecture23:ModernTelescopes Modern Telescopes Lecture 23 “Our atmosphere has many layers that are moving to and fro and causing twinkling of light. It also causes a blurring out of the light. For a long time, there was no way to overcome this problem. A telescope didn’t give you any additional clarity because the atmosphere got in the way.” S tudies of light are what allow astronomers to gather information about the Universe. How do we collect and analyze light? Telescopes can magnify the apparent size of objects, as we discussed in Lecture 6. Magni cation depends on the focal lengths of both the primary lens and the eyepiece lens. Professional astronomers, however, rarely look through telescopes anymore because they can gather data using electronic detectors at the focal plane; no eyepiece is needed to magnify the image. Today, the primary purpose of telescopes is to gather light and make faint objects look brighter. The bigger the collecting area (the size of the mirror or lens), the more light can be captured and the brighter a given object will appear. Special detectors can collect even more light and store it or even create a digital image. The human eye sees a new image roughly every 1/30 of a second, refreshing an image in your brain 30 times a second. Exposing lm with a telescope, on the other hand, allows us to collect light over a longer time; therefore, cumulatively, we would be able to see fainter stars. Photographic plates can store a lot of information over a wide area of the sky, but they also have some disadvantages. Like the human eye, they actually detect only about 1% or 2% of the incoming light. They also can’t record both bright objects and faint objects simultaneously. Photographic plates are non-linear; thus, if you expose them 10 times as long, the star doesn’t look 10 times brighter. Further, stars that are 10 times brighter than other stars don’t look 10 times brighter in a quantitative way. Modern electronic detectors are much better than photographic plates mounted on telescopes. Modern detectors can capture about 80% of the light from incoming photons, store it, and produce data in a digital format.
  • 117 At optical wavelengths, typically, a device known as a CCD, a charge- coupled device, is used. Digital cameras and camcorders use less expensive versions of CCDs. CCDs have what are called pixels, or picture elements. A star’s image might fall on a group of pixels, each of which registers a certain amount of light; central pixels in a star’s image register the most light. The CCDs have a linear response, so the brightness of a star can be quantitatively and accurately measured. CCDs have a wide dynamic range—very faint and bright stars can be measured in a given image. Unfortunately, CCDs have small elds of view. The eld of view can be increased by bunching together several or many silicon chips, but this can be expensive. Telescopes are important for collecting light, but they also provide higher resolution or clarity in order to detect ner details. Any point-like object looks blurry at some level. Two objects, such as stars, spaced more closely together than their blur circles, will merge together. But as the diameter of the light-collecting lens or mirror increases, the stars’ clarity also increases. Quantitatively, we use angular measure to describe the resolution of a telescope. A full circle is divided into 360 degrees (360°). The Moon and the Sun each subtend (cover) about 1/2°. Each degree consists of 60 arc minutes (60’). Each minute of arc consists of 60 arc seconds (60”). A second of arc is small, approximately the angle subtended by a dime viewed from a distance of 3.7 kilometers. Optical telescopes can be made with an intrinsic resolution Did You Know? The diameter of a typical large telescope is 6 meters. The dilated human eye is about 6 millimeters, or 6/1000 of a meter, in diameter. Recall that the formula for the area of a circle is r2 = D2 /4, in which r is the radius and D is the diameter. The ratio of light-collecting areas of a typical telescope (with diameter D2 ) and an eye (with diameter D1 ) is, therefore, given by A2 /A1 = D2 2 /D1 2 = (D2 /D1 )2 . (Equivalently, you could square the ratio of the telescope radii.) If D1 is 6 × 10–3 m (the dilated human eye) and D2 is 6 meters (a large telescope), then A2 /A1 = (103 )2 = 106 . Thus, all other things being equal, the telescope can detect stars that are about 1 million times fainter than those that can be detected by the human eye.
  • 118 Lecture23:ModernTelescopes of less than 1 arc second. The angular size of a blur circle in seconds of arc = 0.002 × /D, in which is the observation wavelength in angstroms and D is the diameter of the lens or mirror in centimeters. Turbulence in our atmosphere can blur light. Today, there are ways to partially overcome this problem, but for a long time, a ground-based telescope above 10 centimeters in diameter didn’t offer additional clarity. Larger refracting telescopes were built to gather more light, but they became unwieldy because of their size; supporting them at their edges causes them to sag in the middle. In addition, the lenses are dif cult to fabricate, and they absorb some of the incoming light. They also suffer from chromatic aberration, in which incoming light focuses at different points depending on its color. To compensate for the problems associated with refracting telescopes, re ecting telescopes were invented. You recall from Lecture 6 that these telescopes use mirrors to re ect light. The simplest curved mirror to construct is a section of a sphere, but it suffers from spherical aberration: Parallel rays of light are re ected to different foci depending on their distance from the center of the mirror, producing a fuzzy image. One solution is to make the mirror parabolic or hyperbolic to get a single focus. Re ecting telescopes can be very large. The observer can sit in a cage at the prime focus, making sure the telescope is pointing in exactly the right place and taking long exposures of objects. However, one quickly becomes cold and hungry while in the prime focus cage. Today, we often use Cassegrain telescopes, in which the light comes in from the stars, hits the primary mirror, goes back to a secondary mirror, then enters a hole in the primary mirror, going either to an eyepiece or to equipment that analyzes the light. “The whole [telescope] is like some sort of an animal working together to keep the shape exactly the way it is. If you looked at it microscopically, it would be almost as though it’s alive. This technique of actively shaping the mirror in real time is called active optics, and it really works.”
  • 119 For many decades, the world’s largest telescope was the Palomar 200-inch, or 5-meter, Hale telescope, completed in 1948. We didn’t need to build bigger telescopes because we continually improved the detectors, culminating with CCDs. By the 1990s, CCDs became so ef cient that they were detecting up to 90% of the light. To get more than 90% light, even larger telescopes had to be built. Mauna Kea volcano in Hawaii has a collection of some of the world’s biggest telescopes, including the twin Keck telescopes, 10 meters in diameter. These consist of many individual, relatively inexpensive hexagonal segments aligned in a honeycomb structure. Thin monolithic mirrors, up to 8 meters in diameter, can be made without the need for numerous segments, as in the honeycomb structure. Because they are lightweight, they don’t need massive support structures. charge-coupled device (CCD): A solid-state imaging chip whose properties include high sensitivity, large dynamic range, and linearity. resolution: The clarity of detail produced by a given optical system (such as a telescope). Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Preston, First Light: The Search for the Edge of the Universe. Recall that the size of the blur circle is proportional to the wavelength of light divided by the diameter of the mirror. At radio wavelengths, the blur circle is large and the resolution is poor. Thus, radio telescopes tend to be very large so that the ratio of the wavelength divided by the diameter is relatively small, allowing for good clarity. Important Terms Suggested Reading
  • 120 Lecture23:ModernTelescopes Watson, Stargazer: The Life and Times of the Telescope. Zirker, An Acre of Glass: A History and Forecast of the Telescope. 1. What is the light-gathering power of a telescope that is 3 meters in diameter relative to a 1-meter telescope? 2. Describe the relationship between the diameter of a telescope’s mirror and the clarity of a planet viewed through the telescope. Would you expect the clarity to be greater if the planet is viewed through a blue lter (which transmits blue light) or a red lter? 3. Is it a coincidence that major improvements in astronomical detectors were made at nearly the same time as the electronics and computer revolution that began in the late 1970s? Questions to Consider
  • 121 A Better Set of Eyes Lecture 24 “This technique of interferometry works quite well at radio wavelengths because the atmosphere is pretty stable and distorts them in a way that we can compensate. But recently we’ve extended this technique to infrared wavelengths on ground-based optical/infrared telescopes.” W e continue our discussion of telescopes, rst looking at how radio telescopes work. The size of a telescope’s blur circle—the clarity with which a star is viewed—depends on both the wavelength at which it is viewed and the diameter of the telescope. The blur grows in proportion to the observed wavelength divided by the diameter of the telescope. Because radio wavelengths are long, they produce large blur circles, even when the radio telescope is as big as 330 meters in diameter. To compensate for this problem, we use several radio telescopes together over a wide area, which all act as a single large telescope. This collection of radio telescopes can gather light in an interferometricfashion,taking advantage of the property of light that it constructively and destructively interferes with itself. Radio telescopes can be positioned in numerous ways to record the different patterns of interference, reconstruct the shape of the image, and provide a detailed picture of celestial objects. The so-called Very Large Array, a set of 27 dishes in Socorro, NM, has many different baselines A Second Glance Recall from Lecture 20 that light waves in phase—when each of their troughs meet and each of their peaks meet—combine to create a larger amplitude wave. This is constructive interference. Destructive interference occurs where troughs meet up with peaks to cancel each other out, producing no light. Also recall from Lecture 20 that light passing through two holes in a screen will create a speci c interference pattern. In a similar way, two radio telescopes can act as two holes, in a sense, to gather and analyze light and its particular interference pattern.
  • 122 Lecture24:ABetterSetofEyes in order to probe the structure of celestial objects on a variety of scales and at different angular resolutions. The University of California at Berkeley, in conjunction with the Search for Extra-Terrestrial Intelligence (SETI) Institute, is currently building an array of 350 radio telescopes, in part to search for possible signals from extraterrestrial beings. The telescopes will also be used for other, more conventional types of astronomical investigations. Radio telescopes can be set up across a whole continent to achieve a resolution of a 2500- or 3000-mile baseline. These telescopes can also be put on different continents to increase the effective diameter of the telescope even more and get an even smaller blur circle. Because a particular interference pattern depends precisely on the separation of the different telescopes, changes in the separation can be measured very accurately. In this way, we can measure continental drift, the slow movement of continents. Interferometry works well at radio wavelengths because the atmosphere is stable and distorts the wavelengths in a way that we can compensate for. This technique has also been extended to infrared wavelengths on ground-based The Very Large Array of radio telescopes in New Mexico surveys the sky. ©ComstockImages/Thinkstock
  • 123 optical/infrared telescopes, such as the pair of Keck telescopes on Mauna Kea Volcano in Hawaii and a set of four 8-meter telescopes (the Very Large Telescope) on a mountaintop in Chile. The overall image can be improved by building a group of smaller outrigger telescopes around two main telescopes, which gives more baselines. Let’s consider atmospheric turbulence. Atmospheric turbulence can make stars appear to twinkle. In a similar way, it can make stars appear blurry when viewed through a telescope. Astronomers have developed a method, called adaptive optics, to correct for distortion due to atmospheric turbulence. A small deformable mirror, whose shape can be changed quickly, can negate the distortions to produce plane-parallel waves. By monitoring the light from a bright star many times per second, we can correct for distortions to make that star appear less blurred. In addition, the appearance of any objects close to that star will also be corrected to show a clear, accurate view. When no bright star appears next to an object we want to view, we can create a fake star using a laser beam. The laser excites sodium atoms about 90 or 100 kilometers above the Earth’s surface. We can correct for those distortions of the fake star and the nearby object we want to view. One limitation of this technique is that it produces a limited eld of view, only about 30 arc seconds in radius, though with promising new technology, the eld of view will increase. Another limitation is that the technology works well at near- infrared wavelengths but not yet at visible wavelengths. Despite advances in telescopes and their instruments, ground-based observations still have some limitations. As already mentioned, high clarity with adaptive optics is currently being achieved only over small patches of the sky and only at infrared wavelengths. Light pollution causes the sky to glow, which makes viewing celestial objects more dif cult. The sky is especially bright at infrared wavelengths. We can’t see much beyond the optical window into the ultraviolet and infrared wavelengths because of absorption by ozone and water vapor (respectively) in Earth’s atmosphere. In addition, x-rays and gamma rays are blocked by certain molecules in the atmosphere. How, then, do we avoid the atmosphere to observe some of these wavelengths? Airplanes mounted with telescopes and infrared detectors can travel above the 2- to 10-kilometer water layer in the Earth’s atmosphere.
  • 124 Lecture24:ABetterSetofEyes However, we need spacecraft to get above most of the molecules to detect gamma rays and x-rays. We take a look now at some space telescopes. Throughout the 1990s, NASA’s Compton Gamma Ray Observatory provided great data at gamma- ray wavelengths from high above Earth’s atmosphere. The Hubble Space Telescope (HST) is named after Edwin Hubble, who discovered the expansion of the Universe. Developed by NASA and launched into near- Earth orbit in 1990, it has a 2.4-meter-diameter mirror polished to a very smooth surface. HST received some bad press when it was discovered that its mirror was slightly the wrong global shape, creating spherical aberration that blurred images. In 1993, Space Shuttle astronauts were able to t HST with corrective optics, which then produced fantastic images from space. HST is still operating as of mid-2006. Discoveries made with the HST have greatly advanced the eld of astronomy. In some topics, the textbooks have essentially been rewritten. NASA’s Chandra X-Ray Observatory also orbits high above the Earth’s atmosphere. Chandra gives clear views of the Universe at x-ray wavelengths, probing some of the most energetic processes in the Universe. X-ray telescopes have to be constructed so that light is bounced off mirrors at a The Hubble Space Telescope orbits Earth. STScI/NASA
  • 125 glancing angle. In this way, light is focused by a nested set of paraboloids and hyperboloids to achieve a blur circle of about 1 arc second. NASA’s Spitzer Space Telescope observes infrared wavelengths; thus, it is sensitive to dust particles heated to a modest temperature by nearby stars. Spitzer can peer into regions where stars are currently forming. The Swift gamma- ray observatory has detected so-called gamma-ray bursts, which are star explosions that give rise to high-energy electromagnetic radiation. These sharp bursts of gamma rays last from a few seconds to a few minutes. We hope to continue developing the James Webb Space Telescope, to be completed by 2012 or 2013, a successor to the Hubble Space Telescope but optimized for infrared wavelengths. Hubble, Edwin (1889 1953). American astronomer, after whom the Hubble Space Telescope is named. He proved that “spiral nebulae” are galaxies far outside our own Milky Way and discovered the expansion of the Universe (Hubble’s law) by recognizing that the redshift of a galaxy is proportional to its distance. He also proposed a widely used morphological classi cation scheme for galaxies. adaptive optics: Optical systems providing rapid corrections to counteract atmospheric blurring. gamma-ray burst (GRB): A brief burst of gamma rays in the sky, now known to generally come from exceedingly powerful, distant objects. Center for Adaptive Optics, UC Santa Cruz, cfao.ucolick.org/. Cristensen, Fosbury, and Kornmesser, Hubble: 15 Years of Discovery. Kerrod, Hubble: The Mirror on the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Name to Know Important Terms Suggested Reading
  • 126 Lecture24:ABetterSetofEyes Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Petersen and Brandt, Hubble Vision: Astronomy with the Hubble Space Telescope. 1. Was the Hubble Space Telescope worth the roughly $2 billion that it cost? Reconsider this question after nishing the video course. 2. Why is it sometimes better to use a small telescope in orbit around the Earth than it is to use a large telescope on a mountaintop? Conversely, why is it better for some purposes to use a large telescope on a mountain instead of a small telescope in space? 3. What mirror diameter gives 1 arc second resolution for radio radiation of wavelength 1 m? Compare this with the size of existing optical telescopes. 4. Why are optical and radio telescopes sometimes built in groups, or arrays? Questions to Consider
  • 127 Our Sun, the Nearest Star Lecture 25 “I discussed a few lectures ago how electrons can be knocked off when things collide with atoms. To get iron to be 13 times ionized, you have to collide with very high speeds. That’s what a high temperature means; it means that particles are moving with a very high speed.” W ith this lecture, we enter the second and largest section of the course (Lectures 25 through 70), during which we will study the enormous variety of objects in the Universe. The next 12 lectures are devoted to objects in our Solar System—beginning with our Sun. With the proper equipment, we can view many of the Sun’s features, including sunspots, prominences, energetic eruptions called ares, and the corona during an eclipse. Spectra taken of the Sun reveal that its outermost parts are composed mostly of hydrogen. For every million atoms of hydrogen, the Sun has about 85,000 atoms of helium, 850 atoms of oxygen, 400 atoms of carbon, 120 of neon, 100 of nitrogen, and 47 of iron. The Sun also has other trace elements. Earth has silicon, oxygen, carbon, and some hydrogen, among other elements. The Universe is mostly hydrogen. By mass, the Sun is 73% hydrogen, 25% helium, and only 2% elements heavier than helium. Helium was rst discovered in spectra of the Sun. It was not known here on Earth before the Sun was studied. Extreme Ultraviolet Imaging Telescope (EIT) image of a huge, handle-shaped prominence taken on Sept. 14,1999. ©ClarkDunbar/Corbis
  • 128 Lecture25:OurSun,theNearestStar Let’s look at a cross-section of the Sun. The Sun’s core is about 15 million degrees on the absolute Kelvin temperature scale. This is where nuclear reactions generate the Sun’s energy. Surrounding the Sun’s core are the radiative zone and the convective zone; these terms describe how energy moves from the core to the surface. Radiation is the transport of energy from a light-emitting object; for example, a candle radiates visible light and heat (infrared rays), which can warm up a nearby thermometer. The Sun’s gases are so dense and packed with so many moving electrons that the progress of light is impeded. Thus, photons bounce off electrons and atomic nuclei, eventually making their way from the hot interior to the cooler outer regions. This process is similar to conduction, in which a spoon, for example, heated at one end will conduct heat to the other end as a result of atoms colliding with one another, transferring their energy. In this way, the Sun’s energy moves through the radiative zone through a combination of radiation and conduction generally called radiative diffusion. The convective zone surrounds the radiative zone. Convection is the process by which a bubble of gas or liquid is heated, then expands to becomes less dense and more buoyant. As it rises, it deposits energy to the surrounding area above. Bright specks called granules on the Sun’s surface indicate that it undergoes convection. The specks are hot pockets of gas that have risen to the surface, radiating energy to their surroundings before cooling and returning to the interior, where they heat up again. Now let’s look at the Sun’s surface phenomena. The photosphere is the visible surface of the Sun; here, gas becomes suf ciently hot and dense to appear opaque rather than transparent. The photosphere temperature is 5800 degrees Kelvin (K). Photons don’t travel freely through opaque regions. Instead, they bounce around and collide with each other. A thin layer called the chromosphere surrounds the photosphere; it is about 10,000 kilometers thick and 10,000 K. The chromosphere looks pink because electrons in hydrogen atoms in the chromosphere are moving from the third to the second energy level, creating a pink hue. The corona surrounds the chromosphere and is visible to the naked eye during a solar eclipse. The corona is shaped from charged particles traveling along magnetic elds. The magnetic elds of the Sun change with time, changing the corona’s shape. The corona has a temperature of about 2 million K in some parts and a little cooler in other
  • 129 parts. We know it is hot because it emits a lot of x-rays and it has highly ionized atoms. Oddly, though the corona’s particles are moving at high speeds, its density is very low. Therefore, a sentient body immersed in the corona could theoretically freeze to death (ignoring light coming from the photosphere) because that body would radiate energy at a faster rate than it would receive energy from particles colliding with it. The corona merges with an outer extension called the solar wind, where particles escape into space at a variety of speeds, typically less than 1000 kilometers per second. Eruptions on the Sun’s surface are called prominences. These occur when chromospheric gas has been ejected from the Sun at temperatures around 10,000 K. Prominences can be studied in great detail from spacecraft positioned between the Earth and the Sun at one of the so-called Lagrange points to allow a continuous view of the Sun. Two such spacecraft are the Transition Region and Coronal Explorer (TRACE) and the Solar and Heliospheric Observatory (SOHO). Prominences are gentle eruptions; more energetic eruptions are called solar ares, which emit huge amounts of particles at speeds approaching 5% of the speed of light. Prominences and ares take up regions of space on the Sun’s surface that are much bigger than Earth itself. Coronal mass ejections (similar to ares) occur when large amounts of material burst from the Sun. Some of these appear to be associated with speci c solar ares, while others seem to occur at random. Coronal mass ejections are not readily understood but might be related to large pockets of especially strong magnetic elds that tangle together and release their magnetic energy in one burst. What are sunspots and how are they formed? Sunspots are dark blotches on the Sun’s photosphere, consisting of a central dark region called the umbra and a lighter region called the penumbra. Their shapes change with time; sometimes they appear in large groups and sometimes more or less individually. Sunspots appear dark because they represent cooler regions on the photosphere that don’t emit as much light. Against a dark sky, however, a The Sun’s magnetic poles switch every 11 years for reasons that are still not fully understood.
  • 130 Lecture25:OurSun,theNearestStar sunspot would actually glow brightly. Sunspots are about 2000 K cooler than the surrounding photosphere. Per unit of time and per unit area, a sunspot emits about 20% as much energy as the surrounding photosphere. Sunspots are cooler because they have strong magnetic elds, which appear like the magnetic elds of a bar magnet, or the superposition of several bar magnets (producing a more tangled magnetic eld). Strong magnetic elds inhibit or restrain the ow of hot, charged particles from the Sun’s interior as they move upward because these charged particles tend not to cross magnetic eld lines. As charged particles try to move up through the process of convection and become restrained, the gas cools and is not replenished with fresh hot gas. The Sun’s rotation rate can be measured by monitoring the movement of sunspots. The Sun’s average rotation takes about one month. The number of sunspots and the number of ares, prominences, and other instances of solar activity varies with time. This so-called solar activity cycle lasts about 11 years. When sunspots are more active, the Sun has more prominences, more ares, more coronal mass ejections, and more activity in general. Let’s now examine the Sun’s magnetic eld and some of its other characteristics. The Sun’s magnetic eld reverses itself every 11 years, switching the Sun’s north and south poles with each other and resulting in an overall sunspot cycle (including the reversing polarity) that is 22 years long. The magnetic eld, and the reversal of its polarity, may occur as a result of convection, which generates electromagnetic currents within the Sun. If the core temperature is very hot compared to the surface, convection increases and a strong magnetic eld is created. If the core temperature is cooler relative to the surface, convection decreases and a weaker magnetic eld is created. The Sun rotates more quickly at its equator (26 days) than at its poles (36 days). At the equator, the magnetic eld lines become stretched and tangled. This tangling effect may lead to the strong magnetic elds we see in sunspots. Sunspots tend to appear in pairs. In the northern hemisphere, the pairs are aligned with north at the left and south at the right; it’s the reverse in the southern hemisphere. The Sun also vibrates, or oscillates in size, getting a little bit bigger, then a little bit smaller over short intervals of time. Study of these solar oscillations can tells us about the Sun’s interior. If our Sun is a typical star, then much of what we learn from its magnetic activity cycle, sunspots, ares, solar oscillations, and so on should be applicable to our study of other stars, too.
  • 131 convection: Process by which bubbles of gas or liquid repeatedly heat and expand, rise and give off energy, and fall again; seen in the stars and in Earth’s core. core: In a main-sequence star, roughly the central 10% by mass. In an evolved star, usually refers to the degenerate central region. Bhatnagar and Livingston, Fundamentals of Solar Astronomy. Golub and Pasachoff, Nearest Star: The Surprising Science of Our Sun. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Zirker, Journey from the Center of the Sun. 1. Consider a sunspot viewed through a dark lter or reasonably thick fog. If the sunspot is barely visible to the unaided eye (which has a resolution of about 1 or 2 arc minutes), and the Sun’s diameter is 30 arc minutes, physically how large is the sunspot relative to the Earth? 2. If the solar corona is much hotter than the photosphere, why isn’t it much brighter than the photosphere, per unit area? 3. Suppose the temperature of a sunspot is 4000 K and that of the surrounding photosphere is about 6000 K. Per unit area, about how much energy does the sunspot emit per second compared with the photosphere? 4. What is the process of convection? Give an example from everyday life. Important Terms Suggested Reading Questions to Consider
  • 132 Lecture26:TheEarth,ThirdRockfromtheSun The Earth, Third Rock from the Sun Lecture 26 “We begin our study of planets in our Solar System with the four innermost or terrestrial planets: Mercury, Venus, Earth, and Mars. ‘Terrestrial,’ in Latin, means Earth or Earth-like—so, all four of these planets are much like the Earth in their overall characteristics.” W hat does Earth’s structure look like? Earth has a solid iron-nickel core surrounded by a liquid nickel-iron core, which in turn, is surrounded by a thick mantle, separated into the lower mantle and upper mantle. The lower mantle is somewhat viscous, continually owing, and to some degree, the upper mantle moves as well. A solid crust oats on top of the upper mantle. By studying seismic waves, or earthquake waves, and how they travel through the Earth, we can discern its basic structure. There are a number of different types of waves, but the three main kinds are P, K, and S waves. The P and K waves are longitudinal, moving up and down and compressing in the same direction as the direction along which the waves move. They travel through Earth’s layers and bend as each layer’s density changes. S waves, or sheer waves, move transversely through rock; they don’t travel through liquid very well. We know that at least part of Earth’s core is liquid because sheer waves don’t travel through that core. Earth began as a molten substance, undergoing a process calleddifferentiation, in which dense matter—such as iron—sank to the core, and lighter matter— silicates and other substances—moved to the surface. As the crust cooled, it became solid, though parts of the mantle are still liquid because it retains some heat. We think the Earth was formed by the coalescence of dust particles, rock, gas, and other matter. The matter gravitationally attracted more and more material, which—in the process of colliding—released energy in the form of heat and produced an early, molten Earth. The radioactive elements in the matter decayed into stable isotopes. The decaying process freed more energetic particles, which in turn, released heat energy, further contributing to a molten state. Earth remains partially molten because of the continual, long-term decay of radioactive elements.
  • 133 The Earth’s crust oats on the soft, slowly churning mantle, which produces a phenomenon called continental drift. More generally, we call this phenomenon plate tectonics because the crust is divided into different units, or plates, that move relative to one another. The idea of plate tectonics was rst articulated by Alfred Wegener in 1912, when he noticed that Africa’s west coast looked as if it t with South America’s east coast, like a jigsaw puzzle. Other continents exhibited similar features, and indeed, fossil evidence shows similarities in species between these matching coasts. Wegener theorized that Earth’s continents had all been connected at one time and slowly drifted apart. Today, scientists believe his theory is correct. About 200 to 250 million years ago, there was probably one single supercontinent that we call Pangaea. About 180 million years ago, it split into two subcontinents that we call Gondwanaland and Laurasia. Further subdivisions occurred thereafter. Other supercontinents may have existed before Pangaea—such as Pannotia 600 hundred million years ago or Rodinia 1.1 billion years ago. This breaking apart and coming together of continents appears to have been common on Earth throughout most of its history. When Earth’s plates collide, they form mountains and volcanoes along the collision boundaries. When they slide suddenly relative to one another, earthquakes occur, their magnitude related to how much energy is released. A so-called Ring of Fire exists around the Paci c plate through Japan, the Philippines, and the west coast of North America, where Earth experiences many earthquakes and volcanoes. The movement of Earth’s mantle drives continental drift; this movement occurs by convection, when a pocket of material gains enough heat to become buoyant and rise. As the mantle material in the Earth is heated, it expands and rises toward the surface, giving off heat. As the heat is lost, the material becomes dense and sinks again, and the process repeats. Some of this superheated liquid erupts from Earth’s core in volcanoes as magma. Mars, with only about half the size of Earth, lost most of its heat long ago and no longer experiences convection to a degree that would move “The very high abundance or proportion of oxygen in our atmosphere demands an explanation. That explanation is life itself.”
  • 134 Lecture26:TheEarth,ThirdRockfromtheSun plates relative to one another. Instead, the crust of Mars has frozen to a single solid plate. Earth has a 6400-kilometer radius, yet its atmosphere is only about 100 kilometers thick. The thin atmosphere extends from Earth’s surface to a region called the ionosphere, where its constituents are mostly ionized. We live in the Earth’s troposphere, and most weather phenomena take place within about 18 kilometers or so from the surface of the Earth. About 20% of the atmosphere is oxygen, while 79% is nitrogen. This proportion of oxygen is relatively high. Earth’s atmosphere may have begun without any appreciable oxygen. But as plant material began to form, oxygen was produced in the process of photosynthesis. Beginning a few billion years ago, the oxygen content gradually increased to what it is now. Because the complete decay of organisms uses up as much oxygen as the organisms produced when alive, to have a net excess of oxygen today, full decay of these early organisms could not have been possible. Massive sediments likely covered these organisms, preventing them from completely decaying. They now have formed into coal and petroleum, which of course, when burned, complete the process of decay, consuming oxygen. Oxygen in our atmosphere usually occurs in diatomic molecules, O2 . Another form of oxygen molecule is called ozone, O3 , which is poisonous to humans. At altitudes of 20 to 40 kilometers, however, ozone protects us from the Sun’s harmful ultraviolet radiation. Ozone also protects the water vapor in our atmosphere, allowing rain to fall by preventing water vapor molecules from being broken apart by the Sun’s ultraviolet rays. Like the Sun, Earth’s magnetic eld resembles that of a bar magnet, with a north and south pole and well-ordered eld lines around it. The magnetic eld reverses itself from north pole to south pole roughly every 300,000 years, varying from a few tens of thousands of years to a few tens of millions of years. The poles were last reversed about 700,000 years ago, and we don’t know when the reversal will occur again. When reversals occur, the eld is weak, increasing the number of charged particles reaching us from the Sun because the particles don’t get trapped by Earth’s magnetic eld. Evidence in molten rock turned solid over millennia preserves a record of magnetic orientation, proving that reversals occur. Though we’re not certain, the magnetic eld may exist because as Earth rotates, its partially liquid core produces electric currents, which produce magnetic elds. A hotter
  • 135 core produces a stronger magnetic eld because in order for energy to move outward from the core, a higher degree of convection must take place. More convection drives more electric currents, which produce the magnetic eld. Charged particles from solar eruptions can sometimes hit the magnetic eld of the Earth, get trapped, and excite electrons in atoms and molecules of nitrogen and oxygen in our atmosphere to jump to higher energy levels. When the electrons jump back down to lower levels, releasing this energy, the result is the display of the northern and southern lights—the auroras. The Earth’s tides are a consequence of differential forces, mostly caused by theMoon.ThesideofEarth closest to the Moon feels a greater gravitational force than the Earth’s center, which in turn, feels a greater force than the side farthest from the Moon. This is called a differential force, or a tidal force. Thus, relative to Earth’s center, the near side of Earth feels a force toward the Moon, while the far side of Earth feels a force away from the Moon, consequently “stretching” the Earth on both sides. Water ows in the direction of the pull, resulting in a bulge toward and away from the Moon and a de cit of water in other regions. As Earth rotates about its axis during 24 hours, it experiences two high tides and two low tides. One tide is usually bigger than the other because of the tilt of Earth’s axis. The Sun also affects tides but not as much as the Moon because the Sun is so far away. Tides tend to be extreme (very high and very low) when the Sun, Earth, and Moon are aligned. These are known as spring tides, but the term has nothing to do with the season. Differences between high and low tides are smaller when the Sun, Earth, and Moon form a 90-degree (right) triangle. These are known as neap tides. An image of Earth taken from space. NASA/JPL/Caltech
  • 136 Lecture26:TheEarth,ThirdRockfromtheSun isotopes: Atomic nuclei having the same number of protons but different numbers of neutrons. tidal force: The difference between the gravitational force exerted by one body on the near and far sides of another body. Hartmann and Miller, The History of the Earth: An Illustrated Chronicle of an Evolving Planet. Lang, The Cambridge Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Pale Blue Dot: A Vision of the Human Future in Space. 1. Look at a globe and make a list or sketches of which pieces of the various continents probably lined up with each other before the continents drifted apart. 2. Explain why there are typically two high tides and two low tides per 24-hour day at a given coastal location. Also, if the Moon were farther away from the Earth than it actually is, how would tides be affected? 3. Discuss the structure of Earth’s interior, the various physical processes occurring within it, and the methods by which we learn about the Earth’s interior. Important Terms Questions to Consider Suggested Reading
  • 137 Our Moon, Earth’s Nearest Neighbor Lecture 27 “In the famous Pink Floyd CD, Dark Side of the Moon, they must have been referring to the dark side at any given time because there’s no perpetually dark side of the Moon.” J ust as the Moon is the primary cause of tides on Earth, so, too, does the Earth cause tidal forces on the Moon. Though different phases of the Moon illuminate different parts, from Earth, we still see only one face as a result of the Moon’s synchronous rotation. Synchronous rotation means that the Moon’s orbit around Earth takes place at the same rate as its rotation about its own axis. We believe that initially, the Moon rotated about its axis much more quickly than its orbital time around Earth, gradually slowing due to an effect known as tidal friction. In the same way that the Moon’s pull on Earth leads to bulging and the phenomenon of ocean tides, the Earth has been pulling on the Moon over time, changing its shape. As the Moon stretched, rocks rubbed against each other, causing friction and releasing energy that gradually slowed the Moon’s rotation. Ultimately, the Moon’s rotation slowed down to a rate equal to that of its revolution (orbit) around the Earth, xing its orientation relative to Earth. The Earth’s rotation is also slowing because of the Moon’s tidal pull; as the oceans move, they dissipate energy in the same way that the changing shape of the Moon did. Thus, Earth’s 24-hour day slows by about 1 second every 100,000 years. Because of this complex interaction, the Moon is gradually moving away from the Earth at a rate of about 3.8 centimeters per year. In half a billion years, the Moon will be too small to fully cover the photosphere of the Sun, so total solar eclipses won’t occur. The Moon doesn’t have a perpetually dark side. In fact, nearly 15 days of continuous daylight occur on any given spot on the Moon, followed by 15 days of darkness because of its motion around Earth and its synchronous rotation. During its days of light, the Moon’s temperature increases to 130° C; during its nights in darkness, temperatures plummet to about –110° C. Without an atmosphere, the Moon can’t trap heat, as the Earth does.
  • 138 Lecture27:OurMoon,Earth’sNearestNeighbor Through lunar studies, we have learned much about the Moon and its history. Evidence suggests that the Moon has frozen water at the bottom of some craters, possibly deposited by comets hitting it billions of years ago. The Moon has lots of craters, as well as wide basins known as maria, which is Latin for “seas.” We now know that maria are really frozen lava ows. Evidence shows that most of the Moon’s craters are not volcanic but, rather, formed from the impact of space debris, which causes a characteristic peak in the crater’s center. There’s very little erosion on the Moon and no water or atmosphere. The Moon has craters within craters; thus, we can tell the relative ages of features simply by observing what features are on top of other features. Areas with more craters are likely older than those regions without many craters (the maria). But to determine absolute ages, we have to sample the Moon’s rocks using a process called radioactive dating. A radioactive element, such as uranium, decays into daughter products (e.g., lead) with a certain half-life. After a time interval of one half-life, half of the original quantity of the substance remains; after two such time intervals, one- quarter of the original quantity remains, and so on. If the rock is solid, the daughter and parent products cannot mix with their surroundings and become diluted. By measuring the ratios “For a long time, there was a debate: Are the craters impact craters, or are they of volcanic origin? Their shape gives one clue.” Crater 308 on the moon, taken by the Apollo 11 crew from orbit. NASA
  • 139 of parent and daughter products, the ages of the rocks (that is, the time since they were last molten) can be determined. A glorious time in the history of space exploration was the era of the lunar landings of Apollo 11 through Apollo 17 (1969 1972). The astronauts did a number of experiments on the Moon. They also left equipment (e.g., seismographs, radar re ectors). Moon rocks from various regions were returned to Earth. G. The Moon’s oldest rocks are about 4.4 billion years old. The heavily cratered highlands are 3.9 to 4.3 billion years old. Rocks from the maria are between 3.1 and 3.9 billion years old. Because the lava ows (maria) have fewer craters, we know that most of the Moon’s craters were formed more than 3 billion years ago. Indeed, the bombardment of the Moon was heavy shortly after its formation, about 4.5 or 4.6 billion years ago. However, the Moon does have a few “recent” craters, which were formed 1 to 1.5 billion years ago, such as Tycho and Copernicus. The early era of bombardment of the Moon was probably the last stage of the formation of the Solar System. Edwin (Buzz) Aldrin Jr. deploys passive seismic equipment. NASA/JPL/Caltech
  • 140 Lecture27:OurMoon,Earth’sNearestNeighbor Let’s consider the Moon’s overall structure, size, and origin. The Moon has a small iron core surrounded by a region in which moonquakes occur, on top of which is the upper mantle, and nally, a crust. The Moon experiences little internal motion and is, to a large extent, geologically dead. The Moon’s far side—the side that’s perpetually away from the Earth—looks distinctly different from the near side. Its far side has comparatively few lava ows and many more cratered regions. For this reason, it must have formed early in the history of the Moon. The far side may also have a thicker crust than the near side, perhaps accounting for the lower number of lava ows; if the crust were thicker, then there wouldn’t be as many weak spots through which lava could ow from the interior. The mass of the Moon is about 1/80 of the mass of the Earth, and the radius is about 1/4 (actually, 1/3.7) of the Earth’s radius. What would we weigh on the Moon? The gravitational force per unit mass on the Moon’s surface, GM/R2 (in which M is the mass of the Moon and R is its radius), is (1/80)/(1/3.7)2 1/6 times that on the Earth’s surface. Because the weight of an object is a measure of the gravitational force on it, objects weigh about 1/6 as much on the Moon as they do on Earth. The Apollo astronauts were able to jump relatively far, though inhibited by their bulky space suits. The Moon is about 1/4 of Earth’s size. If we compare this size ratio to that of other planets and their associated moons, our Moon is relatively large. Because such a large moon orbits Earth, the inclination of Earth’s rotation axis is stable. A smaller moon would allow the Earth’s rotation axis to chaotically change every few million or tens of millions of years because of the gravitational pull of Jupiter and other planets. Thus, the seasons would change every few million years. FourhypothesesattempttodescribehowtheMoonwasformed.Onehypothesis is that the Moon formed through ssion; that is, it broke off from Earth. Another is that the Moon initially came from far away and was “captured” by Earth. A third is that the Moon essentially condensed out of the material of which the Solar System was made at the same time that Earth condensed. The fourth hypothesis is that a large object, roughly the size of Mars or larger, collided with Earth, expelling some of Earth’s material and forming a disk around the Earth. The Moon subsequently formed from the coalescence of this material. We think this is the most likely explanation because lunar material is very much like that of Earth’s mantle in composition.
  • 141 synchronous rotation: The rotation of a body having the same period as its orbit. weight: The force of the gravitational pull on a mass. Chaikin, A Man on the Moon. Hockey, The Book of the Moon: A Lunar Introduction to Astronomy, Geology, Space Physics, and Space Travel. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Pale Blue Dot: A Vision of the Human Future in Space. 1. It is sometimes said that the U.S. mission to the Moon was entirely motivated by the Soviet Union’s launch of the Sputnik satellite in 1957. Do you think the scienti c bene ts of lunar landings would have been suf cient reason to take the risks and spend the funds? 2. What effect did the heavy cratering of the Earth during the rst half billion years of its existence (as determined by the ages of lunar craters) probably have on the development of life on Earth? 3. Why are we more likely to learn about the early history of the Earth by studying the rocks from the Moon than those on the Earth? 4. Calculate your weight if you were standing on the Moon. Important Terms Suggested Reading Questions to Consider
  • 142 Lecture28:MercuryandVenus Mercury and Venus Lecture 28 “Though broadly similar in nature to the Earth—they are, after all, terrestrial planets—they differ quite a bit in detail, especially Venus, which was thought to be Earth’s sister planet.” L et’s rst explore Mercury. It’s dif cult to study Mercury from Earth because Mercury is nearly always in the same direction as the Sun. As we saw with Venus in a previous lecture, Mercury also transits the face of the Sun a few times per decade. But because it is dif cult to see surface details on Mercury, for a long time, its rotation rate was not known. Mercury’s rotation period was eventually measured using the Doppler effect, which we will discuss in more detail in a later lecture. This effect is an enormously important tool for determining the radial velocity of an object—that is, its speed as it moves toward you or away from you. Essentially, the Doppler effect is seen when we measure the wavelengths ofabsorptionoremission lines in a spectrum. If a source that is emitting light or sound waves is moving relative to an observer, then along the direction of motion, the source partially keeps up with its most recently emitted wave crest before it emits another wave, causing the crests to bunch up. If we stood in front of an approaching source and measured its emitted waves’ lengths, we would nd that they are shorter than waves trailing behind the source (if we stood behind the source as it moved away from us). Mercury as seen by Mariner 10 on March 29, 1974. NASA
  • 143 In a similar way, we can shine a radio wave—radar—at two edges of a rotating planet. If the planet is rotating counterclockwise as seen by us, then the side approaching us will re ect the radio wave toward us with a higher frequency—shorter wavelength. Re ected waves from the edge that recedes from us will have a lower frequency—longer wavelength. From the amount of this shift, the rotation rate and, hence, the period of Mercury’s rotation could be determined. Mercury rotates about its axis in 59 days, or three times for every two times that it orbits the Sun. This so-called 3:2 resonance occurred because the Sun exerts tidal forces on Mercury, slowing down its initially more rapid rotation. Mercury has a 176-day day/night cycle: Nighttime and daytime each lasts for a consecutive 88 days. Moreover, Mercury has an almost negligible atmosphere. Thus, Mercury heats up a great deal during the day (430° C) and plummets to very low temperatures at night (–170° C). This is similar to, but more extreme than, the temperature range on the Moon. Mercury’s gravity at its surface is only about 40% that of Earth. Mercury’s surface is heavily cratered; most of these craters formed more than 4 billion years ago. As we saw on the Moon, some craters near Mercury’s poles appear to contain frozen water that came from comets. Venus is the second planet from the Sun. Much of Venus is covered in clouds made of sulfuric acid. The clouds cause a high degree of re ectivity; this high re ection fraction is called a high albedo in astronomical terms. Despite its proximity to the Sun, the fact that Venus has an atmosphere led people at one time to believe that it might be habitable. In fact, the planet is not habitable because of its high temperatures and high atmospheric pressure, 90 times that of Earth. Venus displays mountains, valleys, craters, and plains. It has only one thick crust with no plates, though it does have some high parts that we call continents—two main continents. Venus may have had global lava ows as recently as half a billion years ago. There also appear to be a few semi-active volcanoes now that emit some sulfur dioxide fumes. Venus’s surface temperature is 480° C all the time, everywhere. Given its distance from the Sun and assuming that it has a transparent atmosphere, Venus’s surface temperature should be only about 100° C. How did the temperature become so high? Venus suffered a runaway greenhouse effect. Its atmosphere consists of 96% carbon dioxide and about 4% nitrogen. Venus is illuminated by sunlight, but much of that light
  • 144 Lecture28:MercuryandVenus re ects off the high clouds, back into space. Some visible sunlight penetrates and heats the surface, exciting the constituent particles of the surface, which then emit infrared radiation. This radiation is absorbed by the carbon dioxide in the atmosphere of Venus, thereby warming the atmosphere, which in turn, reheats the surface of the planet, increasing its temperature. The amount of infrared rays leaking out of Venus’s atmosphere is balanced by the amount of visible light coming in. Venus has reached an equilibrium temperature, which is much higher than it would have been if carbon dioxide allowed infrared light to escape. Though this trapping of heat on Venus is called the greenhouse effect, this is a misnomer because true greenhouses operate differently: Air in a true greenhouse is heated inside, and the structure itself prevents that hot air from mixing with the cooler surroundings. Earth would be about 60° F cooler with no greenhouse effect. In addition, Earth has a very effective way of recycling its greenhouse gases, primarily carbon dioxide and water vapor. Why does Venus not have such an ef cient system as Earth’s? Venus may have once had oceans, but without enough rain to remove atmospheric carbon dioxide (as Earth has), carbon dioxide would build up from volcanic vents. This caused any water to evaporate more quickly, which in turn, would have increased the water vapor content of Venus’s atmosphere. Instead of raining down, Venus’s water vapor rose to an altitude at which ultraviolet radiation from the Sun could break it apart. The hydrogen, being light, escaped from Venus, but the “There is an operating greenhouse effect here on Earth. People say, ‘Oh, that’s bad, a greenhouse effect, something to be feared!’ No—in moderation, it’s a good thing.” Venus as seen from Mariner 10. NASA
  • 145 carbon combined with oxygen to form more carbon dioxide in the atmosphere, creating a runaway greenhouse effect. What can we learn from Venus? Though not entirely unanimous, there is scienti c consensus that Earth is warming at an alarming rate. If global warming is occurring, are people to blame? Our burning of fossil fuels does create an increased amount of carbon dioxide in the atmosphere. The carbon dioxide content in CO2 molecules per million molecules of air from the 1950s to 2005 shows seasonal oscillations. But there has also been a dramatic increase, which—probably not coincidentally—started around the time of the industrial revolution. Some scientists argue that an increase in carbon dioxide will lead to more water vapor in the atmosphere, creating clouds, which would offset global warming by blocking more of the Sun’s radiation from reaching Earth. Other scientists believe that an increase in the water vapor increases greenhouse heating and more than compensates for the extra sunlight re ection off the clouds. An extreme runaway greenhouse effect, like that on Venus, almost certainly won’t occur on Earth for various reasons; however, it is widely acknowledged that even a rise in temperature of a few degrees could cause devastation on Earth. Global warming is a serious concern, and more extensive studies are necessary to determine its effects. In any case, we should do what we can to maintain the atmospheric content of Earth because we don’t yet know what could happen by changing it. greenhouse effect: The effect by which the atmosphere of a planet heats up above its normal equilibrium temperature because it absorbs infrared radiation from the surface of the planet. radial velocity: The speed of an object along the line of sight to the observer. Important Terms
  • 146 Lecture28:MercuryandVenus Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. Lang, The Cambridge Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Pale Blue Dot: A Vision of the Human Future in Space. 1. Do you think the evidence for human-induced global warming of Earth is strong? Will it be too late to reverse the trend, if and when the effect becomes so large that its presence is unambiguous? 2. Suppose a planet had an atmosphere that was opaque in the visible but transparent in the infrared. Describe how the effect of this type of atmosphere on the planet’s temperature differs from the greenhouse effect. 3. If you increased the albedo (re ectivity) of Mercury, would its surface temperature increase or decrease? 4. Why do radar observations of Venus provide more data about its surface structure than a yby with optical cameras outside Venus’s atmosphere? Questions to Consider Suggested Reading
  • 147 Of Mars and Martians Lecture 29 “Though there are some other interesting features on Mars that sometimes appear as though they are produced by intelligence, we are unlikely to receive a Martian valentine entitled ‘From Mars, with love,’ despite heart-shaped craters that do look like they were perhaps carved by some sort of intelligence.” I n addition to Mercury, Venus, and Earth, the fourth and nal terrestrial planet is Mars, about 1.5 times farther from the Sun than Earth is. For a long time, humans have been intrigued by the so-called Red Planet. Mars is named after the god of war, largely because of its reddish-orange color. We now know that its color comes from iron oxides—that is, rust. Additionally, Mars’s surface is more yellowish-brown than red, though when viewed from Earth, it has a distinctly reddish-orange color. Let’s look at some of the basic characteristics of Mars. Mars is about half the diameter of the Earth, though somewhat larger than Mercury. It has two small moons, Phobos and Deimos, which are only about 20 kilometers in diameter. Mars has polar ice caps, predominantly made of frozen carbon dioxide—or dry ice—that grow and shrink with the seasons. However, water does lie underneath the dry-ice caps. Mars’s seasons are similar to Earth’s because the tilt of its rotation axis is 25.2 degrees relative to the Solar System axis. Earth’s axis is tilted 23.5 degrees. Mars also has a 24.5-hour day/night cycle. Earth has anexceptionallyclearview of Mars every two years when it comes close to our planet. Called opposition, the con guration is such that Earth comes between Mars and the Sun. Viking 2 site on the surface of Mars. NASA
  • 148 Lecture29:OfMarsandMartians Mars has a thin atmosphere, only about 1% of the thickness of Earth’s atmosphere. It consists of 90% carbon dioxide. But because it’s such a thin atmosphere and because Mars is signi cantly farther from the Sun than Earth, it goes through extreme temperatures: from –130° C to (rarely) about 30° C. Mars’s atmosphere supports ferocious winds, which sometimes create huge dust storms. In addition, Mars has craters, volcanoes, canyons, and dunes, but it no longer has plates—there is only one thick crust. The planet’s most striking feature is Valles Marinaris, a giant canyon, which if placed on North America, would stretch from coast to coast. Most of the canyon was created as a gash as a result of tectonic motions early in the history of Mars. The main canyon was a rupture in the plate. In addition to the tributaries of Valles Marinaris, Mars shows other evidence that liquid water once existed on the planet. Mars has ancient riverbeds and ood plains. Some impact craters have a teardrop shape, formed as a result of erosion, further indicating that water once owed on the surface. Photographs show what look like ancient dry riverbeds, as well as evidence of sedimentation and melting permafrost, which may have created the gullies we see. The Mars Odyssey spacecraft measured neutrons coming from the surface of Mars as a result of interactions with charged particles from the Sun. It found a de cit, which—by inference—is associated with the presence of hydrogen atoms that block neutrons dislodged from the soil. Presumably, the hydrogen is in the form of water. The presence of ne sediments may indicate water, and so might the existence of a substance called hematite, which forms in the presence of water. Moreover, a mineral called jarosite has been identi ed on Mars, a hydrated sulfate, which contains water and forms in its presence. If Mars used to have liquid water, why doesn’t it exist anymore? Mars’s atmosphere is too thin to support liquid water; its atmospheric pressure is only 1% that of Earth’s, and a much higher pressure is needed to support liquid water. The strong evidence for the long-ago existence of liquid water suggests that Mars’s atmosphere must have been thick at one time. We think “Unlike our Grand Canyon, which was carved by the action of water, most of Valles Marineris was created as a gash due to tectonic motions early in the history of Mars.”
  • 149 that, indeed, Mars did have a lush atmosphere for the rst half billion to billion years of its existence. What happened to Mars’s thick atmosphere? There are two main hypotheses. If Mars experienced a cooling trend, then some of its atmospheric carbon dioxide would freeze, decreasing the degree of greenhouse warming. In turn, this would lead to lower temperatures, more freezing of carbon dioxide, and even less greenhouse heating, and so on. This is called an inverse greenhouse effect and is the opposite of what seems to have happened on Venus. Another suggestion is that because Mars is small and lost its heat early in its history, its magnetic eld was weak. Without a strong magnetic eld, the intense solar wind from the young Sun could help blow away Mars’s atmosphere, accounting for the thin atmosphere. At this point, an inverse greenhouse effect could have taken over. Did Mars ever support life and could it support life now? Investigations of Martian soil samples by the Viking spacecraft in the mid-1970s failed to prove that some form of life exists on Mars. In fact, no organic compounds whatsoever were found in soil analyses. The lack of evidence thus far, however, doesn’t mean that life never existed on Mars; indeed, life may exist deeper in the soil, but there is still no clear evidence for it. The most intriguing evidence for Martian life comes from a 4.5-billion-year-old chunk of rock from Mars that hit Earth and landed in Antarctica about 13,000 years ago. An analysis of this meteorite found that it contains carbonate globules, which generally form in liquid water. Polycyclic aromatic hydrocarbons Astronomy in History Part of our fascination with Mars was fueled by the Italian astronomer Giovanni Schiaparelli, who in 1877, reported seeing canali on Mars. In Italian, this word means “channels,” but it was improperly translated to “canals” in English. People thought that the canals might have been built by intelligent life forms. Percival Lowell subsequently made detailed telescopic observations of Mars, also reporting a network of straight- lined canals crisscrossing the planet. As telescopes improved, it became obvious that Lowell’s observations were awed. Further, missions to Mars have proved that there are no canals as such on Mars.
  • 150 Lecture29:OfMarsandMartians (PAHs) were also found. Though PAHs can be formed in ways other than by life, the ones found in the meteorite are relatively unusual. The Martian meteorite contains magnetite, a mineral produced by some types of bacteria. In addition, it has tube-like organisms that resemble nanobacteria on Earth. However, they are much smaller than the nanobacteria found on Earth. Most researchers feel that the evidence for microbial life in the Martian meteorite is not compelling. All of the observed phenomena have more conventional non-biological explanations. The results are highly controversial, and additional tests are necessary. It is conceivable that if Mars did have primitive bacteria and microbes early in its history, and if a meteorite from Mars landed on Earth a very long time ago, this could have “polluted” the Earth with life for the rst time. Then, through evolution, all of the modern life forms came about. If so, we may be the descendants of Martians. Though this is a highly speculative idea, it’s not impossible. terrestrial planets: Rocky, earth-like planets. In our Solar System: Mercury, Venus, Earth, and Mars. Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Boyce, The Smithsonian Book of Mars. Goldsmith, The Hunt for Life on Mars. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Kargel, Mars—A Warmer, Wetter Planet. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Important Term Suggested Reading
  • 151 Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Squyres, Roving Mars: Spirit, Opportunity, and the Exploration of the Red Planet. 1. Plan a set of experiments or observations that you, as a Martian scientist, would have an un-crewed spacecraft carry out on Earth to nd out if life exists here. What data would your spacecraft radio back if it landed in a corn eld, in the Sahara, in the Antarctic, or in New York’s Times Square? 2. How likely do you think it is that humans will eventually “terraform” Mars so that its climate becomes suitable for humans? 3. What evidence exists that there is, or has been, liquid water on Mars? Where is some of that water now? Questions to Consider
  • 152 Lecture30:JupiterandItsAmazingMoons Jupiter and Its Amazing Moons Lecture 30 “What a wonderful system Jupiter presents, with a whole variety of moons, each having a personality of its own, and lots of cool features to study.” W e now move from the small terrestrial planets in our Solar System to the gas, liquid giants—the Jovian planets—beginning with a look at Jupiter. Jupiter, named after Jove—the king of the gods— is 11 times the diameter of the Earth and about 320 times its mass. It is the largest planet in our Solar System, being roughly 1/10 the Sun’s radius. It is about 5AU from the Sun and takes 12 years to revolve around the Sun. Jupiter is somewhat squashed, or oblate, because of its rapid rotation. Despite its size, Jupiter rotates fully about its axis in only 10 hours, causing its equatorial region to bulge signi cantly. Jupiter consists mostly of hydrogen and helium; thus, its composition is much more representative of the Universe than Earth’s and close to the composition of our Sun. The planet is about 86% hydrogen and 14% helium (by number of atoms) but includes small quantities of other elements, mostly in such compounds as methane and ammonia. Jupiter has a rocky core, resembling Earth’s, surrounded by an icy layer, which is itself surrounded by a layer of extremely compressed hydrogen known as metallic hydrogen. Above the layer of metallic hydrogen is molecular hydrogen, where hydrogen forms a diatomic (two-atomic) molecule. It also has a strong magnetic eld—10 times stronger than Earth’s—probably caused by the rapid rotation of the conducting layer of metallic hydrogen. Thus, Jupiter has polar auroras because its magnetic eld is highly ef cient at trapping charged particles from the Sun. It is easy to understand why the giant planets, such as Jupiter, retained so much hydrogen and helium, whereas the terrestrial planets did not. Because the giant planets are much farther from the Sun, they are heated less. Hydrogen and helium move less rapidly and, therefore, were retained by the planets’ gravitational elds. Jupiter’s surface is gaseous, as opposed to our own solid surface on Earth. In this sense, its surface is like the Sun’s photosphere—a place beyond which the gases become thick enough to be opaque.
  • 153 Unlike the Sun’s photosphere, however, Jupiter’s surface re ects visible sunlight. Because it doesn’t generate visible energy from within, it doesn’t glow visibly from within, though it does glow from within at infrared wavelengths. Jupiter’s colorful bands are seen predominantly parallel to the equator, but they do twist and form oval shapes. The various colors are caused by slight differences in composition, including more methane, ammonia, and sulfur compounds. Jupiter’s most famous landmark is the so- called Great Red Spot, which has been seen for more than 300 years. The Red Spot is two to three times the size of Earth and is like a giant hurricane. Unlike hurricanes, however, which are low-pressure systems on Earth, Jupiter’s Great Red Spot is a high-pressure system. Jupiter is still contracting on the inside. This contraction liberates energy and is the likely explanation for the planet’s stormy atmosphere. The liberated energy heats Jupiter’s interior before escaping from the hot core to the cooler surface, creating convection currents. Convection, coupled with Jupiter’s rapid rotation, causes the complex and active surface storms. Spacecraft, such as the Pioneer missions, the two Voyagers, Galileo, and Cassini, have provided a wealth of information about Jupiter and its moons. Jupiter has four main moons, called the Galilean satellites in honor of Galileo Galilei, whose observations in 1610 advanced the Copernican revolution. These moons are easily seen through amateur telescopes and sometimes create eclipses (or even double eclipses) of the Sun. Three of Jupiter’s moons are larger than Earth’s Moon and one is larger than the planet Mercury. The moon Io is the most geologically active body in our Solar System, with erupting volcanoes spewing sulfur compounds. The magma differs from that on Earth, but clearly, Io’s interior is molten because of tidal forces caused by Jupiter. Tidal forces stretch Io just as Earth’s Moon stretches our oceans to create tides. Io is close to Jupiter, “Some of these things you could hardly even call moons. They’re smaller than 4 kilometers in diameter. They’re captured asteroids, things like that. There might be hundreds or even thousands of moons. Some of them are pretty interesting. None are quite as interesting as the four main moons.”
  • 154 Lecture30:JupiterandItsAmazingMoons orbiting in only about two days, and Jupiter’s mass is enormous, so the tides are extreme. In addition, because of a gravitational interaction with the other Galilean satellites, Io’s orbit is forced to be quite eccentric; that is, at one end of its orbit, it comes close to Jupiter, and at the other end, it’s farther away. Thus, Jupiter’s tidal force causes Io to become more stretched when it’s close to Jupiter and more round in shape at the farther end of its orbit. This constant change in Io’s shape creates friction in its interior and causes heat to build up, melting the material. Magma then penetrates weak spots in the crust, erupting in volcanoes. Another moon, Europa, has a relatively smooth, icy surface with some fractures. We know this moon is young because it doesn’t have many craters. When craters form on ice and the ice is not too hard, the craters will be destroyed over time because of the shifting of the ice. Europa also shows ridges, similar to those found on a frozen layer of water with slushy water Io is the most geologically active body in our Solar System. NASA/JPL/Caltech
  • 155 underneath that continues to shift and fracture. Europa is partially molten inside because it, too, suffers from a changing tidal effect, though not as extreme as that of Io because Europa is farther away from Jupiter than Io is. With liquid water, or at least a slush, under its frozen surface, Europa is a prime candidate for the search for life elsewhere in our Solar System. Farther out, Ganymede is even less affected by changing tidal forces than Europa, and thus, its interior is less molten. Ganymede has some grooved terrain that may have been produced in the last billion years or so. Most of the terrain, however, is covered with craters that are perhaps 2 to 4 billion years old and remain preserved because of little tectonic activity or erosion. Callisto, the outermost of Jupiter’s Galilean moons, has perhaps the oldest surface in the Solar System, heavily pockmarked with craters that formed 4 billion years ago. Jupiter has many more moons; about 60 are known now and more are being discovered all the time. Many are very small, less than 4 kilometers in diameter; these are probably captured asteroids. Jupiter has a thin ring, discovered by the Voyager spacecraft, about 1.8 Jupiter radii from its center. asteroid: Chunk of rock, smaller than a planet, that generally orbits the Sun between Mars and Jupiter. Galilean satellites: The four large moons of Jupiter (Io, Europa, Ganymede, Callisto). A close-up of Jupiter’s moon Europa shows its ridges. NASA/JPL/Caltech Important Terms
  • 156 Lecture30:JupiterandItsAmazingMoons Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Beebe, Jupiter: The Giant Planet. Fischer, Mission Jupiter: The Spectacular Journey of the Galileo Spacecraft. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Given that Jupiter’s diameter is 11.2 times that of Earth, about how many Earths could t inside of Jupiter? (Neglect the empty spaces that exist between closely packed spheres.) 2. Do you think it is possible to determine Jupiter’s mass by measuring the orbital properties of its moons? 3. How can we determine the approximate age of a moon’s surface from the number of visible craters per unit area? (Assume the cratering rate as a function of time was similar to that on Earth’s Moon.) 4. Through a telescope on Earth, can you sometimes see Jupiter in its crescent phase, just as the Moon is sometimes a crescent? Why or why not? Suggested Reading Questions to Consider
  • 157 Magni cent Saturn Lecture 31 “The decades ahead promise a lot for the further study of Saturn, to see how this system developed and to determine whether it, too, may have formed life as we know it.” S aturn is the sixth planet from the Sun and is much like Jupiter but smaller. It is 9.5 AU away from the Sun. Saturn is mostly hydrogen and helium, with an Earth-like core. Its average density is only 0.7 g/cm3 , less than that of water. It could oat in a bathtub of water on Earth, if Earth (and the bathtub) were big enough. Saturn’s internal structure resembles that of Jupiter, with a rock and ice core surrounded by a layer of metallic hydrogen (though not as thick as Jupiter’s), in turn surrounded by a vast layer of molecular hydrogen. Saturn has an outer atmosphere similar to Jupiter’s. It has bands and spots, but there is less energy driving Saturn’s storms. The different colors are the result of different amounts of ammonia, methane, and other trace contaminants. Saturn has a moderately strong magnetic eld that causes auroras, the glowing polar lights. Saturn’s most notable feature is its magni cent rings, though all four of the giant planets have some rings. The rings are about 20 meters thick; compared to the extent of Saturn’s size, the ratio of ring thickness to ring diameter is similar to a CD with normal thickness but 30 kilometers in diameter. The rings are made of chunks of ice and rock, which may have been a moon that never formed or, perhaps, a weakly structured moon or comet that came too close to Saturn and was torn apart. How could this occur? Every planet is surrounded by a region called the Roche limit, where tidal forces are suf ciently strong to prevent an object from coalescing due to the gravitational interactions of all the minor particles. The rings of Saturn are within this Roche limit. If a strong rock reaches the Roche limit, it won’t be broken apart because it’s held together by its internal strength. Why haven’t Saturn’s rings dissipated with time? If they formed 4.5 billion years ago, when Saturn formed, they should have disappeared long ago because collisions among the particles tend to dissipate the rings with time.
  • 158 Lecture31:MagnicentSaturn There may be some physical effect we don’t know of that holds the rings in place. More likely, the rings are a fairly young phenomenon, only about 100 million years old. There might be a system of moons holding the rings’ particles in place, but we don’t really know why the rings are still there. Saturn rotates on its axis tilted at 27 degrees, compared to Earth’s tilt of 23.5 degrees. Because of this tilt and the planet’s orbit, from Earth, we view Saturn’s rings from a different perspective as the years pass. Sometimes, we see the rings as if looking down on them; about seven years later (roughly a quarter of Saturn’s orbital period around the Sun), we see the rings edge-on. Seven years later, we see the underside of the rings, relatively face-on, and so on. Thus, twice per 30-year revolution around the Sun, the rings come into view edge-on, appearing as a thin dark line on the face of the planet. Let’s take a closer look at Saturn’s rings. From Earth, only two to four rings are visible. The main two rings (A and B) are separated by a dark gap called Cassini’s Division, discovered in 1675. The faint ring C is interior An image of Saturn’s rings taken by Voyager 2 at a distance of 8.9 million km on August 17, 1981. NASA/JPL/Caltech
  • 159 to ring B. In ring A, there’s another gap called Encke’s Division, but that is hard to see. Cassini’s Division is caused by what we think is a resonance between one of Saturn’s moons, Mimas, and the particles that would have been in the location of the gap. Those particles orbit Saturn twice for every one time that Mimas orbits Saturn. Mimas repeatedly exerts a gravitational tug on the particles, causing them to wander away from that location. This repeated gravitational tug clears out a region of Saturn’s ring corresponding to Cassini’s Division. We think that some of the other gaps are caused by resonances with other moons. Saturn has more than 100,000 individual minor ringlets; some appear in groups. But within major rings, there are many other smaller subdivisions. In fact, even Cassini’s Division has a few minor ringlets within it. It is also possible that small moonlets occur within the rings, clearing away the rings’ gaps that we see through gravitational tugs. One of Saturn’s main moons is called Titan, discovered in 1655 by Christian Huygens. Titan has a thick nitrogen atmosphere, just as Earth does (though 1/5 of Earth’s atmosphere is oxygen). Reactions within that nitrogen atmosphere—for example, when lightning occurs—form hydrocarbons, particulate matter, and other compounds. Titan has smog and haze, which along with possible hydrocarbons raining out of the atmosphere, led to the theory that Titan could have hydrocarbons on its surface, possibly dissolved in methane lakes. Titan’s thick atmosphere, along with some greenhouse warming, could make it a relatively warm planet compared to its neighbors, the frozen giants. Using radar, we have mapped Titan’s terrain and know that it has high areas and valley-like features. Some darker areas could possibly be methane lakes, but we have no direct evidence for this so far. The Huygens probe sent to Titan from the Cassini spacecraft revealed what appeared to be a shoreline with rivers emptying into a lake or what was once a lake. Again, we have no direct evidence that these features now contain liquid, yet the images are intriguing. The probe also saw boulders on what appears to be a ood plain. “Saturn, to me, is the most beautiful planet other than Earth. I know beauty is in the eye of the beholder, but nevertheless, who could not say that Saturn is beautiful?”
  • 160 Lecture31:MagnicentSaturn Saturn has other interesting moons, including one called Enceladus. Enceladus has a high albedo, or re ectivity, in some parts where there are few craters, suggesting that it’s a young surface. Some other parts have many craters. The Cassini spacecraft also found plumes of particles and gas arising from certain regions of this moon, and studies showed that they are water- ice and water vapor. The source of the plumes was traced back to striated regions on the surface. Temperature measurements of those regions showed that, though much of the area is cold (75 K), other parts are signi cantly warmer by as much as 15 K. The warmer regions coincide with ssures or valleys within this striated region. The current hypothesis is that Enceladus is covered by cold water-ice, below which may be pressurized liquid water at roughly the melting point of ice, 273 K. Through these ssures, water can ow and turn into vapor and ice, causing the plumes. In the same way that Jupiter’s tidal forces heat Io’s interior, Enceladus has changing tidal forces that occur during its elliptical orbit around Saturn. The liquid water on Enceladus may be very close to the surface, and there’s a chance that a probe sent to this moon someday could dig down into one of those ssures and take a sample of water, in search of life. The moon Iapetus has one very bright side and one dark side, as though its bright side has some freshly fallen snow, probably methane, ethane, or maybe some water-ice. The moon Mimas is highly pockmarked with craters, including one giant one. Rhea also has a very old surface, highly pockmarked with impact craters. Saturn has dozens of other moons, many of which are probably captured asteroids or, perhaps, remnants of former bigger moons that collided with each other and broke apart. Roche limit: The distance from the center of a planet at which the planet’s tidal forces prevent particles from forming a moon through their mutual gravitational attraction. Important Term
  • 161 Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Why are the chemical compositions of Jupiter and Saturn so close to that of the Sun but those of the terrestrial planets are not? 2. How do studies of other planets and moons in the Solar System potentially help us understand various aspects of Earth better, such as its climate, surface features, interior, and history? 3. Using a ground-based telescope equipped with a spectrograph, how might you deduce that Saturn’s rings are rotating, and how would you measure the rotation speed as a function of distance from the planet’s center? Suggested Reading Questions to Consider
  • 162 Lecture32:UranusandNeptune,theSmallGiants Uranus and Neptune, the Small Giants Lecture 32 “Uranus and Neptune were not known to the ancients. The ancients knew about the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn.” B oth Uranus and Neptune are considered the outer giant planets. Uranus and Neptune are only about 4 times the diameter of the Earth, which is smaller than Jupiter (11 times Earth’s diameter) and Saturn (9.5 times Earth’s diameter). Uranus and Neptune are more closely aligned with Jupiter and Saturn in their overall characteristics than they are with the terrestrial planets. For example, they consist mostly of hydrogen and helium, and they have rocky and icy cores. Their masses are only about 14.5 times (Uranus) and 17 times (Neptune) that of Earth. Because they have less mass, Uranus and Neptune never compress hydrogen into the metallic form; molecular hydrogen is the most compressed form of hydrogen on these planets. A much larger portion of their masses is made up of a rocky, Earth-like core with an icy layer around it. The ice is water-ice, as well as frozen carbon dioxide, methane, ammonia, and other compounds. For some reason, Uranus and Neptune have considerably less hydrogen and helium than Jupiter and Saturn. Let’s look at Uranus rst in greater detail. Its correct pronunciation is YOUR- uh-nus. Uranus is named after the mythological father of the god Saturn, who in turn, is the father of the god Jupiter. Uranus was discovered by Sir William Herschel in 1781. Uranus is the seventh planet from the Sun, about 20 AU away, and takes about 84 years to orbit the Sun. It’s composed mostly of hydrogen and helium but has outer layers of methane and ammonia. Methane re ects blues and greens well, giving the planet a bluish-green tinge. Uranus’s axis of rotation is tilted 98 degrees relative to the perpendicular to its orbital plane. Thus, its axis of rotation is nearly coincident with the orbital plane, resulting in 21-year-long seasons having extreme conditions, in terms of the lengths of the day and night. We don’t know what causes this extreme tilting, but perhaps the planet collided with a large object early in its history. Uranus’s extreme tilt isn’t unique: Venus tilts 177 degrees (actually spinning
  • 163 on its axis opposite its motion around the Sun). Pluto’s axis is tilted 120 degrees (though, as we will see in the next lecture, Pluto is now considered to be only a dwarf planet). Given Uranus’s large tilt toward the Sun, we might expect that the heating of its surface would be extreme from season to season and that it would experience many storms. However, its atmosphere shows little activity, and its surface was essentially devoid of features in the rst detailed photographs obtained with the Voyager spacecraft. Some storms have recently been observed with ground-based telescopes equipped with adaptive optics. Nevertheless, the amount of atmospheric activity is less than that of the other giant planets. The planet’s magnetic eld is tipped by 60 degrees relative to the axis of rotation, and it is offset by a large amount from the center of the planet. In most planets, the magnetic eld and the axis of rotation are relatively aligned, and the offset from the planet’s center is small. The peculiarities of the magnetic eld likely were not caused by a collision with another celestial object because Neptune has a similarly strange magnetic eld, yet its axis of rotation is nearly perpendicular to its orbital plane. Rings were discovered around Uranus in 1977, when Uranus passed in front of a bright star; these rings blocked the star’s light for a short time. The narrow rings are only about 10 kilometers wide, and there are about 10 of them. Astrophysicists theorized that shepherd moons on either side of each An image of Uranus and its satellites. NASA
  • 164 Lecture32:UranusandNeptune,theSmallGiants ring may keep the ring particles in place through a complex gravitational interaction. For example, if a particle tries to move toward an outer shepherd moon, that moon absorbs some of the particle’s energy and forces the particle back. A particle that tries to move toward an inner shepherd moon gains some energy as that moon passes it up, and that energy ings the particle back toward the rings. Indeed, spacecraft have con rmed the presence of shepherd moons orbiting Uranus’s rings; two such moons are Cordelia and Ophelia. Uranus has 27 known moons, the most interesting of which is Miranda. It’s a relatively small moon but still has many surface features, including striations, craters, canyons, and what look like fault blocks. Now we turn to Neptune, roughly the same size as Uranus and consisting mostly of hydrogen and helium. Neptune was discovered in 1846 and is named for the Roman god of the sea, a son of Saturn. Interestingly, Galileo actually saw Neptune in late 1612 and early 1613, drawing what he thought was a xed star—but even noting that its position had moved some time later. If we use the known position of Jupiter at the time that Galileo made his measurements and take his plotted position of Neptune relative to Jupiter, we can re ne our knowledge of Neptune’s orbit. The discovery of Neptune was one of the great triumphs of celestial mechanics. The predicted and observed orbits of Uranus disagreed in detail. Urbain Leverrier and John C. Adams independently concluded that another planet must perturb Uranus, and they calculated its expected location. Johann Galle searched around the predicted position and found Neptune. In 1989, the Voyager spacecraft took pictures of Neptune, capturing such features as icy methane clouds skirting above the main part of the atmosphere, as well as storms, such as the Great Dark Spot, reminiscent of Jupiter’s Great Red Spot. Neptune’s atmosphere is much more dynamic than Uranus’s, which is unusual given that Neptune is farther from the Sun and, therefore, heated less. Neptune has rings as well, although they are full of clumps. There is some material between the clumps. One hypothesis is that the material in the clumpy rings is from a moon that was relatively recently torn apart by the tidal gravitational force of Neptune. As in the case of Uranus, Neptune’s magnetic eld is offset from the center of the planet and tilted by 55 degrees relative to the rotation axis, which is odd. But Neptune’s rotation axis is tipped by only 30 degrees relative to the perpendicular to its orbital plane.
  • 165 We don’t really know what causes this offset magnetic eld, but it may be due to a circulation of charged particles—that is, currents—in a shell around the rocky, icy core of both Uranus and Neptune. Neptune has a notable moon, Triton, which is larger than our own Moon and has a thin nitrogen and methane atmosphere. Triton moves backward around Neptune, whereas its other moons orbit in the same general direction as Neptune’s orbit around the Sun. This may indicate that Triton did not form out of a disk of gas from which Neptune itself formed; rather, Triton was probably another body captured by Neptune long ago. The capture probably occurred in such a way as to initially give Triton an elliptical, highly eccentric orbit around Neptune. (Tidal forces later made the orbit become circular.) This initially eccentric orbit means that Triton should have been subjected to large variations in the tidal forces; its interior was initially molten. Thus, there could be signs of activity on its surface. Indeed, Voyager’s images of Triton captured some signi cant features, such as a series of depressions about 30 kilometers in diameter, crisscrossed with various ridges, possibly faults similar to fault blocks on Earth. Triton’s surface also shows dark streaks thought to be the result of icy volcanoes that may spew nitrogen gas from below the surface. “It really does look like Neptune’s moon, Triton, had a geologically active history in the relatively recent past.” An image of Triton, Neptune’s largest moon. NASA
  • 166 Lecture32:UranusandNeptune,theSmallGiants Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What fraction of its orbit has Neptune traversed since it was discovered and since it was last seen by Galileo? 2. Compare the rings of Jupiter, Saturn, Uranus, and Neptune. 3. Given that we have already learned so much about the Jovian planets with un-crewed spacecraft, should we next send humans to them, or do you think using un-crewed spacecraft and robots (such as the Spirit and Opportunity rovers on Mars) makes more sense? Suggested Reading Questions to Consider
  • 167 Pluto and Its Cousins Lecture 33 “Pluto is named after the brother of Jupiter and Neptune, the Roman god of the underworld. That’s kind of appropriate because Pluto is way out there. Moreover, the god of the underworld had this ability to render himself invisible for some periods of time; so that’s really an appropriate name.” F or more than 75 years, the ninth known planet was Pluto, an odd body that is actually a member of a much larger cloud of incipient comets. It was recently (in August 2006) demoted to the status of a dwarf planet, rather than a genuine planet. The existence of Pluto, originally known as “Planet X,” was suspected because of an apparent discrepancy between the observed and predicted orbits of Uranus, even after taking Neptune into account. The additional planet would gravitationally affect the orbit of Uranus, and Percival Lowell made detailed calculations about its probable location. Clyde Tombaugh, a 23-year-old amateur astronomer, was hired by the Lowell Observatory in 1929 to search for Planet X, long after Lowell’s death (1916) and despite the fact that some previous astronomers elsewhere had failed to nd the planet. He used a blink comparator to discover Pluto in 1930, close to the position predicted by Lowell. He compared two photographs taken a week apart and noticed that one faint object had moved substantially, indicating that it was not a star. However, it is now known that Pluto’s mass is far too small to have produced the perceived discrepancy in Uranus’s orbit. Moreover, the discrepancy wasn’t real: The wrong mass had been assumed for Neptune when predicting the orbit of Uranus. Thus, Pluto just happened to be in the predicted part of the sky! Tombaugh was lucky, but he was also a skillful and thorough observer; Pluto was a very faint dot among tens of thousands of stars in the photographs that he examined. Pluto is named for the Roman god of the underworld, the brother of Jupiter and Neptune, able to make himself disappear or remain hidden for long periods of time. The name was suggested by an 11-year-old British schoolgirl, Venetia Burney. The name Pluto begins with the letters PL, and can be thought of as a tribute to Percival Lowell. Because it has an eccentric
  • 168 Lecture33:PlutoandItsCousins orbit (eccentricity 0.25), Pluto actually comes closer than Neptune to the Sun for 20 years of its 250-year orbit. This happened most recently during 1979– 1999. The relative tilts in the orbits of Pluto and Neptune, together with the fact that Neptune orbits the Sun three times for every two of Pluto’s orbits (a 3:2 resonance), prevent the collision of the two planets; they are never in the same place at the same time. Pluto’s semimajor axis is 40 AU, and because of this distance, its features are dif cult to view, even with the Hubble Telescope. The determination of Pluto’s mass and radius was made possible with the 1978 discovery of Pluto’s moon— Charon—that orbits Pluto in 6.4 days, the same time it takes Pluto to rotate on its own axis. Because Pluto’s axis of rotation is 120 degrees relative to the perpendicular to its orbital plane, occasionally, Pluto and Charon eclipse each other as viewed from Earth. This happens twice every 250 years for a 6-year period each time. By measuring these eclipse cycles, we can determine the masses and radii of Pluto and Charon. Charon is nearly half the diameter of Pluto; therefore, some astronomers have suggested calling it a double planet. Pluto is 1/500 the mass of Earth and about 1/5 of Earth’s radius. Before it was discovered, Lowell had predicted Pluto to be 6.6 times the mass of Earth, thereby earning it planet status. In 2005, two additional moons of Pluto—Nix and Hydra—were discovered, but those moons are very small compared with Charon. Pluto is a mixture of ice and rock, unlike the terrestrial planets (mostly rocky with an iron core) and the giant planets (mostly liquid with gaseous outer regions). Because it doesn’t seem to t with the other planets in our Solar System, astronomers began to wonder if Pluto should be considered a planet at all. To further understand Pluto’s characteristics, we must look at Trans- Neptunian objects (TNOs) in the Kuiper belt. In 1951, Gerard Kuiper “For a long time, people didn’t know about the KBOs that are scattered way out of the plane because people didn’t look outside the plane of the other planets orbiting the sun; everyone just looked in the ecliptic. But if you scan the sky far away from the plane, you can come up with unexpected objects.”
  • 169 suggested the existence of a swarm of icy, rocky bodies orbiting at and beyond Neptune’s orbit, which he thought was the source of some short- period comets. At least two other astronomers had previously postulated the presence of such a region, but it is now known as the Kuiper belt. Ironically, Kuiper didn’t think there were many objects in this belt. In 1992, astronomers found the rst Kuiper-belt object (KBO) by taking very deep photographs of the sky—deep meaning that they enabled observation of faint objects. A series of photographs of the same part of the sky over the course of one night or several nights can record the potential movement of any KBOs, indicating that an object is something other than a star. More than 1000 KBOs, most of them quite faint, have been discovered. Many of them have a 3:2 resonance with the orbit of Neptune—that is, Neptune orbits three times for every two times that the KBO orbits. Others have a 1:2 resonance or no resonance. Some KBOs travel far beyond most of the others, which could mean that they were scattered (gravitationally ung) to eccentric orbits; they are not con ned to the plane of our Solar System. Some KBOs are quite large, such as Quaoar, discovered in 2002, which is somewhat over half the size of Pluto. Other KBOs at least half the diameter of Pluto have also been found. Many KBOs, especially the large ones, have moons. Another odd KBO, called 2003 EL61 (and nicknamed “Santa”), is oblong and spins about its axis in just 4 hours. This object is thought to be mostly a rocky system, but its high re ectivity (albedo) suggests that it has a crust or a thin layer of ice that re ects much of the incoming sunlight. Its oblong shape, high albedo, and rapid spin might be attributable to a collision with another KBO. Perhaps even its two moons were produced during the collision. An illustration of Quaoar’s orbit. NASAandA.Feild(STScI)
  • 170 Lecture33:PlutoandItsCousins In 2005, a KBO was found that is 10% to 30% larger than Pluto itself. Initially given the formal designation 2003 UB313, it was informally known as Xena until August of 2006, when it was of cially named Eris, after the goddess of chaos and strife. It has a semimajor axis of 97 AU and has a highly eccentric orbit that is tilted 45 degrees relative to the plane of the Solar System, dwar ng Pluto’s already strange inclination of 17 degrees. It even has a moon, nicknamed Gabrielle until it was of cially named Dysnomia, after the daughter of Eris and the spirit of lawlessness. Some astronomers believe that Eris should be designated our Solar System’s 10th planet. Many if not most astronomers would not call Pluto or Eris genuine planets because they are both part of a swarm. Indeed, in August 2006, Pluto was demoted to a dwarf planet. We will discuss this in further detail in the next lecture. Sedna, another bizarre rocky, icy body, was discovered in 2003 and named for the Inuit goddess of the ocean. Sedna’s orbital period is 11,000 years, and the orbital plane is tilted 12 degrees to the plane of the Solar System. Right now, it is 90 AU from the Sun, but it has an eccentric orbit, at times reaching a distance of about 1000 AU from the Sun. Probably not a true KBO, Sedna could be the innermost scattered member of the more distant Oort cloud, in a sense, an escapee from the Oort cloud. The discovery of Sedna suggests that at least the innermost part of the Oort cloud is within our realm of exploration. Kuiper belt: A reservoir of perhaps millions of Solar-System objects, orbiting the Sun generally outside the orbit of Neptune. Eris and Pluto are the two largest known Kuiper-belt objects, though some astronomers consider them to be planets. Beatty, Peterson, and Chaikin, The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. Important Term Suggested Reading
  • 171 McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Compare Pluto to the terrestrial planets and the Jovian planets. Consider as many physical properties as you can. 2. What are Kuiper-belt objects, and how is Pluto thought to be related to them? 3. What fraction of Pluto’s orbit has Pluto traversed since its discovery in 1930? Questions to Consider
  • 172 Lecture34:AsteroidsandDwarfPlanets Asteroids and Dwarf Planets Lecture 34 “The Kuiper-belt objects (KBOs) constitute a swarm of planetary debris. The asteroid belt is a similar family of small bodies. How do these objects call into question the de nition of a planet?” W e begin with a look at asteroids. Based on an empirical description of the planets’ spacing, a planet was expected to exist somewhere between Mars and Jupiter, in addition to those already known. Thus, astronomers searched the skies for such a planet and discovered the asteroid Ceres in 1801. For a short time, Ceres was called a planet. However, within a few years, several more asteroids were discovered. Moreover, it was realized that Ceres is very small, much smaller than Mercury. Ceres and its brethren were subsequently designated asteroids or minor planets (which were not considered true planets). There are several hundred thousand known asteroids, the four largest being Ceres, Pallas, Vesta, and Hygiea. About 5000 new ones are discovered each month. It is estimated that there are 1 to 2 million asteroids with diameters greater than 1 kilometer and even more with diameters less than 1 kilometer. Together, all of the asteroids have a mass smaller than that of our Moon. Asteroids come in three main types: the stony, rocky ones made of silicates; iron-nickel ones, which are dense; and carbon-rich asteroids. Asteroids probably came from bodies that had tried to form planets, and some became partially differentiated; that is, the iron core sank to the middle, as on Earth, with rocky regions surrounding the core. Jupiter’s gravitational force likely caused the various newly forming bodies to have more eccentric orbits, thereby causing violent collisions that tended to break these bodies apart. Asteroids are ancient objects that might provide clues to the origin of the Solar System and the formation of planets. Not all asteroids are con ned between the orbits of Mars and Jupiter.Afamily of so-called Trojan asteroids occupies the same orbit as Jupiter—about 5 AU from the Sun—but they are 60 degrees away from Jupiter, as viewed from the Sun, in both the east and west directions. Jupiter forces objects to
  • 173 congregate at these locations. Some asteroids have orbits that bring them fairly close to Earth; they are called the near-Earth asteroids. Spacecraft have visited a few of them, and one even crash-landed on the asteroid Eros. As in the case of KBOs, some asteroids have moons, such as Ida and its diminutive moon Dactyl. Collisions can shape asteroids, and some have been shattered by collisions; these are no longer solid objects but rubble piles, rather loosely held together by gravity. Another class of objects, neither asteroids nor KBOs, is called centaurs, which occupy the space between the orbits of Saturn and Neptune. Chiron, the rst known centaur, was discovered in 1977. We believe they escaped from the Kuiper belt, but no one is certain. Our study of asteroids, KBOs, and centaurs leads us to consider the interesting question: What is a planet? A more concrete de nition for a planet would be easier to articulate if there were no objects in the gray area: KBOs, asteroids, and centaurs. Part of the reason why the rst known asteroid, Ceres, was demoted from planethood is that several asteroids were discovered in a relatively short amount of time. They share similar characteristics that were easy to classify over the short time span of their discoveries, without having to give them planet status. Pluto, on the other hand, was known for more than 70 years before other similar objects were discovered. The KBO Eris is larger than Pluto; thus, technically, Eris should be called a planet if Pluto were a planet. After the discovery of Eris, many astronomers argued that Pluto is simply another KBO and shouldn’t deserve planet status. If astronomers had known how small Pluto was at the time of its discovery and had other KBOs been discovered near the same time, Pluto would likely not have been given planet status. What characteristics might constitute a planet? Perhaps a planet should be an object that is larger than 300–400 kilometers in diameter, thus achieving a relatively spherical shape due to its suf ciently strong gravity, and is itself not orbiting another body (the Sun excluded). We know of at least seven “planets” among the asteroid belt larger than 300 kilometers in diameter, in addition to at least six KBOs that qualify as planets by the above de nition. Probably many “Remarkably, astronomers don’t have a consistent, well-de ned, generally accepted de nition for what a planet is.”
  • 174 Lecture34:AsteroidsandDwarfPlanets more KBOs at least this large will be found in the next few years. Even 2003 EL61 (“Santa”), which is oblong shaped, would qualify because its odd shape is caused by its rapid rotation. If it didn’t rotate so quickly, it would be spherical. Thus, we would have at least 14 additional planets. In August 2006, the International Astronomical Union (IAU) met in Prague for its triennial meeting. How to de ne a planet had been a growing issue ever since the discovery of the rst KBOs. An initial proposal at the 2006 meeting de ned a planet as follows: It primarily orbits the Sun and is roughly spherical, and the center of mass in a binary system has to be outside the primary object’s surface (otherwise, it’s a moon, not a planet). A counterproposal reached only on the last day of the 10-day conference replaced the center-of-mass criterion with the idea that a planet gravitationally clears its path. Although the IAU has almost 10,000 members, only about 400 astronomers were still in attendance by the time the de nition came to a vote. The de nition sanctioned by the IAU in August 2006 was technically awed. Even many genuine planets, such as Neptune, Jupiter, Mars, and the Earth, have not gravitationally cleared out their respective paths, though each is dynamically dominant (that is, has by far the largest mass) within that path. The de nition offered no guidance about other solar systems, much less planetary objects that have escaped from their planetary systems or planets that formed in the absence of a sun. The de nition did not preclude nuclear fusion from having occurred; that is, it did not even preclude stars. The term dwarf planet was offered as a double noun, but it sounded, confusingly, like an adjective plus a noun. A term such as mesoplanet (coined by Isaac Asimov) might have been clearer. Pluto’s demotion makes sense, scienti cally. Changing the classi cation of objects based on new knowledge is part of the process of science. Nevertheless, a large number of astronomers are upset with Pluto’s demotion, regardless of whether it is primarily a KBO. They are also unhappy with the voting process that was used or with the technical details of the new de nition of a planet. It would not be surprising if the demotion were overturned in the next few years. At the very least, a more rigorous de nition of a planet will probably be formulated.
  • 175 We conclude our discussion of asteroids and minor planets with a look at meteoroids. Meteoroids are chunks of asteroids that have broken off from asteroid collisions. They could also be material left over from the formation of the Solar System that didn’t happen to be in the family of asteroid orbits or other centaur-type orbits. Most meteoroids are small (less than 10 meters) and have random trajectories. Some of them come from disintegrating comets. When meteoroids enter Earth’s atmosphere, they slow down because of friction. As they enter the atmosphere, they heat up and the air in front of them is so compressed that they simply disintegrate. We sometimes call meteors “shooting stars” or “falling stars,” though they have nothing to do with stars. A meteoroid that penetrates the atmosphere is called a meteor—that’s the visible phenomenon—and, in some cases, is large enough to land on Earth. Those that do land are called meteorites. Many meteorites are found in Antarctica, but only because such rocks stand out on the ice of Antarctica, as opposed to those that land in places where we expect to see rocks. Chemical analysis can tell us about their origins. A few came from the Moon and from Mars. At 4.6 billion years old, many meteorites are among the oldest objects known in the Solar System—even older than rocks found on the Moon. They are thought to be primitive remains from the birth of the Solar System. meteoroid: An interplanetary rock that is not in the asteroid belt. minor planets: Asteroids. Some astronomers now reserve this term for the largest asteroids and Kuiper belt objects. nuclear fusion: Reactions in which low-mass atomic nuclei combine to form a more massive nucleus. Bell and Mitton, eds., Asteroid Rendezvous: NEAR Shoemaker’s Adventures at EROS. Important Terms Suggested Reading
  • 176 Lecture34:AsteroidsandDwarfPlanets Hutchison and Graham, Meteorites. Kowal, Asteroids: Their Nature and Utilization. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Asteroids are among the oldest, most primitive objects known in the Solar System. However, given that there are three main types (stony, iron-nickel, and carbon-rich), is it fair to say that all asteroids consist of original, completely unprocessed (raw) material? 2. Now that many objects, some of them quite large, have been discovered in the Kuiper belt, do you think Pluto should still be called a planet? 3. Do you think Ceres would have retained its planetary status all the way until the 21st century, as Pluto did, if other asteroids had not been discovered shortly after the discovery of Ceres? 4. What is the physical nature of a shooting star or falling star? Questions to Consider
  • 177 Comets—Gorgeous Primordial Snowballs Lecture 35 “ ‘Comet’ comes from the Greek aster kometes, which means ‘long- haired star.’ To the Greeks, it appeared that these were stars that had these beards, or mustaches, or hair sticking out from them.” I n addition to the planets of the Solar System, there are various nomads, such as the KBOs, asteroids, centaur-type objects, and random meteoroids. Let’s now look at comets. Comets appear as diffuse, luminous patches in the sky, sometimes with long tails that can stretch over many tens of degrees in the sky. Really bright comets appear only about once per decade. Comets are what we might call dirty snowballs that evaporate as they approach the Sun. Sunlight and the solar wind push the comet’s gases away, which in turn, re ect the sunlight, forming the comet’s tail. Comets vary in their ice and rock composition, but some ice is present in the form of water-ice, carbon dioxide, ammonia, methane, and other substances. The evaporated gases are pushed away from the comet by the Sun’s radiation pressure—the photons—and by electrons, protons, and atomic nuclei in the solar wind. The evaporating gases re ect light to form the tail, which always ows in a direction away from the Sun, regardless of whether the comet is approaching the Sun or moving away from it during the comet’s trajectory. A comet usually has two tails, a dust tail and an ion tail. The ion tail consists of charged particles—ions—coming from the nucleus, pushed away by the solar wind at a very high speed. The ion tail tends to be long and straight. The dust tail consists of particles that are heavier than ions, so they lag behind and curve away. Periodic comets circle the Sun once per orbital period. According to Kepler’s second law (equal areas are swept out in equal times), periodic comets spend less time near the Sun and more time away from it. Comets are only about 10–11 of the Sun’s mass. Each time one passes near the Sun, it loses a little bit of that mass. For example, Halley’s Comet loses mass every 76 years, when it comes around the Sun. It will take some tens of thousands of years before it disintegrates. Short-period comets (less than about 200 years) in the plane of the Solar System come predominantly from
  • 178 Lecture35:Comets—GorgeousPrimordialSnowballs the Kuiper belt. Collisions and gravitational interactions among objects in the Kuiper belt occasionally send comets careening toward the Sun. Others might escape from the Solar System. Large planets, such as Jupiter and Saturn, can alter these comets’ orbits, capturing them and turning their initially long periods into short ones. Longer-period comets are believed to arise from the Oort cloud, some 50,000 AU from the Sun. If a planet does not alter the trajectory of such a comet, it will pass by the Sun before disappearing again. Sedna, as we discussed in the previous lecture, could have been a comet that was altered by a passing star and sent into a much shorter-period orbit. Spectra of comets show that some contain many organic compounds. If they crashed into Earth early in its history, they may have brought some of the organic compounds that later provided the seeds for life on Earth. Water on Earth may have come largely from comets. Comets are made of primitive, cold material whose properties were not affected by planet formation. They therefore offer clues to physical conditions in the early Solar System, and we are very interested in studying them. The Stardust mission visited the Comet Wild 2 in 2004 and collected dust particles. Some of these particles turned out to be large, a few hundred micrometers in diameter. Another way to study comets is to force collisions. On July 4, 2005, a projectile from the spacecraft Deep Impact collided with a comet called Tempel 1. The collision excavated some material, which could then be studied by cameras and spectrometers aboard the satellite. Before the impact, the comet had already experienced outbursts of activity, during which chunks broke off. The data are still being analyzed, but the comet’s density and size were determined. Its density is so low that it must be at least 75% empty space; it is porous like a sponge. Studies also found comparatively little water in this comet but a fair amount of organic compounds. We can also study the breakup of comets in a natural way—that is, not by hitting them with a projectile. As a comet breaks up on its own, we can study the spectra of its constituent pieces to nd out what they are made of. “We don’t know how much of today’s water came from comets, but certainly at least some of it probably did.”
  • 179 When a comet breaks up, a swarm of particles can intersect the Earth during its trajectory around the Sun, causing a meteor shower. As we said in the previous lecture, we often see sporadic meteors. But occasionally, we notice that several meteors appear to come from a particular area in the sky. Meteor showers occur when Earth passes through the debris of a long-dead or still- disintegrating comet. This happens at the same time each year for a given shower. During a shower, the meteors appear to come from a common point in the sky, known as the radiant. This is the vanishing point of the essentially parallel trajectories of the individual chunks of debris. The Leonid meteor shower occurs in November, with the individual meteors coming from the direction of the constellation Leo. The Perseids come from the direction of the constellation Perseus in August. A weak meteor shower occurs when Earth passes through a part of the comet’s orbit that doesn’t have much debris. But every 33 years or so, thanks to Comet Temple-Tuttle, the Leonid meteor shower turns into a meteor storm. This occurs when Earth intersects the comet’s orbit near its head, where a clump of debris still remains. There was a spectacular Leonid meteor storm in 1966 and a minor Halley’s comet. NASA
  • 180 Lecture35:Comets—GorgeousPrimordialSnowballs one in 1999. In 1833, Earth traveled through a large clump of Temple-Tuttle’s debris, leading people to believe that the sky was literally falling. In general, most comets and meteoroids are nothing to worry about. However, as we will see in the next lecture, occasionally, there are meteoroids or comets that we do have to watch out for: They are on a collision course with Earth. Beatty, Peterson, and Chaikin, The New Solar System, 4th ed. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Use Kepler’s third law and the known orbital period of Halley’s Comet (about 76 years) to deduce its semimajor axis. Which planet has a comparable semimajor axis? 2. What creates the tail of a comet? Is something chemically burning? 3. How far is the Oort comet cloud from the Sun relative to the distance from the Sun to Pluto? 4. Why might some meteor showers last only a day while others can last several weeks? Suggested Reading Questions to Consider
  • 181 Catastrophic Collisions Lecture 36 “You’d need a really massive object hitting us really hard to cause the Earth to break apart. That’s not going to happen. But the crater that forms, the dust thrown into the atmosphere, the res that result, and everything else can cause much of life on Earth to be extinguished—so you have to watch out.” S ome groups of asteroids, called near-Earth asteroids, have orbits that cross Earth’s orbit. In the prehistoric past, they have hit Earth, causing signi cant destruction and at least one mass extinction. The Apollo asteroids are the best known; we know of about 2000 relatively large Apollo asteroids (greater than 100 meters in diameter). Icarus is an example of an asteroid that crosses Earth’s orbit, but usually an asteroid and Earth are not at the same place at the same time. The Barringer meteor crater in Arizona is about 1 kilometer in diameter and was formed by the impact of an iron- rich meteorite—perhaps only 50 meters in diameter—about 50,000 years ago. The Tunguska event was recorded in 1908 in Siberia, where an object might have broken up in Earth’s atmosphere before actually hitting the surface. It leveled 2000 square kilometers of forest with an estimated force of the equivalent of 15 megatons of trinitrotoluene, TNT. For comparison, the largest hydrogen bomb ever exploded had an energy of 60 megatons. Throughout the Moon’s early history, mostly in the rst few hundred million years, meteorites have pockmarked the surface. Most of the resulting craters have been preserved; there is little erosion. As a result of erosion on Earth, craters tend to be obliterated after a relatively short time, though we do know of about 180 craters on Earth that have survived. When a meteorite hits Earth, the material surrounding the point of impact is vaporized. Material at a greater distance from the impact is excavated, creating the crater, which is always much bigger than the meteorite itself. For example, a 1-kilometer projectile hitting Earth could form a crater 10 or 20 kilometers in diameter, depending on the projectile’s composition and speed. We know of more than 800 near-Earth asteroids whose size is greater than 1 kilometer, though we think that the total is about 1100. We expect a
  • 182 Lecture36:CatastrophicCollisions meteoroid of this size to collide with Earth every million years or so; the explosive energy released would be equivalent to about 105 to 106 megatons of TNT. Smaller meteoroids (with diameters greater than 100 meters) could also collide with Earth, and we know of perhaps 100,000 of them. We would expect a collision with a smaller meteoroid to occur every 10,000 years or so, producing an explosion equivalent to 102 to 103 megatons of TNT. Even smaller blasts, like the Tunguska event of 1908, happen roughly every 1000 years, or maybe even every few hundred years, on average. Given that Earth stands to collide with meteoroids and comets, should we be worried? Statistically, averaged over 100 million years, we are as likely to die from a cosmic collision as from an airplane crash, a ood, or a tornado. An Earth impact from a meteoroid larger than 10 kilometers in diameter could cause the end of human civilization. An object of this size would produce an energy equivalent of about 108 to 109 megatons of TNT. Such a collision and the subsequent ery aftermath would lead to what is called an impact winter. So much dust would ll the atmosphere that sunlight would be prevented from reaching Earth’s surface. Temperatures would plummet, The Barringer meteor crater in Arizona. ©Jupiterimages/Photos.com/Thinkstock
  • 183 killing plants, then herbivores, and eventually, those at the top of the food chain. The atmospheric particulates would eventually come down as acid rain. Elevated levels of carbon dioxide in the atmosphere would cause high temperatures for up to thousands of years—the greenhouse effect. Some scientists believe that mass extinctions, regardless of their cause, are periodic, resulting in the destruction of life on Earth roughly every 62 million years. The evidence for periodic impacts of large objects is not very strong. As far as we know, such impacts are fairly random, but the average is every 100 million years or so. The last large extinction that we know of—the Cretaceous/Tertiary (K/T) extinction 65 million years ago—was probably caused by a cosmic collision with an object greater than 10 kilometers in diameter, killing the dinosaurs and other life on Earth at the time, including small marine creatures called foramonifera. Fossil records show the sudden death of two-thirds of all living species on Earth during the K/T extinction and an abundance of iridium in the Earth strata from that era. Iridium is attracted to iron, and when Earth was young and molten, iridium attached itself to iron, which sank to the Earth’s core during the process of differentiation. Thus, Earth’s surface layers are relatively de cient in iridium. But when a celestial body collides with Earth, dispersing its material over the surface, a thin layer with an anomalously high concentration of iridium will appear. The probable impact site of the K/T extinction event was found off the coast of the Yucatan peninsula, called the Chicxulub crater. It is now covered by 500 meters of sediment, although through measurements of the local gravity, we know there is a deformation there. The crater has been dated to 65 million years. The crater is about 200 kilometers in diameter, comparable to what would have been produced by a comet with a diameter of 10 or 20 kilometers hitting the Earth. Evidence of huge tsunamis along the Gulf Coast 65 million years ago further supports the hypothesis for this impact crater. In addition, there are vast deposits of charcoal from forest res at around that time. Recent cosmic collisions demonstrate that such events can be predicted, as in 1994, when Comet Shoemaker-Levy 9 collided with Jupiter. Over the course of a week, about 20 comet fragments hit Jupiter, releasing an estimated equivalent of 40 million megatons of TNT. Some of the
  • 184 Lecture36:CatastrophicCollisions individual comet fragments had energies of up to 6 million megatons of TNT, equivalent to about 100,000 of the most powerful nuclear weapons ever made by humans. The amount of energy released was determined largely through studies at infrared wavelengths. We were able to study how the shape of the ejected debris from the impacts changed over time, giving us information about Jupiter’s atmospheric currents. In addition, spectra of the impacted areas showed molecular sulfur, carbon disul de, ammonia, and other molecules that were excavated from underneath Jupiter’s surface, providing information about the planet’s composition. The impact with Jupiter gave scientists additional impetus to nd all large objects that might hit the Earth. The pace of discovery of Earth-crossing asteroids is rapidly increasing for those objects less than 1 kilometer in diameter but leveling off for those greater than this size. Though we don’t know of any imminent threat, Earth has experienced some relatively close calls. In July 2006, an Apollo asteroid came within 270,000 miles of Earth—only 1.1 times the Moon’s distance from Earth. Toutatis, a well-known asteroid 4.6 kilometers long, came within four lunar distances in 2004. By studying the trajectories of celestial objects, astronomers can predict when Earth is likely to experience a collision. If we know such information, we could send spacecraft to de ect the threat. Perhaps such a threat might even unify the nations of Earth to work together, rather than ghting among ourselves. Alvarez, T-Rex and the Crater of Doom. Chapman and Morrison, Cosmic Catastrophes. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. “Maybe what we really need is a wakeup call to get all of us to unify behind a common cause—that is, saving all of humanity rather than ghting amongst ourselves all the time.” Suggested Reading
  • 185 Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Verschuur, Impact! The Threat of Comets and Asteroids. 1. Do you worry about asteroid or comet collisions with Earth? What could be done to save the Earth if an asteroid were discovered suf ciently far in advance of the collision? 2. Can you argue that the presence of humans on Earth may have impeded the rise of some other animal to a position of great prominence? 3. Some scientists have suggested that the dinosaurs were about to become extinct anyway, without an asteroid or comet collision, because of changes in Earth’s climate and for other reasons. If so, does this detract from the impact theory, in view of evidence that two-thirds of all species perished quite suddenly during the K/T extinction and a large crater having the right age has been found? Questions to Consider
  • 186 Lecture37:TheFormationofPlanetarySystems The Formation of Planetary Systems Lecture 37 “We think that most planetary systems formed in about the same way. Although the words ‘solar system’ are technically reserved for our own Solar System, people loosely call other planetary systems ‘solar systems’ as well.” I n this lecture, we discuss the formation model not only for our own Solar System but for others, as well. We think that most planetary systems formed in roughly the same way. Our Solar System has two main characteristics: All the planets orbit the Sun in the same direction, and most of them rotate about their rotation axes in that same direction and with an axis roughly perpendicular to the plane of the Solar System. The Sun also rotates about its axis in the same direction. The Solar System looks like a thin disk, and most of the planets are nearly in the same plane, though they are tilted relative to one another. This thin, spinning disk suggests that our Solar System arose from a rotating structure that may have contracted and formed regions where material accumulated into planets. In such a nebular hypothesis, initially there is a gravitationally contracting, slowly spinning cloud of gas and dust. Occasionally, regions denser than average occur, which become gravitationally unstable and begin to collapse.A passing star can cause the region to rotate somewhat. As the region collapses, its rotation rate increases as the result of a principle called the conservation of angular momentum. Angular momentum (L) is a measure of the total amount of spin of an object or a system: In simple cases, L = mvr, in which L is angular momentum, v is the rotation speed, m is the material’s mass, and r is its size radius. Contracting objects of a given mass become smaller; therefore, the spin rate must increase in order to keep the angular momentum constant. The contracting cloud, in a similar way, spins faster with time. Spinning objects are ung away from the axis of rotation, experiencing centrifugal force, a manifestation of the rotating frame of reference. For example, we feel this force when riding in a car that turns a corner rapidly. Particles feel more centrifugal force as they contract because of their greater
  • 187 spin rate. At some point, they are held back from contracting further because the centrifugal force balances the gravity trying to pull them in. On the other hand, a particle along the axis of rotation doesn’t have any distance from the spinning axis; thus, the total amount of angular momentum is zero, causing that particle to fall. Similarly, particles away from the axis of rotation fall toward the equatorial plane of the spinning cloud, but their inward motion toward the axis of rotation is inhibited by the centrifugal force. In this way, contraction plus conservation of angular momentum leads to a attening of the spinning cloud, eventually forming a disk in which all the particles are balanced and the gravity they feel inward is equal to the centrifugal force outward. Material accumulates in the attened disk’s center, and that, presumably, is where a star (a sun) forms. Is there evidence of this nebular hypothesis? We see a giant cloud of gas and dust in the Orion nebula, where a cluster of young stars has formed as a result of gravitational contraction. We see many such nebulae in our Milky Way Galaxy and in other galaxies. When these giant clouds of gas and dust contract, the cloud can fragment into many smaller units that are denser than average. Each of these units contracts and forms a spinning disk with a central region where a star and planetary system can form. As each of these units contracts, the temperature and pressure rise; the individual particles of gas move more rapidly. Eventually, the outward pressure from the hot, rapidly moving particles nearly balances the inward gravitational force, and the object continues to contract very slowly. It is now called a “pre-main-sequence star.” When the temperature in the center of the pre- main-sequence star becomes suf ciently high, nuclear reactions begin to occur, signaling the birth of a star/sun. It is dif cult to see this process of star formation in detail at optical wavelengths because the gas and dust become opaque if they’re suf ciently dense. However, radio and infrared wavelengths allow us to peer into these central star-forming regions. “Centrifugal force is a ctitious force; it’s not one of the fundamental forces like gravity, or electromagnetism, or the forces that hold the nuclei of atoms together. It’s a force that’s a manifestation of the rotating frame of reference.”
  • 188 Lecture37:TheFormationofPlanetarySystems Many of these star-forming regions show debris around a young star or still- forming star. This debris often has a disk-like shape, called a protoplanetary disk, or proplyd for short. Many young stars deep in the heart of nebulae show debris disks surrounding them, providing good evidence for the nebular hypothesis of planetary formation. In addition, at debris disks are needed to form planets. Eventually, the remaining debris is blown away by the wind from the young star (the solar wind). With the exception of some asteroids and other small debris, the cleared space is relatively empty, forming what we would call a planetary system (solar system). There are many such disks An optical image of the Orion nebula. NASA,ESA,M.Robberto(SpaceTelescopeScienceInstitute/ESA)andtheHubbleSpaceTelescopeOrionTreasuryProjectTeam
  • 189 in which we can see these clumps of accumulating debris. However, not all planetary systems will be alike. Let’s look at how planets form, though many of the details are unclear because we don’t yet know enough about the process. In the early stages of a planet’s birth, we believe, particles begin to clump together and grow in size. Clumps can hit each other and grow even bigger, especially if they’re icy, because ice sticks together better than rock. This may be how the outer giants (Jupiter, Saturn, Uranus, and Neptune) in our Solar System formed. Clumps between 1 and 100 km in size are called planetesimals, or little planets. Once a number of planetesimals have formed, their gravitational in uence on one another brings them together, and they accumulate into bigger structures, forming the core of a planet. Regions suf ciently far from the inner sun are icy and attract other ice clumps, forming large planets. These massive objects can accumulate hydrogen and helium left over in their vicinity. Closer to the center of the attened disk, the sun region, temperatures are higher and ices don’t form. Here, it is harder for objects to stick together and form large cores, such as those in the icy giants. Such gases as hydrogen and helium evaporate or are blown away by the solar wind. These regions of the disk are where we expect terrestrial-like planets to form. Beyond a certain distance from the center of the disk, particles don’t collide with each other frequently enough because of the vast distances between them. This region would be like the Kuiper belt in our Solar System. In our own Solar System, much farther out from the Kuiper belt, is the Oort cloud, which we think was formed by a gravitational slingshot effect caused by the large planets. Similar processes could well occur in other planetary systems, though we don’t yet have any direct evidence. If material comes close to a large planet, it can be ung outward; in the case of the Oort cloud, this material may have been ung generally perpendicular to the plane of our Solar System. We think that Uranus and Neptune contributed more to the Oort cloud than Jupiter and Saturn. There are more icy rocks near Uranus and Neptune than Jupiter and Saturn. Moreover, Jupiter and Saturn have accumulated into their own masses more of the material in their vicinity, whereas Uranus and Neptune are not as massive and likely ejected more material into the Oort cloud.
  • 190 Lecture37:TheFormationofPlanetarySystems Jupiter formed quickly; its gravitational tugging led to collisions among the planetesimals and the asteroid belt that were too energetic to allow them to stick together. Jupiter also cleared out certain parts of the asteroid belt. For example, there were regions of the asteroid belt where a particle orbited two or three times for every one time that Jupiter orbited. This created additional tugging in the same direction, clearing out that region. The cleared region in the asteroid belt is known as the Kirkwood gaps, which are a form of resonance such that a big planet can affect the amount of material in the region by progressively tugging on it. A competing hypothesis for how big planets formed in our Solar System, and perhaps in others as well, is that in a certain region of the disk, the gas collapsed all at once into a giant planet. Currently, however, the evidence for this suggestion is not strong. There are certain impediments to the formation of disks around stars. Some bright stars can emit so much radiation that they effectively evaporate the surrounding cloud of gas and dust. Luminous stars outside of gas clouds can also evaporate those clouds. Another problem is that the spinning cloud must expend angular momentum. We think that the angular momentum is taken away through bipolar out ows, jets of material streaming away from the star perpendicular to the axis of rotation, like spinning bullets shot from a ri e. Though we don’t yet have all the details, we’ve come a long way in understanding at least some of the methods by which stars and their associated planetary systems form. angular momentum: A measure of the amount of spin of an object; dependent on the object’s rotation rate, mass, and mass distribution. bipolar out ow: A phenomenon in which streams of matter are ejected from the poles of a rotating object. Important Terms
  • 191 centrifugal force: The outward force felt by an object in a rotating frame of reference. nebular hypothesis: Theory of the formation of the Solar System, asserting that spinning clouds of interstellar matter gradually contracted and allowed for the formation of the Sun and the planets. planetesimals: Small bodies, such as meteoroids and comets, into which the solar nebula condensed and from which the planets subsequently formed. protoplanetary disks: Also called proplyds; concentrations of matter around newly formed or still forming stars out of which planets may form. Cohen, In Darkness Born: The Story of Star Formation. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Smith, The Origin of Stars. 1. A solitary star that is still forming must expend its angular momentum through the ejection of spinning jets (and, to some extent, by storing it in planets that form in the disk). Is there as much of a problem for a cloud from which a double star forms? 2. Do you expect to nd massive planets, consisting mostly of gases and liquids, in the inner regions of other planetary systems? 3. In what way do the Kuiper belt and the Oort cloud provide clues to the origin and early history of our Solar System? Suggested Reading Questions to Consider
  • 192 Lecture38:TheQuestforOtherPlanetarySystems The Quest for Other Planetary Systems Lecture 38 “Other worlds—what do they look like? Our imaginations run wild. Someday, we hope to have actual pictures of these planets, but it was a challenge just to detect them.” W e have seen ample evidence for the existence of other solar systems, and though nding other planets has been challenging, we have succeeded in doing so. We can say without any doubt that there are planets around many other stars in our Galaxy and, presumably, in other galaxies. We call these extra-solar planets, or exoplanets. We don’t yet have actual pictures of exoplanets because just discovering them was a challenge. The main problem in detecting these planets is that the glare of the star they orbit is so much greater than the amount of light the planet re ects. The key is to measure the slight re ex motion of the star induced by the orbit of a planet around it. Planets do not orbit a perfectly stationary star; the star actually wobbles some in response to the planets’ motions. Two objects, such as a star and a planet, orbit each other around their common center of gravity, or center of mass. The general equation is as follows: The mass of one object multiplied by its distance from the center of mass is equal to the mass of the other object multiplied by its distance from the center of mass, or 1 1 2 2M R M R , in which 1 and 2 simply denote the two objects. This formula applies in general for two objects being held together by their mutual gravitational force, 2 1 2F GM M d , in which M is the mass of each object and d is the distance between them. The star, with its larger mass, orbits closer to the common center of mass than the less massive object, the planet. A very massive star and a relatively low-mass planet will have a common center of mass that occurs nearly at the center of the star itself. This re ex motion can be detected through a series of photographs of the star over the course of time. Measurements of positions of stars and their motion is a sub eld of astronomy known as astrometry. However, no extra-solar planets have been discovered thus far with this technique.
  • 193 Another way to detect re ex motion is to examine the star’s light and search for a periodic shift in the wavelength of the absorption lines in the spectrum. The shift is caused by the Doppler effect, which we discussed in a previous lecture. Remember that a stationary emitter of waves sends out spherical wavefronts with a well-de ned, measurable wavelength. But if an object is moving, the waves in front of it are “squished” (creating a blueshift, or shorter wavelengths) and the waves in back are more elongated (creating a redshift, or longer wavelengths). If we look at a star from our position near the Sun and the star is moving perpendicular to our line of sight, then an absorption line in the star’s spectrum will show no shift. The formula for the Doppler shift is = v/c, in which v is the speed of the object relative to the observer, c is the speed of light, and = ( being the rest wavelength of the line, as measured in a gas at rest relative to the observer, and is the observed wavelength of the line). Application of the Doppler Shift Formula = v/c Given observed wavelength) = 6,565 Å rest wavelength) = 6,563 Å c (speed of light) 3 × 105 km/s Find v (speed of object relative to observer) (shift in wavelength) = – = 6,565 Å – 6,563 Å = 2 Å = 2 Å / 6,563 Å 3 × 10–4 Å v/c = 3 × 10–4 Å v = c(3 × 10–4 Å) (3 × 105 km/s) (3 × 10–4 Å) 90 km/s
  • 194 Lecture38:TheQuestforOtherPlanetarySystems How can we detect exoplanets? If an unseen planet is orbiting a star, the star itself moves, too, because they both orbit their common center of mass. If the star is moving toward us, its spectrum will show a blueshift; if it’s moving away from us, its spectrum will show a redshift. We look for a periodically changing shift of the absorption lines in the star’s spectrum; this is known as the Doppler wobble. If a planet’s mass is large and its distance from the star is small, the planet causes the star to move around the common center of gravity more quickly. If the planet’s mass is smaller, its gravitational in uence is less, and the star moves less—its wobble (re ex motion) is less. The farther apart a star and planet are, the less the star wobbles, too. Knowing the period and amplitude (maximum change in radial velocity) of the Doppler wobble, the mass of the detected planet can be calculated by using Newton’s form of Kepler’s third law. Actually, one gets a minimum mass for the planet, because the inclination of the orbit is generally not known. The measured radial velocity of the star is only part of the total orbital velocity unless the orbital plane is perpendicular to the line of sight (i.e., edge-on). The planets in our Solar System cause our Sun to wobble, and each has a slightly different effect on the Sun according to each planet’s mass and distance from the Sun. Until 1995, we had not found other planets. But using this technique of measuring re ex motion, astronomers have since found about 200 exoplanets. The rst discovery in 1995 was detected by a wobble in what is called 51 Pegasi, a star in the constellation Pegasus. Michel Mayor and Didier Queloz found the planet, and their discovery was quickly con rmed by Geoff Marcy and Paul Butler. Marcy and Butler used the 3-meter telescope at Lick Observatory to measure the spectrum of 51 Pegasi to con rm the results of Mayor and Queloz. The nd was unexpected because the large planet had an orbital period of only 4.2 days, and the re ex motion of the star was about 50 meters per second. Typically, such large planets are much farther from their stars and, therefore, take much longer to orbit. As an example, remember that Jupiter’s orbital period is 12 years, and the Sun’s re ex motion is only about 10 meters per second. The star 51 Pegasi was originally misclassi ed as being not sun-like in its properties, which meant that Marcy and Butler had not included it in their extensive search for companion planets.
  • 195 Among the rst dozen discovered exoplanets, we see some interesting trends. First, they are all massive, ranging in size from half the mass of Jupiter to 10 times Jupiter’s mass. The fact that we are nding only big planets, however, doesn’t mean that there are no smaller planets to be found. Larger planets are simply easier to detect. Second, some of these exoplanets are very close to their respective stars, some even less than 1/10 AU away. Again, these planets are easier to detect because the closer they are to their stars, the greater the stars’ wobble, and the easier it is to detect. Third, some of these exoplanets have very eccentric orbits, not circular like that of 51 Pegasi. A good example is 16 Cygni B. We did not anticipate that so many planets would have such eccentric orbits. These discoveries proved that some of our assumptions about other solar systems were wrong, as we will see in the next lecture. astrometry: Measurement of the position and motion of the stars in the plane of the sky. Doppler shift: The change in wavelength or frequency produced when a source of waves and the observer move relative to each other. Blueshifts (to shorter wavelengths) and redshifts (to longer wavelengths) are associated with approach and recession, respectively. redshift: De ned to be z = ( 0 )/ 0 , where 0 is the rest wavelength of a given spectral line and is its (longer) observed wavelength. The wavelength shift may be caused by recession of the source from the observer or by the propagation of light out of a gravitational eld. rest wavelength: The wavelength radiation would have if its emitter were not moving with respect to the observer. Important Terms
  • 196 Lecture38:TheQuestforOtherPlanetarySystems California and Carnegie Planet Search, www.exoplanets.org. Croswell, Planet Quest: The Epic Discovery of Alien Solar Systems. Dorminey, Distant Wanderers: The Search for Planets beyond the Solar System. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Goldsmith, Worlds Unnumbered: The Search for Extrasolar Planets. 1. Under what conditions can we measure the true mass of an extra-solar planet, not just its minimum mass, with the Doppler wobble technique? 2. Does the Doppler wobble method for deducing the existence of a planet orbiting a star depend on the star’s distance from Earth? (Assume the star’s apparent brightness is independent of distance.) 3. It turns out that the ratio of the speed of a planet to the speed of the star it orbits is equal to the inverse of the ratio of their masses. If Earth orbits the Sun with a speed of 30 km/s, what is the Sun’s corresponding orbital speed (that is, its re ex motion, induced by the Earth’s motion)? Considering this, is the current precision of the optical Doppler techniques (about 1 m/s) close to suf cient for a detection of Earth-like planets orbiting other stars? Suggested Reading Questions to Consider
  • 197 Extra-Solar Planets Galore! Lecture 39 “Quite a few exoplanets have highly eccentric orbits. In our Solar System, the orbits are circular or nearly circular.” A s we saw in the last lecture, many of the exoplanets discovered so far are very close to their central stars and have short orbital periods. These large exoplanets, known as hot Jupiters, range from about 0.3 AU to less than 0.1 AU from the stars they orbit. It is dif cult to understand how such planets could form so close to their stars because these planets have large amounts of gas. Gas tends not to get gravitationally bound to a planet so close to a hot star; the thermal motions of the gas are too fast. Hot Jupiters could have formed farther away from their stars, where conditions were colder. Through gravitational accretion, their iron-rock- ice cores could then gather surrounding gas. Most stars are at least 98% hydrogen and helium. The remaining 2% (or less) is composed of heavy elements, such as iron, carbon, and nitrogen. Stars with more than 2% heavy elements tend to have more exoplanets. Stars with a low percentage of heavy elements tend to not have planets. Both the stars and their exoplanets formed from the same gas and dust. Clouds having relatively large amounts of heavy elements were more likely to form iron-rock-ice cores than those having small amounts of heavy elements. Thus, it seems likely that large Jupiter-like planets rst formed iron-rock-ice cores, accreting more heavy matter until they were gravitationally strong enough to attract hydrogen and helium. One hypothesis is that planets farther out encountered a lot of material, rubbing against it and creating frictional drag. Gradually, the planets spiraled toward their stars. Or the planets could have formed farther out, and gravitational interactions among them sent some careening toward the star in an elliptical orbit. Through tidal effects, the elliptical orbit gradually became circular. Passing stars could also have perturbed some planets that were initially far out, sending them into closer orbits with their stars. Another common trait among exoplanets is that many have highly eccentric (elliptical) orbits, while others have nearly circular orbits. The planets with elliptical orbits tend to be
  • 198 Lecture39:Extra-SolarPlanetsGalore! farther from their stars than those with circular orbits. It’s possible that these planets were relatively close together and interacted gravitationally, with some planets being ejected, while others rebounded with a kick that gave them eccentric orbits. The hot Jupiters that are close in don’t have elliptical orbits because when a planet is close to its star, subtle tidal effects eventually create circular orbits. Let’s take a look at some of the planets that have been found. In 1999, astronomers found a multi-planet system around Upsilon Andromedae, the rst of its kind to be found. Now, about 20 such multiple systems are known. This three-planet system has one planet close to the star, another that orbits as if it were between Venus and Earth, and a third much farther away at 3 AU from the star. Another system, called 55 Cancri, was believed to have three planets until a fourth was discovered in 2004. This star has two planets with a Mercury-like orbit and one big planet roughly where Jupiter would be; the fourth is close to the star, with only a 2.8-day orbital period. Two planets were discovered orbiting the star Gliese 876. They had masses of about 0.6 of Jupiter and 1.9 times Jupiter, with orbital periods of about 30 and 60 days, respectively. In 2005, a third planet was discovered, but it was much smaller than many of the other hot Jupiters we had been nding—only 7.5 times Earth’s mass. Ultimately, we would like to nd planets about Earth’s size and more Earth- like, but this is dif cult using the Doppler wobble technique. How do we nd them? The Doppler wobble technique isn’t suf cient for detecting Earth-like planets because at Earth’s distance from the Sun, Earth induces only a 10 cm/s motion in the Sun—not very fast. The current precision limits for the Doppler technique are about 1 m/s. In addition, certain fundamental properties of stars may inherently limit the precision of the Doppler technique, such as turbulence in the star’s atmosphere causing motions of gas that obscure the tiny Doppler wobble. Another technique used involves planetary transits, as we saw in two previous lectures when we discussed the transit of Venus. Occasionally, a planet will appear to cross the face of its star as seen from Earth. As the planet transits, it will block part of the star’s light, causing the star to dim. We can
  • 199 measure the star’s brightness as a function of time (that is, its light curve) to obtain information on the planet’s size. If rings or moons are present, these may also show up in the light curve. During the transit of a planet around the star HD 209458, an atmosphere was detected around the planet. Photons from the star were absorbed by sodium in the planet’s atmosphere, which appeared as sodium absorption lines in the star’s spectrum. A big planet, such as Jupiter, produces a signi cant dip in the star’s light curve; a small planet, such as Earth, produces a small dip. Earth is 1/109 of the Sun’s diameter, and its area in the sky is about (1/100)2 of the Sun’s disk area. If Earth were to pass across the Sun, the Sun’s light curve would show a dip of about 0.01%. We can detect terrestrial planets around other stars by looking for minute dips of this sort. One problem with measuring small dips is that presumably other stars, like our Sun, have sunspots. As these spots traverse a rotating star, the star will dim or brighten in a non-periodic way. Therefore, a star varies slightly in brightness, regardless of whether a planet traverses its face or not. By monitoring stars over a long time, we would presumably begin to see dips in the light spectra occurring in a periodic way, indicating the presence of a planet, not just spots.Another problem with measuring transits is that the odds of our viewing a planetary transit of a monitored star are only 0.5% Most planetary systems are not viewed suf ciently edge-on. To improve these odds, NASA will launch the Kepler spacecraft in 2009. It will monitor 100,000 stars continuously for four years. Another way to nd planets is by measuring the apparent brightness of stars at infrared wavelengths over the course of time. At infrared wavelengths, we can see the planet’s emitted light; this is the thermal emission from the planet. When a planet moves behind its star, the star blocks some of the planet’s light. If the planet is not blocked by the star, the total brightness of the star plus the planet is greater than when the planet is blocked. “NASA hopes to build an instrument called the Terrestrial Planet Finder, which would be launched sometime between 2020 and 2030, to take images of terrestrial [exo]planets.”
  • 200 Lecture39:Extra-SolarPlanetsGalore! A nal way to detect planets is through gravitational microlensing. To understandthistechnique,recallthattheSunbendslightbecauseofthewarping of space and time. If a star comes between Earth and a background star along our line of sight, a focusing (lensing) effect occurs of the star’s light onto the Earth—the background star appears slightly brighter than it would in the absence of the passing star and its planet. When the planet is perfectly aligned with the background star and Earth, a temporary spike—a short brightening— of the background star’s light occurs because of the microlensing effect of the planet. In 2005, a planet was detected for the rst time using this gravitational microlensing technique. The planet is only 5 times the mass of Earth, even lower than the least massive of the planets discovered by the Doppler wobble technique. light curve: A plot of an object’s brightness as a function of time. planetary transit: The passage of a planet directly along a star’s line of sight, causing a momentary dimming of the star’s light; can be used to detect planets in other solar systems. California and Carnegie Planet Search, www.exoplanets.org. Dorminey, Distant Wanderers: The Search for Planets beyond the Solar System. Goldsmith, Worlds Unnumbered: The Search for Extrasolar Planets. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What are the pros and cons of the different techniques used (or potentially used) to detect and study extra-solar planets? Important Terms Suggested Reading Questions to Consider
  • 201 2. If a transiting exoplanet has 10% of the diameter of the star it orbits, by what percentage will the observed brightness of the star decrease during the transit? 3. How would you expect the radial velocity of a star to change with time if more than one exoplanet orbits it?
  • 202 Lecture40:LifeBeyondtheEarth Life Beyond the Earth Lecture 40 “Headlines like, ‘The Birth of Planets’ and ‘Scientists Discover New Solar Systems and Rethink the Odds of Life Beyond Earth,’ appear on national magazines because this is the kind of stuff that excites the public’s attention.” T he recent discovery of exoplanets has rekindled our question of whether life exists beyond planet Earth. To reduce speculation, we will restrict our attention to life as we know it. The emerging eld of astrobiology or exobiology is the pursuit of nding life elsewhere. Vast numbers of galaxies exist beyond the Milky Way, each possibly containing up to 300 to 400 billion stars like our own and planets where life forms could thrive. Life, as we de ne it, must consist of organic compounds. Organic compounds are chains of carbon with hydrogen on the side and occasional molecules of oxygen and nitrogen. We call these amino acids. Long chains of amino acids form proteins, and although hundreds of thousands of such proteins are possible given the various combinations, life on Earth appears to select a relatively small number of proteins. Living organisms have a genetic code that is contained in deoxyribonucleic acid, or DNA, the famous “double helix” and the key to life. We don’t really understand how DNAformed, but we do know that it is an extremely long and complex structure built to self-replicate and evolve through mutations. [Note: During the lecture, it was erroneously stated that DNA is a protein. Actually, DNA consists of nucleotide bases, not amino acids, with a backbone of phosphates. DNA requires proteins to function, and proteins require DNA to form.] In order for DNA to form proteins, organic compounds must be made. Laboratory experiments have replicated the formation of organic compounds for the simplest amino acids. The most famous experiment, conducted in 1953 by Stanley Miller and Harold Urey, used water vapor, methane, ammonia, and hydrogen—at one time, thought to be the constituents of Earth’s primitive atmosphere. However, we now know that Earth’s primitive atmosphere was
  • 203 mostly carbon dioxide and nitrogen molecules, without much methane and ammonia. In replicating the experiment using nitrogen and carbon dioxide, amino acids are not produced. The experiment, however, was important for demonstrating that complex molecules can form under not-so-farfetched conditions. Such conditions may have existed around some exoplanets or the moons of exoplanets. We know that the formation of amino acids is not that complex because simple amino acids have been found in some carbonaceous meteorites. We also nd amino acids in comets. How, then, was life rst formed? How did cells arise? We don’t know exactly, but we do know that primitive life—microbes and bacteria—must have arisen quite early in Earth’s history. Earth is about 4.6 billion years old, but for at least the rst half billion years or so, it was still pummeled by space debris (planetesimals), making conditions too harsh for life to exist. There is fossil evidence for life (in the form of cyanobacteria called stromatolites) from 3 billion years ago, and 3.5-billion-year- old evidence for cellular life, though this is still controversial. There is also chemical evidence from 3.8 billion years ago for some forms of life. If life arose in a simple manner on Earth, perhaps it could also arise on moons and planets orbiting other stars in galaxies. We could argue that conditions on Earth were “just right” for life to form. However, there are many places on Earth where conditions vary drastically and where life exists without seeming to have derived its energy from the Sun, such as geothermal vents deep under the ocean surface. The thermal features of Yellowstone National Park contain bacteria that exist in extremely high temperatures and acidic conditions. Algae exist beneath the surface of Antarctic rocks, thriving on hydrogen generated by a chemical reaction between water and iron silicates in the volcanic rock. Conditions may have been similar on Mars. It is estimated that up to half of the biomass of life on Earth might occur in various microbial forms in extreme conditions. “We know of geothermal vents on Earth where there is a source of energy that’s not the Sun; it’s, rather, geothermal activity underneath the Earth’s crust, and the magma seeps up and heats the surrounding regions.”
  • 204 Lecture40:LifeBeyondtheEarth We can look for life elsewhere in our Solar System and Milky Way Galaxy. The discovery of even a single species of life would support the hypothesis that simple life forms easily. We know that whatever life may have formed in the Solar System (other than on Earth), it most likely was primitive—microbes and bacteria. So far, there has been no good evidence for what we call “intelligent” life elsewhere in our Solar System. Analysis of Martian soil has shown no evidence of primitive life, but perhaps there is life under the planet’s surface. Further testing is necessary if we are to nd organic compounds on Mars. As discussed in a previous lecture, studies of a meteorite from Mars (ALH 84001) initially suggested that the planet could have primitive microbes. Though many scientists now believe that particular evidence to be weak, it still doesn’t prove that life doesn’t exist on Mars. Life could possibly have formed early in Mars’s history because conditions there may have been very favorable at one time, maybe even preceding the time when conditions were good on Earth. It’s possible that microbes did form 4 billion years ago on Mars, and it’s even possible that some meteoroid hit Mars, excavated a crater, and sent debris ying through the Solar System. That debris could have landed on Earth, releasing microbes and making us descendants of Martians! (The odds for this, however, seem low.) It’s even thought that a particular Martian crater may have been the crater from which the meteorite in question came, although clearly, that meteorite didn’t provide the seeds of life on Earth. One of Saturn’s moons, Enceladus, has a thin layer of surface water ice that came from geysers. NASA/JPL/SpaceScienceInstitute
  • 205 Jupiter’smoonEuropaisat least partly molten inside. Its surface is covered with cracked and ssured water ice, suggesting that ice sheets oat atop a layer of water slush. Such conditions could support primitive life. Saturn’s moon Enceladus also has a layer of surface water ice, but it is much thinner than Europa’s. Erupting geysers release water vapor, and these regions would be a good place to begin the search for life. Jupiter’s moon Io, with its sulfur compounds and erupting volcanoes, could also produce sulfur-based life forms. Indeed, biologists are studying the possible formation of life deep beneath the Earth’s surface where sulfur compounds and iron silicates are found. Thus, it is conceivable that life exists in other places in our Solar System; all we have to do is search. proteins: Molecules consisting of long chains of amino acids. Croswell, Planet Quest: The Epic Discovery of Alien Solar Systems. Goldsmith and Owen, The Search for Life in the Universe, 2nd ed. McKay, “The Origin and Evolution of Life in the Universe,” in The Origin and Evolution of the Universe. Ice jets send particles streaming into space hundreds of kilometers above the south pole of Enceladus. NASA/JPL/SpaceScienceInstitute Important Term Suggested Reading
  • 206 Lecture40:LifeBeyondtheEarth Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. How restrictive do you think we are being when we consider only “life as we know it”? 2. Do you think gas/liquid giant exoplanets resembling Jupiter are necessarily inhospitable to life? Consider also the moons that might orbit them. 3. Would you support the use of federal funds for the search for bacteria and primitive microbes on Mars and some of the moons of Jovian planets? Questions to Consider
  • 207 The Search for Extraterrestrials Lecture 41 “It’s hard to detect life, especially if you don’t go there. Even if you go there, it can be hard. We’ve gone to Mars, and we still don’t really know whether there ever was or is microbial life there.” I n the preceding lecture, we saw that the existence of life on other planets and moons, at least in our Solar System, is possible. Yet even if we do land probes in such places, detecting life can be dif cult, as our studies of Mars have proved. How can we conduct such studies from a distance? An alien looking at the Earth from afar could deduce from the atmospheric composition that there might be extensive life on Earth. For example, a spectrum of Earth would show free oxygen in the atmosphere, which comes from photosynthesis (although this isn’t the sole source of free oxygen). The spectrum would also show free methane, which comes, in part, from decaying organic matter. Methane easily reacts with oxygen to form other compounds, thus basically disappearing. Methane and oxygen together in an atmosphere suggest some process by which the methane is continually replenished. That process could be life. If there weren’t living creatures on Earth, any initial methane in the atmosphere would quickly react with oxygen, leaving no methane. Uranus and Neptune have lots of methane but no free oxygen; there’s nothing for methane to react with, leaving methane in their atmospheres. In our search for intelligent life, we could look for electromagnetic signals from extraterrestrials, particularly radio waves. Radio waves are inexpensive to produce in vast quantities. Also, radio waves travel through celestial gas and dust essentially unimpeded. Gamma rays and x-rays are expensive to produce and are easily blocked by thick clouds of gas and dust, just as optical or ultraviolet photons are. However, recently, astronomers have been using optical radiation to try to nd evidence for extraterrestrials on planets orbiting nearby stars. They look for sharp pulses of light all having the same wavelength (like from a laser). Most of our radio telescope studies concentrate on detecting unnatural patterns in space signals—that is, patterns that could not have been produced by a rotating star or a disk of gas and dust
  • 208 Lecture41:TheSearchforExtraterrestrials that might form planets. Instead, we look for signals that have been produced by intelligent beings. The Very Large Array set of radio telescopes in New Mexico collects and analyzes radio signals to search for unusual patterns. We also use the Arecibo radio telescope to collect signals from outer space during times when other science projects are conducted, such as astronomers studying a galaxy and its radio waves. We don’t really know how many communicating civilizations there might be in our Milky Way Galaxy, but we can make an educated guess using the Drake equation. A reasonable estimate is R = 10 stars/year. The number is lower now but was higher in the past, when there was more free gas and dust in our Galaxy. What fraction of the stars are actually “good” suns (fs ), lasting a reasonable amount of time for life to form and evolve on planets The Drake Equation Developed by Frank Drake, the Drake equation highlights our sources of uncertainty in an estimate of the number of intelligent, communicating civilizations at any given time. The equation is 1s p e i cN Rf f n f f f L . The number (N) of communicating civilizations is a product of several factors: R = the rate at which stars form fs = the fraction of stars that are good suns fp = the fraction of good stars that have planetary systems ne = the number of planets or moons per star that occur within what is called the ecosphere, the habitable zone fl = the fraction of those habitable planets and moons on which life actually develops fi = the fraction of living species that develop intelligence fc = the fraction of living species that reach the electromagnetic communicative phase L = the lifetime of the communicative phase
  • 209 orbiting them, but not having such a low mass that the luminosity and ecosphere are very small? Perhaps 0.1 is a good estimate. The fraction of suitable stars actually having planetary systems (fp ) might be 1, or maybe it is only 0.1 (that is, 1 in 10), on average. The number of Earth-like planets or moons per planetary system (ne ) could be between 0.1 and 1, or it could be larger (perhaps as high as 10, including the suitable moons). The fraction of Earth-like planets or moons (fl ) on which even primitive life can be found is speculative but might be in the range of 10 3 to 1. The fraction of life- bearing planets on which intelligence actually arises (fi ) is perhaps even more speculative, but might be 10 6 to 1. The fraction of intelligent life that has the ability and desire to communicate with aliens (fc ) is also very speculative, so let’s guess 10 3 to 1. The typical lifetime of a communicating civilization (L), or the cumulative lifetime of such civilizations on a given planet, might be somewhere between 100 or 109 years; we really don’t know. Multiplying these factors together, from the pessimistic view, there is only 1 chance in a trillion (10–12 ) that a galaxy like the Milky Way has intelligent, communicative life forms. In other words, among a trillion galaxies (1012 ), more than the total number of galaxies in the observable parts of the Universe, our Galaxy is the only one with communicating intelligent life. On the other hand, according to the optimistic view, multiplying the numbers gives us 10 billion communicating civilizations in our Galaxy at any given time. Our two calculations show a vast range, from 1 in a trillion up to 10 billion, which doesn’t tell us how many communicating civilizations are out there. It does, however, show us where the greatest uncertainties are— the lifetime of an intelligent, communicating civilization (L) and the fraction of life-bearing planets on which intelligence develops. It is quite possible that primitive life—bacteria and microbes—are fairly common elsewhere. Intelligence at or above our level, however, may be rare. During Earth’s history, there have been about 10 billion species. If civilizations don’t last long while communicating, there won’t be enough at any given time whose signals we could detect. The longer they live, the greater is our chance of nding them.
  • 210 Lecture41:TheSearchforExtraterrestrials As far as we can tell, only one, Homo sapiens, has reached this level of intelligence. We arrived only relatively recently on Earth; thus, other life forms could have examined Earth during most of its history and concluded that Earth didn’t have intelligent life. In addition, intelligence at our high level could, in a sense, be considered detrimental to species survival. We’re the rst species known that has the capability to destroy itself and most other complex lifeforms. Other intelligent life, on other planets, may have existed for a short time but subsequently destroyed itself. Many scientists believe that Earth had to meet a number of amazing conditions for it to exhibit the stability needed to develop intelligent, communicative life. For example, if we didn’t have a large orbiting moon, our axis of rotation would undergo chaotic variations, leading to signi cant changes in the climate over rapid time scales. If Jupiter were not present, the debris in the Solar System would not have been cleared out, and Earth would still be bombarded by meteoroids, causing extinctions before communicating intelligence had a chance to develop. By the same token, if Jupiter had a highly eccentric orbit rather than a nearly circular one, it would eventually knock the small terrestrial planets out of the Solar System. Finally, life on Earth could be considered a rarity because we needed heavy elements, such as carbon, oxygen, and calcium, from which to form. The earliest stars in our Galaxy did not have those heavy elements because there hadn’t been enough time for other stars to form them and eject them into the cosmos. luminosity: Power; the total energy emitted by an object per unit of time; intrinsic brightness. “Unless we continue trying, it’s almost certain that we’ll never detect other intelligent civilizations.” Important Term
  • 211 Drake and Sobel, Is Anyone Out There? The Search for Extraterrestrial Intelligence. Goldsmith and Owen, The Search for Life in the Universe, 2nd ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan and Shklovskii, Intelligent Life in the Universe. SETI@Home, seti.berkeley.edu. (Download a program that, as a background task, will analyze data from radio telescopes, searching for signs of extraterrestrial life.) Ward and Brownlee, Rare Earth: Why Complex Life Is Uncommon in the Universe. 1. In the Drake equation, use your own preferences for each quantity to derive the number of intelligent, communicating civilizations in our Galaxy. Discuss the importance of the value of L, the lifetime of the civilization. 2. If 10% of all stars are of suitable type for life to develop, 30% of all stars have planets, and 20% of planetary systems have a planet or moon at a suitable distance from the star, what fraction of stars have a planet suitable for life? Roughly how many such stars would there be in our Galaxy? 3. Do you think the conclusion that Earth had to be “just right” for intelligence to develop might be too anthropocentric? Suggested Reading Questions to Consider
  • 212 Lecture42:SpecialRelativityandInterstellarTravel Special Relativity and Interstellar Travel Lecture 42 “We come now to Lecture 42, which, of course, provides the answer to the question of Life, the Universe, and Everything—at least according to The Hitchhiker’s Guide to the Galaxy.” O ur Galaxy is huge, and the distances between the stars are vast. Is interstellar travel possible with the right spacecraft? Interstellar travel is possible at relatively slow speeds. For example, at the escape velocity from Earth (11 km/s), a large spaceship could reach one of Earth’s nearest stars—Sirius, 8.7 light years away—in about 240,000 years. Voyager II is heading toward Sirius in the constellation Canis Major and will pass close to it in about 160,000 years. On average, it is traveling a bit faster than 11 km/s. Voyager I is heading toward the constellation Camelopardalis (the Giraffe) and will pass close to a star there in about 300,000 years. The Pioneer spacecraft, which passed Jupiter in the early 1970s, are heading toward other stars and will reach them in about 2 to 3 million years. Is it possible to travel to another star within our lifetime? We turn to Albert Einstein’s special theory of relativity to see how it could be done. At the time Einstein was working on his special theory of relativity, other physicists were working on similar concepts, namely Poincaré and Lorentz. However, Einstein received the credit because he brought it all together in a consistent physical framework, rather than just developing mathematical equations. Einstein concluded that Maxwell’s equations of electromagnetism were incompatible with Newtonian mechanics, which was based on Galileo’s observations. One of the problems in Maxwell’s equations was that the speed of light, c, was always the same, regardless of one’s reference frame. In Newtonian mechanics, velocities add up in a linear way, which didn’t seem compatible with electromagnetism. Einstein concluded that there was a problem with Newtonian mechanics, not electromagnetism. Experimental evidence showed that the speed of light is a constant regardless of the motion of the source or the observer. We are uncertain whether Einstein knew about that result or how much he was in uenced by it if he did.
  • 213 The special theory of relativity is “special” because it deals with constant speeds and no gravitational eld. Later, we will discuss Einstein’s general theory of relativity, which differs. Einstein made two fundamental assumptions in developing his theory. The rst was the principle of relativity, which states that the laws of physics are the same for all observers moving at constant speeds relative to one another. More simply, if you are moving with uniform speed and direction relative to your surroundings, you cannot tell that you are moving; rather, your surroundings seem to be moving past you. It is similar to ying in a jumbo jet, where we feel like we’re not moving (in the absence of turbulent air), but the ground, instead, is moving beneath us. The second assumption states that the speed of light is measured to be the same for all observers, regardless of their state of motion. This is consistent with electromagnetism. There are four important consequences to Einstein’s two fundamental assumptions. The rst consequence is called time dilation; moving clocks slow down as viewed by an observer at rest. For example, consider a particular kind of clock at rest in which a light pulse emitted from a source takes time 0 2t L c to make a round trip (from the source to a mirror and back to the source). Here, L is the distance between the source and the mirror, and c is the speed of light. If the clock is moving relative to a stationary observer, then the observer sees the light travel a longer distance along a diagonal path, from the source to the mirror and back again. Thus, the length of the second line, t1 —or time required—is longer than t0 : t1 = t0 , and 2 2 1/ 1 /v c . The second consequence is called length contraction; moving objects contract in the direction of motion. If a meter stick moves past us, it will look shorter than it really is by a factor of 1 . Thus, 1 0 /L L . The third consequence is called lack of simultaneity; people in different reference frames will not necessarily see two events as being simultaneous. Einstein considered a “thought experiment” (that is, a hypothetical experiment whose results can be deduced through logical thinking, not an actual measurement) in which one train passes another at rest. When the trains are exactly aligned, an explosion ignites on each end of the resting train. To a person on the moving train, the explosion at the end of the train in the direction of travel would appear to ignite before the explosion at the other
  • 214 Lecture42:SpecialRelativityandInterstellarTravel end. However, the person on the stationary train would see both explosions igniting at the same time. Finally, and most famously, Einstein came up with the equation E = mc2 . More correctly, E = mc2 = m0 c2 , in which E is energy and m0 is the mass of an object at rest, known as its rest mass. If an object moves, its mass will change by a factor of . We simply use E = mc2 , in which it is understood that m = m0 . As one considers progressively higher speeds, initially, the factor of increases only slightly. But as the speed approaches that of light, increases quickly. Indeed, as v/c approaches 1, approaches in nity. We can’t travel at the speed of light, but if we could, time would slow down so much that it would essentially stop. If we could travel faster than the speed of light, time would actually go backward! However, it is impossible for us to travel at the speed of light because of the equation E = mc2 . If E = m0 c2 and approaches in nity as the speed approaches c (the speed of light), then the energy required to actually reach the speed of light is in nite. Let’s consider an example illustrating the essence of relativity. Relativity is well demonstrated by an experiment using a particle called a muon (a negatively charged particle somewhat like an electron but 209 times more massive), which is unstable and decays at rest in 2.2 microseconds, or 2.2 millionths of a second. A muon traveling at 99% of the speed of light for 2.2 microseconds should be able to travel only 0.653 km before decaying into other kinds of particles. Thus, a muon emitted at one end of a laboratory 3 km long will not reach the other end. However, time for the muon slows down by a factor of 7.09, according to the laboratory observer. That is, the muon, which is at rest relative to itself (the principle “Interstellar travel, though possible in principle, is very, very dif cult in practice. It’s conceivable that the reason we have not seen any evidence for intelligent extraterrestrials traversing vast distances is that neither we nor they have gured out how to do it.”
  • 215 of relativity), thinks that it lived only 2.2 microseconds, but laboratory observers see the traveling muon experience a lifetime 7.09 times longer, or about 15.6 microseconds. In that amount of time, the muon could travel 4.63 km and, hence, will reach the other end of the laboratory. According to the muon, on the other hand, the laboratory is moving past it at 99% of the speed of light, and hence, its length gets contracted by a factor of 7.09, from 3 km to only 0.423 km. In 2.2 microseconds, the laboratory would have moved 0.653 km, more than its apparent length. Thus, the muon thinks that it was emitted from one end of the lab, and then the other end rushed over and hit it. The time and distance over which the muon (or laboratory) moved depends on our frame of reference. To laboratory observers, the muon moved farther than expected because of time dilation. To the muon, the lab was shorter than expected because of length contraction. They agree on the measurable quantities (muon emitted at one end of the lab and detected at the other end), but they disagree about how this happened. Both are right, because they are in different frames of reference. Now we apply special relativity to interstellar travel. A rocket heading for Sirius at 99.5% the speed of light would take 17.5 years to make a round trip, as experienced by someone remaining on Earth. But at that speed, someone aboard the rocket would experience only 1.75 years and would, thus, age by only 1.75 years, while those on Earth aged 17.5 years. At 99.99% the speed of light, 17.4 years will have passed on Earth, but only 3 months will have passed for the traveler. In principle, if we could approach the speed of light without physical harm, we could make the journey in shorter amounts of time as our speed increased. From the traveler’s point of view, the length of time for the trip is greatly shortened because the traveler experiences rest rather than motion, making it seem as if the Universe is moving by very quickly and, hence, is contracted in length. For a spacecraft to move at speeds approaching the speed of light would require truly vast, almost unfathomable, amounts of energy. Our current technology has not solved this problem; therefore, rapid interstellar travel is, as yet, possible in theory only. Moreover, to avoid serious bodily injury or death, one would need to accelerate to high speeds very slowly and decelerate very slowly upon reaching one’s destination. Thus, for much of the journey, one’s speed would be low, and there would not be substantial savings from time dilation and length contraction.
  • 216 Lecture42:SpecialRelativityandInterstellarTravel E = mc2 : Einstein’s famous formula for the equivalence of mass and energy. in nity: All numbers. A countable in nity can be put in one-to-one correspondence with the counting numbers, whereas an uncountable in nity cannot. special theory of relativity: Einstein’s 1905 theory of relative motion, gravity excluded. time dilation: According to relativity theory, the slowing of time perceived by an observer watching another object moving rapidly or located in a strong gravitational eld. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Mallove and Matloff, The Star ight Handbook: A Pioneer’s Guide to Interstellar Travel. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Explain how it is possible, in principle, to travel many light years in a short time interval as measured by the traveler. 2. How long would it take a rocket ship traveling at 100 km/s to reach a star that is 20 light years away? Important Terms Suggested Reading Questions to Consider
  • 217 3. Suppose you are in a rocket ship that is moving at 97% of the speed of light. If your journey to another star appeared to take 30 years from the perspective of an Earth-bound observer, how long did it take in your frame of reference? How far did you travel in your frame of reference? 4. Do you think humans or their successors (machines?) will ever overcome the enormous barriers to rapid interstellar travel?
  • 218 Lecture43:Stars—DistantSuns Stars—Distant Suns Lecture 43 “I’ll be discussing stars—their births, their lives, their deaths. What happens to them? How do they produce the elements of the Universe? What kind of compact and weird remains come about when stars die?” S tars are distant versions of our Sun—glowing, opaque balls of gas held together by gravity. Nuclear reactions occur deep in the core, providing the light that we see. In the next several lectures, we will discuss stars, their births, lives, and deaths. We start by describing how we measure the distances between relatively nearby stars and Earth. There is a seemingly countless number of stars in the Milky Way Galaxy, but the number of stars is, in fact, nite. A big galaxy like our own has roughly 300 to 400 billion stars. Despite the large number of stars, the distances between them are vast. We can measure these distances using a method called triangulation, which is based on the concept of parallax shifts in apparent position of objects (relative to more distant objects) as viewed from different physical locations. We discussed this concept in a previous lecture. First, we photograph a relatively nearby star, then take another photograph 6 months later, after the Earth has moved 2 AU in its orbit around the Sun. We then measure the angular shift with respect to more distant stars whose positions appear relatively stationary. The parallax (p) of a star is half the angular shift produced over a 6-month baseline (2 AU, the diameter of Earth’s orbit). Thus, as viewed from the star, the parallax is simply the angle subtended, or covered, by 1 AU. As the distance of a star increases, the parallax decreases. All known stars have parallax shifts of less than 1 arc second. The distance of a star whose parallax is 1” (1 second of arc) is called 1 parsec (1 pc). One parsec is about 3.26 light years. Recall that a full circle is 360°; 1° = 60 minutes of arc (60’); 1’ = 60 seconds of arc (60”). To illustrate, 1” is the angle subtended by a dime seen from a distance of 3.7 km. Using the parsec unit, the relationship between distance and parallax is simple. A star’s distance, d (in parsecs), is
  • 219 the inverse of its parallax, p (in seconds of arc): d = 1/p. The measurement works because a distant set of stars will shift very little as the Earth orbits the Sun, while nearby stars shift much more. However, it’s dif cult to accurately measure a shift of less than 1/100 of an arc second. The most distant stars that we can measure from the ground have distances of about 100 pc; those large distances aren’t very accurate, however. We can accurately measure a star’s shift if its parallax is 1/10 of an arc second, or 10 pc. We know accurately the distances of stars within 10, 20, or 30 pc and less accurately the distances of stars up to about 100 pc. To measure stars more distant than 100 pc, we use satellites. In 1989, the European Space Agency launched a satellite called Hipparcos (in honor of the ancient Greek astronomer) that catalogued about 120,000 stars out to 100 pc in distance, or about 300 light years away. Now let’s look at the surface temperatures of stars. As viewed from Earth, stars in the night sky have different colors. Hot stars appear blue, cool stars appear red, and medium-temperature stars appear white. As discussed in Lecture 21, the spectra of hot, opaque objects glowing on their own—because of the random motions of particles within them—produce Planck curves. Strictly speaking, these curves apply in their precise mathematical form only to objects that are perfect absorbers and emitters of radiation, known as ideal radiators, or black bodies. To review, an ideal radiator (black body) doesn’t re ect any radiation and doesn’t transmit any radiation. It only absorbs radiation, which causes it to heat up. It is a perfect absorber and a perfect emitter because the spectrum of its emitted light follows a very precisely de ned mathematical form, the Planck curve. Stars are roughly—but not ideally—black bodies; they do have some absorption lines, so the spectrum depends a little on variables other than surface temperature. However, the shape of the emitted spectrum depends mostly on the surface temperature. Cool stars peak in the red or infrared parts of the spectrum; hot stars peak in the green, blue, or even violet parts of the spectrum. We describe this mathematically through Wien’s law, which says that the wavelength of the peak of the spectrum multiplied by the surface temperature of the star is a constant: peak T = a constant, in which the constant is about 2.9 107 in units of angstrom-Kelvins. We can calculate a star’s surface temperature by measuring the wavelength of the peak of the star’s spectrum.
  • 220 Lecture43:Stars—DistantSuns The main stellar classi cation scheme, OBAFGKML , depends on surface temperature. The traditional mnemonic is “Oh, Be A Fine Girl, Kiss Me Lovingly!” O-type stars have surface temperatures of more than 25,000 Kelvin (K), while B-type stars are from 11,000 to 25,000 K. Stars in these two classes appear to be bluish. A-type stars are between 7500 and 11,000 K, F-type stars are between 6000 and 7500 K, and G-type stars are between 5000 and 6000 K. Stars in these three classes appear white. K-type stars are between 3500 and 5000 K, M-type stars are between 2200 K and 3500 K, and L-type stars (recognized only in the past decade or so) are below 2200 K. These types of stars appear orange or even red. Each main class is divided into 10 subclasses, ranging from 0 (hottest) to 9 (coolest). Our Sun is a G2 star, with a temperature of 5800 K. The surface temperature of a star also largely dictates which absorption lines are visible in the spectrum. Each star’s spectrum shows different absorption lines spanning a range of strengths from various chemical elements near the star’s surface. At very high temperatures, hydrogen is ionized and, thus, doesn’t produce absorption lines; for this reason, O-type stars don’t show hydrogen in their spectra. In cool stars, hydrogen is generally in its lowest electronic energy level. As discussed in Lecture 22, the resulting absorption lines therefore appear in the ultraviolet part of the spectrum Name to Know Cannon, Annie Jump (1863 1941) was an American astronomer. She classi ed the photographic spectra of several hundred thousand stars, demonstrating that the spectra depend mostly on the stellar surface temperature. She arranged the spectral types into the sequence OBAFGKM. Name to Know Cannon, Annie Jump (1863 1941) was an American astronomer. She classi ed the photographic spectra of several hundred thousand stars, demonstrating that the spectra depend mostly on the stellar surface temperature. She arranged the spectral types into the sequence OBAFGKM. “How can you remember this sequence? You could say, ‘Oh, Be A Fine Girl; Kiss Me Lovingly— or Oh, Be A Fine Guy; Kiss Me Lovingly,’ depending on your preferences. Some of my students have a different way of remembering it. They say, ‘Oh, Boy, Alex Filippenko Gives Killer Midterms, Laughing.’ ”
  • 221 (Lyman series) but not in the visible range (Balmer series). Thus, cool stars also don’t show hydrogen in their visible spectra but for a different reason than hot stars. All other elements can be explained in a similar way. Though a star’s surface temperature mostly sets the strength of the observed absorption lines, for any given temperature, two different stars will have different absorption-line strengths, depending on the abundance of each element near the star’s surface. We assume, to a good rst approximation, that the interior composition is similar to that of the surface. Astronomers have determined that more than 98% of the mass of typical stars consists of hydrogen and helium, elements that were produced early in the Universe, at the time of the Big Bang or shortly thereafter. black body: An object that absorbs all radiation that hits it; none is transmitted or re ected. It emits radiation due to thermal (random) motions of its constituent particles, with a spectrum that depends only on the temperature of the object. parsec: A unit of distance equal to about 3.26 light years (3.086 1013 km). Cooper and Walker, Getting the Measure of Stars. Hirschfeld, Parallax: The Race to Measure the Cosmos. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What is the distance of a star whose parallax is 0.3 seconds of arc? What is the parallax of a star whose distance is 40 pc? Important Terms Suggested Reading Questions to Consider
  • 222 Lecture43:Stars—DistantSuns 2. Though it would take longer to measure the parallax of a star from Jupiter than from Earth, would you be able to determine the distances more accurately, as well as determine larger distances? (Assume you are above Jupiter’s atmosphere and have a clear view of the sky.) 3. The Sun’s surface temperature is about 5800 K and its spectrum peaks at 5000 Å. An O-type star’s temperature may be 40,000 K. (a) According to Wien’s law, at what wavelength does its spectrum peak? (b) In what part of the spectrum might that peak be? (c) Can the peak be observed with the Keck telescopes? 4. Make up your own mnemonic for spectral types, through type L.
  • 223 The Intrinsic Brightnesses of Stars Lecture 44 “An important characteristic of a star is how much energy it produces. That, together with these other fundamental properties of stars that we’ve been discussing, will give us a more complete understanding of the physical way in which stars work, and generate their energy and shine.” A star’s brightness can be de ned in terms of both its observed (apparent) brightness and its intrinsic brightness (luminosity, or power). The most obvious observed fact about stars is that they have different apparent brightnesses. Astronomers use the term apparent magnitude to quantify this observed quality; the term dates back to the ancient Greek astronomer Hipparchus, who rst catalogued the positions and apparent brightnesses of more than 850 stars. Hipparchus categorized the typical brightest stars as magnitude 1. The faintest stars visible to the naked eye were classi ed as magnitude 6. Later, astronomers determined quantitatively that a 1st -magnitude star is 100 times brighter than a 6th - magnitude star. That is, per second, 100 times more photons hit our eyes from a 1st -magnitude star than from a 6th -magnitude one. The difference of 5 magnitudes corresponding to a factor of 100 in brightness is due to the fact that our eyes respond according to a logarithmic scale, to a reasonable rst approximation. For every equal factor in brightness, there is a one-step increase or decrease in observed magnitude; every 1 magnitude of difference must correspond to the 5th root of 100 (an irrational number: 2.512…) in brightness. Thus, a 1st -magnitude star is roughly 2.5 times brighter than a 2nd - magnitude star, and so on. In general, for two stars, a and b, with apparent brightnesses aB and bB and apparent magnitudes am and bm , we have ( ) / 2.512 b am m a bB B . What are the apparent magnitudes of some common celestial objects? The Sun is –26.8 (apparent magnitudes can be negative); the full Moon is about –12.6, depending on how close it is to Earth; Venus at its brightest is –4.4; Mars at its brightest is –2.8, and Jupiter is comparable. Sirius, the brightest star, is –1.5; Canopus, the second brightest star, is –0.7. Many stars
  • 224 Lecture44:TheIntrinsicBrightnessesofStars have magnitudes of 0 or 1. The very faintest ones visible with the naked eye are magnitude 6. The faintest stars observable in long exposures with powerful telescopes, such as the Hubble or the Keck telescopes, are about magnitude 30. If we look at stars through different-colored lters, we can isolate the light in either the blue or the red part of the spectrum or in other parts, as well. Note that in astronomical jargon, a red lter is one that passes (transmits) red light and blocks all other colors, while a blue lter is one that passes blue light and blocks all other colors. Technically, the apparent magnitude of a star depends on which part of the spectrum we are observing. For example, Betelgeuse looks red to the naked eye. Thus, through a blue lter, it appears fainter (higher magnitude) than through a red lter. We de ne the intrinsic brightness (power) of stars as their luminosity. Luminosity can be quanti ed as absolute magnitude, which is the apparent magnitude a star would have at a distance of 10 parsecs (about 32.6 light years) from Earth. If all stars were the same distance from Earth, the differences in their apparent brightnesses would correspond to differences in their intrinsic powers. If our Sun were 10 pc from Earth instead of 1 AU, it would have a magnitude of 4.8 instead of –26.8. One pc is about 200,000 AU, and 10 pc is about 2 million AU; therefore, the Sun would look much fainter at 10 pc. Remember, the higher the magnitude, the fainter the star. The qualitative relationship between apparent magnitude and absolute magnitude is as follows: 5log( /10)m M d , in which m is apparent magnitude, M is absolute magnitude, d is distance in parsecs, and the logarithm is base 10. In this course, we will use the more physical units of apparent brightness (instead of apparent magnitude) and luminosity (instead of absolute magnitude). The apparent brightness, b, is de ned in terms of the amount of energy that hits the pupils of our dilated eyes each second. Speci cally, the “When you see patterns, you know that there’s got to be some physics behind those patterns. Watching the patterns and quantifying them allows you to get to that rst step of a complete physical understanding of the object that you are studying.”
  • 225 apparent brightness is the amount of energy per second per square centimeter of the collecting device, be it our eyes or some kind of telescope. Apparent brightness is clearly related to the intrinsic (true) brightness, also called the luminosity (power) of a star: The greater its luminosity, all other things being equal, the greater its apparent brightness. But a star’s distance is a factor in its apparent brightness, as well; an intrinsically powerful (luminous) star looks dim when it’s very far away. The relationship between apparent brightness, the luminosity, and the distance is known as the inverse- square law, analogous to the inverse-square law of gravity discussed in Lecture 16. Mathematically, 2 (4 )b L d , in which the intrinsic brightness is L (luminosity), and d is the star’s distance from Earth. Using this inverse-square law, we can see how luminosity, brightness, and distance are related in a quantitative way and how we can use this relationship to determine luminosity. Stars emit a great deal of energy; the Sun, for example, emits 4 1033 ergs per second. An erg is close to the amount of energy required to lift 0.001 gram a distance of 1 centimeter at the surface of the Earth. [NOTE: During the lecture, the mass was erroneously given as 1 gram instead of 0.001 gram, leading to a value a factor of 1000 too high.] It is roughly equivalent to the amount of energy it takes a y to do a pushup. A more convenient unit than ergs is solar luminosity, designated sunL = 3.83 1033 ergs per second, or about 4 1033 erg/s. Thus, if a star’s luminosity is 8 1033 erg/s, we say it is a 2-solar-luminosity star. Lsun is often denoted by L with a circle subscript, and that subscript has a dot in the middle of it. The dotted circular subscript is the astronomical symbol for the Sun. If we plot stars’ luminosity (vertical axis) against their surface temperature (horizontal axis), we get what is called the Hertzsprung-Russell (H-R) diagram, or the temperature-luminosity diagram. In contrast with the usual convention in graphs, the surface temperature decreases from hot to cool as one goes from left to right. We nd that most stars fall along a well-de ned main sequence in the diagram, going from the upper left (hot, luminous stars) down to the lower right (cool, low-luminosity stars). There are some additional regions where stars tend to appear but in smaller numbers. It is striking that certain parts of the diagram contain very few stars. Thus, something about the structure of stars allows them to have only certain
  • 226 Lecture44:TheIntrinsicBrightnessesofStars combinations of surface temperature and luminosity. These combinations can change as a given star evolves with time. When we observe such speci c patterns—not randomly produced—in our studies of the stars, we conclude that some physical explanation accounts for these patterns. This provides the rst step in our understanding of the objects we study. absolute magnitude: Logarithmic measurement of the luminosity of stars; assumes all the stars to be at the same distance of 10 parsecs from Earth. Hertzsprung-Russell (H-R) diagram: A plot of the surface temperature (or color) versus luminosity (power, or absolute brightness) for a group of stars. Also known as a temperature-luminosity diagram. inverse-square law: Decreasing with the square of increasing distance. For example, the brightness of a star is proportional to the inverse-square of distance, as is the gravitational force between two objects. main sequence: The phase of stellar evolution, lasting about 90% of a star’s life, during which the star fuses hydrogen to helium in its core. Cooper and Walker, Getting the Measure of Stars. Dickinson, Nightwatch: A Practical Guide to Viewing the Universe, 3rd ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Important Terms Suggested Reading
  • 227 1. Star Albert appears to have the same brightness through red and blue lters. Star Bohr appears brighter in the red than in the blue. Star Curie appears brighter in the blue than in the red. Rank these stars in order of increasing surface temperature. 2. If a star that is 100 light years from us appears to be 10th magnitude, would its absolute magnitude be a larger or a smaller number? 3. If one star has twice the apparent brightness of another star but is a factor of 8 farther away, what is its luminosity relative to the other star? 4. Besides distance and luminosity, what other factor might affect the apparent brightness of a star? (Consider the headlights of an oncoming car viewed through fog and through clear conditions.) Questions to Consider
  • 228 Lecture45:TheDiverseSizesofStars The Diverse Sizes of Stars Lecture 45 “If you plot the luminosity on the vertical axis versus the surface temperature on the horizontal axis, most stars fall in distinct regions of that temperature-luminosity diagram. … Now let’s see how we can use the diagram to infer the sizes or radii of stars, another fundamental property of stars.” L et’s review the relationship among temperature, radius, and luminosity before seeing how we can infer a star’s radius. The Hertzsprung- Russell diagram, or temperature-luminosity diagram, can be described as follows. On the vertical axis, luminosity is listed in units of absolute magnitude, though we will refer to the less arbitrary solar luminosity. On the top horizontal axis, spectral types are listed (O, B, A, F, G, K, M, L), which as we noted previously, are related to surface temperature. On the bottom horizontal axis, surface temperature is given in units of 1000 Kelvin. The main sequence on which most stars fall in this temperature-luminosity diagram crosses diagonally from the upper left-hand side to the lower right-hand side. Remember that stars are nearly perfect emitters of radiation; thus, their spectra are nearly those of a perfect thermal emitter—that is, a Planck curve. The area underneath each curve grows with increasing surface temperature of the star. Recall from Lecture 21 that this phenomenon is quanti ed by the Stefan-Boltzmann law. The law says that hotter stars emit more energy per second than cooler stars per unit of emitting area, and the amount they emit is proportional to their surface temperature raised to a power of 4, or T4 . Mathematically: 4 E T , in which E is energy emitted per second per unit surface area, is the Stefan-Boltzmann constant, and T is surface temperature. For example, if two stars have equal areas and the surface temperature of one is 6000 K and the other is 3000 K, the ratio of surface temperatures = 6000/3000 = 2, and 24 = 16. Therefore, one star that is twice as hot as another emits 16 times as much energy per second as the cooler star, if they have the same surface area.
  • 229 The luminosity (power) of a star is equal to the amount of energy emitted per second per unit surface area, multiplied by the total surface area. The surface area of a star can be approximated as 4 R2 (that is, proportional to the square of its radius), because most stars are roughly spherical. Thus, L = 4 R2 T4 for a star of radius R and surface temperature T. O-type main-sequence stars are much more luminous than M-type main-sequence stars, primarily because their surface temperatures are considerably higher than those of M-type stars. The radius of the star—in this case—is not as important along the main sequence. In the Hertzsprung-Russell diagram, the temperatures of stars are plotted against their luminosities. The position of a star in the diagram provides information about its present evolutionary stage and its mass. ESO
  • 230 Lecture45:TheDiverseSizesofStars The luminosity of cooler stars can be much greater than that of hotter stars only when the cooler stars are very large. Some stars can be 10,000 to 1 million times more luminous than the Sun yet have roughly the same temperature, only somewhat cooler than the Sun. We call these supergiants or red supergiants because, being somewhat cooler, they tend to be redder than the Sun. If a star is 1 million times as luminous as the Sun but has the same temperature, the radius of the star must be 1000 times greater than the radius of the Sun. The stars Betelgeuse in Orion and Antares in Scorpius are good examples of red supergiants. Stars that are only about 100 times more luminous than the Sun but somewhat cooler are called red giants. Some other stars are about the same temperature as the Sun but emit much less energy per second, typically 1/10,000 that of the Sun. These stars are much smaller than the Sun (about 1/100 of the Sun’s radius) and are called white dwarfs. Sirius B is a good example of a white dwarf. The terminology can sometimes be confusing: Main-sequence stars can be white, and main-sequence stars are also called dwarfs in comparison to giants and supergiants. However, a white main-sequence star, such as the Sun, is not a white dwarf, even though it is white and it’s a dwarf in comparison to the supergiants. Remember that white dwarfs have a much lower luminosity than the Sun does. Let’s look at how we can determine the radii of stars. In the case of relatively nearby stars, we can infer their distance from their parallax. We can also measure their apparent brightness, b. This allows us to calculate their luminosity, L = 2 4 d b, from the inverse-square law of light. We can also infer their surface temperatures from the wavelength at which their spectrum peaks, using Wien’s law (recall Lecture 21). But above we saw that L = 4 R2 T4 . Setting this equal to L = 2 4 d b, the only unknown quantity is R, the star’s radius. When calculating radii, it’s important not to “Looking at Betelgeuse in the upper-left shoulder of Orion, we calculate that it should be about as big as the radius of Jupiter’s orbit around the Sun. Can you imagine that? If we were orbiting that star, we would be well inside it.”
  • 231 confuse the 4 R2 in the Stefan-Boltzmann formula, which is the surface area of the star, with the 2 4 d in the inverse-square law of light. In some cases, we can verify the measured radii of stars by taking direct images of those stars that are suf ciently large and close. In addition, we can use the technique called interferometry, which we discussed in Lecture 24. This has been done at infrared wavelengths for some stars. Not all stars have a constant radius; some stars vary in their size. This variation in size also causes a variation in luminosity and, hence, in apparent brightness. Mira, in Cetus the Whale, is an example of a star whose size varies. Its apparent magnitude can change from 3 (bright) to 9 (much dimmer) over time. Mira is called a long-period variable star because it takes more than a year to go through a full cycle of changing brightness. Because the star is unstable, or nearing the end of its life, the plot of brightness versus time (the light curve) does not look exactly the same from cycle to cycle. Another type of variable star, called a Cepheid variable, is important for determining the size and age of the Universe—which, as we will see later, are fundamental questions of cosmology. Cepheid variables change from faint to bright rapidly, fading again more slowly to form a distinct and easily recognizable light curve having a period of between 1 and 100 days. All Cepheids are quite luminous stars, but those whose average luminosity is higher have longer periods of oscillation than those whose average luminosity is lower. This period-luminosity relation was proved through studies of the Magellanic Clouds, two satellite galaxies of our Milky Way, in which the changing apparent brightness of Cepheid variables was noted. In the Magellanic Clouds, all the stars are about the same distance from Earth. Thus, distance becomes irrelevant in comparing apparent brightness, Name to Know Leavitt, Henrietta (1868 1921) was an American astronomer who demonstrated a relationship between the period and luminosity of Cepheid variable stars. This was done by analysis of Cepheids clustered together and, therefore, at the same distance, so that differences in brightness indicate luminosity differences. Name to Know Leavitt, Henrietta (1868 1921) was an American astronomer who demonstrated a relationship between the period and luminosity of Cepheid variable stars. This was done by analysis of Cepheids clustered together and, therefore, at the same distance, so that differences in brightness indicate luminosity differences.
  • 232 Lecture45:TheDiverseSizesofStars and differences in apparent brightness must correspond to differences in luminosity. Knowing a particular Cepheid’s period, we can infer its average luminosity. From its average apparent brightness, we can determine its distance. Because the Cepheids in other galaxies appear very faint yet are intrinsically very luminous, astronomers deduced that those galaxies must be extremely far away. Having determined star sizes, we can now deduce the sizes of some of the exoplanets that orbit them, using the transit technique discussed in Lecture 39. During the transit of an exoplanet, the apparent brightness of a star decreases somewhat because the planet is covering part of the star. This creates a dip in the star’s light curve. By measuring the amount of this dip, we derive the planet’s area relative to that of the star: It is equal to the amount of fractional decrease in the star’s brightness. Knowing the star’s radius, we calculate its area, and hence, we infer the planet’s area and its radius. It is through measurements such as these that we hope to nd and measure the sizes of many terrestrial-like exoplanets with the Kepler spacecraft. Cepheid variable: A type of pulsating star that varies in brightness with a period of 1 to 100 days. cosmology: The study of the overall structure and evolution of the Universe. red giant: The evolutionary phase following the main sequence of a relatively low-mass star, such as the Sun; the star grows in size and luminosity but has a cooler surface. variable star: A star whose apparent brightness changes with time. Important Terms
  • 233 Cooper and Walker, Getting the Measure of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. If a red giant has half the Sun’s surface temperature but 100 times its radius, what is the giant’s luminosity relative to that of the Sun? 2. Suppose you were to double the Sun’s surface temperature. What would you need to do to its radius in order for the luminosity to remain unchanged? 3. Consider two stars of the same spectral type and subtype but not necessarily both on the main sequence. Describe whether this information is suf cient to tell you how the stars differ in (a) surface temperature, (b) size, and (c) distance. 4. Why do you think the radii of very few exoplanets have been determined thus far? Suggested Reading Questions to Consider
  • 234 Lecture46:BinaryStarsandStellarMasses Binary Stars and Stellar Masses Lecture 46 “I’ve described how astronomers determine the intrinsic properties of stars—and it turns out that these intrinsic properties are dictated by the mass of the star. In this lecture, I will describe how this key property of stars is determined.” W e must realize that many stars are parts of multiple star systems; that is, usually, we nd at least two stars orbiting each other. In almost all cases, the naked eye sees only a single star, because the light from the multiple stars merges together. The two stars in a binary system orbit their common center of mass (center of gravity), or their balance point, as we discussed when we talked about exoplanets and their stars. The high-mass star is closer to the center of mass than the low-mass star. Mathematically, M1 r1 = M2 r2 , in which M1 is the mass of the high-mass star and r1 is its distance from the center of mass; M2 and r2 are the equivalents for the lower-mass star. If the two masses are equal, the center of mass is equidistant from the two stars. The two stars are held together according to Newton’s law of universal gravitation, F = GM1 M2 /d2 . According to Kepler’s second law, when the two stars are close to each other, they move faster than when they are farther apart. Let’s look at some types of binary stars, which can be broadly divided into optical doubles and physical binary stars. Optical doubles, or fake doubles, are two stars that appear to be gravitationally bound, because viewed from Earth, they seem to be close together. However, optical doubles just happen to be along the same line of sight and are not gravitationally bound to each other. A good example is Alcor, the second star from the end of the Big Dipper’s handle, which has an apparent companion called Mizar. Physical binary stars are gravitationally bound to each other. There are four main categories (visual, eclipsing, astrometric, and spectroscopic), though they are not mutually exclusive. Visual binaries are those that appear as one star to the naked eye, but through a telescope, it is obvious that there are two
  • 235 stars. Polaris, the North Star, is good example of a binary star system, which is made up of Polaris A (actually two more stars in itself) and Polaris B. Eclipsing binaries appear as single stars through a telescope. Yet when we monitor the brightness of an eclipsing binary star, we notice that the brightness changes with time because of another orbiting star. The two stars orbit around their mutual center of mass, but from Earth’s perspective, one star periodically passes in front of the other, blocking all or part of the other star’s light. The size of the dip in total apparent brightness of the star system depends on whether the hotter star (with a greater amount of emission per unit area) or the fainter star (with a smaller amount of emission per unit area) is blocked. When the hotter star eclipses the cooler star, the light curve (plot of brightness versus time) shows a small a dip in brightness. When the cooler star eclipses the hotter star, the dip is deeper. Astrometric binaries are stars that appear to move slightly backward and forward in the sky over the course of time. This happens when two stars orbit each other, but one star is so faint that we can’t really see it (at least, not easily). We deduce its presence by noting this wobble, or backward-forward motion. Sirius is such a star. It has a faint white dwarf companion (now known as Sirius B), whose presence was rst noted through measurements of its position over time (a process called astrometry). The most common binary stars are the spectroscopic binaries. Even through a telescope, those stars appear as one. The brightness doesn’t appear to change, but when we take multiple spectra of the star over time, we see some unexpected results. In the spectra, we see pairs of absorption lines— two hydrogen lines or two iron lines, for example—closely spaced together and shifting from night to night. In general, each line appears doubled, but they periodically move back and forth toward bluer or redder wavelengths (blueshifted or redshifted due to the Doppler effect). This movement is evidence that two stars are orbiting each other, accounting for the shifting spectral lines. Sometimes, only one set of absorption lines is visible, but these periodically shift back and forth. The second star is simply much fainter than the rst star in such cases.
  • 236 Lecture46:BinaryStarsandStellarMasses Spectroscopic and eclipsing binary stars can tell us much about the star system; some can be both spectroscopic and eclipsing. We can take all possible measurements of eclipsing spectroscopic binary stars—their orbital periods, light curves, distances from Earth, spectra—and determine the masses, radii, and luminosities of the individual stars. In fact, from these systems, we have deduced the masses of a few hundred stars fairly accurately. What does mass tell us about stars, at least those on the main sequence of the temperature-luminosity diagram? Stars that fall on the main sequence are in their prime of life—stable, fusing hydrogen into helium in their cores. Their luminosities don’t change much with time, nor do their radii. Our Sun is a main-sequence star, as are most stars. It is roughly halfway through its life. The luminosity of a main-sequence star is very roughly proportional to its mass to the 4th power: L M4 , in which M is the star’s mass. Thus, the luminosity is highly dependent on mass. (The dependence is actually not as sensitive to mass at high masses and somewhat more sensitive to mass at low masses.) For example, main-sequence stars that are 10 times as massive as the Sun are roughly 10,000 times as luminous. Conversely, stars that have 1/10 of the Sun’s mass have roughly 1/10,000 of the Sun’s luminosity. This mass-luminosity relationship implies that more massive main-sequence stars have shorter lifetimes than less massive stars. They live fast and die young because they are burning fuel at a much higher rate than low-mass stars. A star’s main-sequence lifetime is the amount of fuel divided by its luminosity, which is proportional to M/L. (Although not all of a star’s total mass is available as fuel, most stars have about the same fraction of their mass available as fuel.) But given that L M4 (roughly), we nd that the lifetime is very roughly proportional to M/M4 = 1/M3 . Thus, a star twice as “I know how a rainbow works, but that doesn’t detract from its beauty and wonder. There’s still the awe and mystery of how it all got here, why the laws of physics even exist, and why they lead to such an interesting and complex Universe, with an essentially in nite variety of objects.”
  • 237 massive as the Sun lives only 1/8 as long on the main sequence. A star 10 times as massive as the Sun lives only about 1/1000 as long on the main sequence. The Sun will live about 10 billion years on the main sequence. A 10-solar-mass star would live, accordingly, only about 10 million years on the main sequence. We know that very massive main-sequence stars, such as those in the heart of the Orion nebula, are young (a few million years old); otherwise, they wouldn’t be on the main sequence any more. Such massive stars older than a few million years would have turned into supergiants or blown up as supernovae (exploding stars). To summarize, massive stars are the most luminous main-sequence stars; low-mass stars are the dim main-sequence stars; our Sun is somewhere in the middle. Mass, therefore, is critical to a star’s life. Massive main-sequence stars (O-type and B-type stars) have large radii, high luminosities, and high surface temperatures. All these properties decrease as a star’s mass decreases. Sometimes, facts and gures can seem to take away from the beauty of the heavens; however, by determining these facts, we have been able to gure out how stars work, what makes them shine, and how they change throughout their lifetimes. Knowing such details only enhances our appreciation for celestial wonders and can be a springboard to the greater mysteries of the Universe. binary star: Two stars gravitationally bound to (and orbiting) each other. spectroscopic binary stars: Binary stars detected by examining the periodically varying Doppler shift in their absorption lines. Cooper and Walker, Getting the Measure of Stars. Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Important Terms Suggested Reading
  • 238 Lecture46:BinaryStarsandStellarMasses Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. If one main-sequence star is 3 times as massive as another one, what is the ratio of their luminosities? What is the ratio of their main-sequence lifetimes? Physically, why do you think the massive star uses up its fuel much faster than the low-mass one? 2. Do you think that planetary systems are more or less likely to form around binary stars than around single stars? 3. Albireo ( Cygni), the “Cal Star” (that is, the of cial star of the University of California, Berkeley, because of its colors), is a physical binary system consisting of a bright, yellow (“gold”) star and a fainter, blue star. Can you argue that the gold star is signi cantly larger than the blue star? Questions to Consider
  • 239 Star Clusters, Ages, and Remote Distances Lecture 47 “The ages of stars are obviously a fundamental aspect of their existence. We want to know how old each star is in order to be able to see how stars evolve as they age.” A s we have seen, the mass of a star determines its luminosity, radius, and surface temperature. Let’s look at star clusters and learn how we can determine their age. Star clusters are gravitationally bound groupings of stars, and many stars are found in such clusters. Indeed, stars are often born in clusters of hundreds or even thousands. There are two main types of clusters. The rst is an open cluster, consisting of a loosely bound set of stars, from a few dozen up to a few thousand. Also called galactic clusters (not to be confused with clusters of galaxies), they are not bound in a tight sphere. We know of about 1000 open clusters in our Milky Way Galaxy. The best-known example can easily be seen with the naked eye: the Pleiades, or Seven Sisters. Open star clusters are often composed of young stars because, we believe, after they have formed, they are gradually torn apart. Stars escape from the cluster as stars outside the cluster gravitationally tug on them. A gravitational slingshot effect among stars within a cluster can also cause stars to become unbound from the cluster. Open clusters appear in spiral galaxies, usually in the arms of the galaxy, which is where most of the gas and dust are found—substances from which stars are born. The second type of cluster is the globular cluster. These are much more massive clusters, as well as more spherical and denser, consistent with their name. They contain hundreds of thousands to a million stars. In our Milky Way Galaxy, we know of about only 150 to 170 globular clusters. They tend to occur in what is called the halo, or the outer regions surrounding our Galaxy. This suggests that these globular clusters were among the rst structures to form in our Galaxy. Some massive elliptical galaxies have a very large number of globular clusters, about 20,000 in the case of M87. It’s crucial to recognize that all the stars in a given cluster are roughly the same distance from Earth. Certainly, some are farther away than others, but
  • 240 Lecture47:StarClusters,Ages,andRemoteDistances the differences in distance are minor compared to the overall distance of the cluster as a whole. Thus, on the temperature-luminosity diagram, if we plot the apparent brightness (or apparent magnitude) of the stars (instead of their true luminosity or absolute magnitude) on the vertical axis against their surface temperatures on the horizontal axis, we see a well-de ned main sequence; the distance, d, is about the same for all stars in the equation L = 4 d2 b. Next, we can compare the main sequence of the cluster stars (apparent magnitudes) to the main sequence of nearby stars of known distances (absolute magnitudes). The difference in apparent magnitude versus absolute magnitude, or the factor by which apparent brightness is less than luminosity, allows us to derive the distance of the whole cluster. We can also determine the ages of stars in the cluster. Stars in the same cluster all formed at the same time from the same cloud of gas (the same collapsing nebula). What differs is each star’s mass. A given cluster will form low-mass stars, intermediate-mass stars, and high-mass stars. We can assume that, One of the densest of the known globular star clusters in the Milky Way, M80 (NGC 6093), contains hundreds of thousands of stars and is located 28,000 light years from Earth. NASA
  • 241 initially, a cluster was born with stars having O-type main-sequence stars down to K, M, and L main-sequence stars, which translates to a range of luminosities. We know that the more massive stars use up their fuel quickly and burn out and that the lower-mass stars are more stable and live longer. Therefore, noting the spectral type of the top end of the main sequence in the temperature-luminosity diagram (that is, the turnoff point of the main sequence), we can estimate the approximate age of the cluster. For example, if the main sequence of a cluster is missing the higher-mass stars (O-, B-, and A-type stars), but the F, G, K, M, and L stars are still present, the cluster must be old enough for the more massive stars to have burned out. Clusters that are missing main-sequence stars of type F or G are even older because those stars require more time to burn out. The gradual decrease in the height of a candle is analogous to the declining length of the main sequence. Knowing the initial length of the candle and the rate at which it is burning, we could determine how long it has been burning by measuring its current height. The amount of time it takes each type of main-sequence star to use up its central reservoir of fuel and leave the main sequence is determined from its luminosity and amount of available fuel. Clusters with O-type main-sequence stars are only a few million years old; clusters without G-type main-sequence stars have to be at least 10 billion years old because that’s how long it takes G-type stars to burn out. Our Universe is not yet old enough to have burned out M-type main-sequence stars, which can live more than a hundred billion years, even a trillion years. Most open clusters are young, but some are as old as 5 billion years. Globular clusters are the oldest clusters that we know of and have low main-sequence turnoff points. Because some are as old as 12 or 13 billion years, we know that the Universe is at least that old. It’s much more dif cult to determine the ages of individual stars that are not in clusters. We can use the temperature-luminosity diagram to determine the distances of stars that are too far away for the trigonometric parallax method to work. This method is called spectroscopic parallax, in which we use a star’s spectrum to help determine its distance. From the spectrum, we can tell what spectral type of star we are looking at—for example, O, B, A, F, G, K, M, or L. The spectrum can also tell us the star’s luminosity class—whether it is on the main sequence, a red giant, a white dwarf, or a supergiant. Knowing the spectral type and the luminosity class, we can determine where the star
  • 242 Lecture47:StarClusters,Ages,andRemoteDistances falls on the temperature-luminosity diagram. Then, by measuring the star’s apparent brightness and knowing its spectral type and luminosity class (and, hence, its luminosity), we can calculate its distance from Earth using the inverse-square law of light. For example, if a star is just like our Sun (a G2 main-sequence star) but appears faint, we can compare it with the known luminosity of the Sun and derive its distance. One complication with this method is that often gas and dust obscure the star’s light in what is called interstellar extinction, causing the star to appear dimmer than it really is. If we don’t account for this light extinction, we will deduce that the star is farther away than it really is. We can measure this extinction because a star that is dimmed by the absorption and scattering of light also appears redder—the overall spectrum becomes de cient in blue photons relative to red photons, because the blue photons are preferentially affected. Not to be confused with a redshift (caused by the Doppler effect or the expansion of the Universe), this effect is analogous to that of the setting Sun, which looks not only dim but also red. We know the true color of a given star because we measure its spectral type. Knowing the true color, we can account for this dimming by observing the amount by which it is reddened, just like the setting Sun. Taking account of this dimming effect, we can get a more accurate distance. How typical is our G-type Sun? Our Sun isn’t typical in that it’s a single star, not part of a binary system. Most of the apparently brightest stars in the sky are more luminous than the Sun—however, these are not typical stars either. Most of the stars within a given volume around the Earth (say, a radius of 10 or 20 pc) are less luminous than the Sun. Thus, although our Sun is a G-type star in the middle of the main sequence, it’s more massive and luminous than a majority of stars but not as massive and luminous as the most massive and luminous stars. Overall, we consider the Sun to be an average star, with average mass and luminosity. “There are stars that completely dwarf the Sun. Nevertheless, the Sun is more luminous and massive than the majority of the little pipsqueak stars. Overall, the Sun is pretty much a garden-variety star.”
  • 243 interstellar extinction: The obscuration of starlight by interstellar gas and dust. globular cluster: A bound, dense, spherically symmetric collection of stars formed at the same time. open cluster: A loosely bound cluster of stars, usually consisting of young stars that eventually break away from the cluster. Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Suppose you nd two clusters, one whose main sequence doesn’t have O, B, and A stars and the other whose main sequence doesn’t have any O, B, A, and F stars. Which is older? Why? 2. Massive main-sequence stars are much rarer than low-mass main- sequence stars. Thus, how might one accidentally overestimate the age of a very sparse cluster from its main-sequence turnoff? 3. When the temperature versus apparent brightness (not luminosity) is plotted for the stars in a cluster, why is the result a much cleaner-looking diagram than it is when this is done for random stars (not in a cluster)? Important Terms Suggested Reading Questions to Consider
  • 244 Lecture48:HowStarsShine—Nature’sNuclearReactors How Stars Shine—Nature’s Nuclear Reactors Lecture 48 “Amain-sequence staris in the prime of its life. It has a stable luminosity, surface temperature, and radius. It just doesn’t change very much. In this lecture, I’ll explain how a star achieves this stability. What is it actually doing while it’s on the main sequence?” N ebulae are vast clouds of gravitationally unstable gas and dust. Some areas collapse inward and coalesce into denser and denser regions in the centers; this is where stars are born. Larger clouds of gas typically fragment into smaller units, or cores, forming protostars, which themselves collapse and eventually turn into individual stars. These stars are initially gravitationally bound together to form open star clusters or globular clusters. The protostars are essentially in free-fall, and as they fall, or collapse, the particles pick up speed and collide with one another. The energy is converted into thermal energy, which creates pressure that eventually impedes the free-fall collapse. As the pressure and temperature rise, the collapse becomes a slower contraction. When the contraction is suf ciently slow and steady, the protostar becomes a pre-main-sequence star, slowly contracting and releasing half of its gravitational energy in the form of photons while the rest is transformed into heating the star, causing the temperature and pressure to rise still further. Eventually, the pressure and temperature become high enough to ignite nuclear fusion, which typically happens at about 10 million K. Fusion occurs at a controlled, non-explosive rate. Once the fusion reactions begin, they occur at the rate necessary to keep what is now a main-sequence star in a stable form, with nearly constant luminosity, radius, and surface temperature. Continually created energy keeps the star hot and pressurized inside, halting gravitational contraction and achieving stability. This mechanical stability is called hydrostatic equilibrium, in which gravity is pulling in and the net pressure is pushing out by an equal amount. The star is also in thermal equilibrium, which means that the nuclear reactions occur at exactly the rate they need to in order to keep the star from
  • 245 getting too hot or too cool. If the star became too hot inside, the nuclear reaction rate would increase, causing the star to expand and cool—making the reaction rate subside. Conversely, if the star were cooled on the inside, its pressure would decrease, causing contraction, which would cause the star to heat up again—making the reaction rate increase. Thus, a star’s core is self- regulating, like a thermostat. What is nuclear fusion, and how does it occur? In the center of a star such as the Sun, the temperature is very high and varies with the star’s mass. The Sun’s temperature is about 15 million K, for example. At such temperatures, hydrogen, helium, and other light atoms are completely ionized; that is, they’ve lost their electrons. The nucleus of a hydrogen atom (H) is simply one proton. We designate it as 1 H1 , in which the subscript 1 denotes the number of protons and the superscript 1 denotes the total number of protons and neutrons (collectively called nucleons). A helium nucleus is denoted as 2 He4 , indicating that it has two neutrons and two protons, for a total of four nucleons. In the central part of a star, where temperatures are high, the protons move very rapidly; these are simply the thermal motions of the protons. Although protons tend to repel one another (because they have the same electrical charge), under such high temperatures, they are often able to get reasonably close to each other. At this point, they can sometimes bind together because of the strong nuclear force. Eventually, four protons bind together and turn into an alpha particle, or a helium nucleus. Energy is liberated in the process, allowing the star to shine. Two of the protons turn into neutrons and release particles called positrons, the antiparticles of electrons. When an electron and a positron meet, they annihilate each other, turning into a burst of energy, or photons. The binding process releases additional light in the form of gamma rays (high-energy photons). Further, some released energy takes the form of particles called neutrinos, which don’t contribute to a star’s temperature or pressure, as the positrons and photons do. The fundamental result is that the “This binding energy seems like kind of a weird concept. How is it produced? Does it have something to do with the nuclei, or does it appear more commonly in life?”
  • 246 Lecture48:HowStarsShine—Nature’sNuclearReactors helium nucleus is more tightly bound than the four original protons of which it was made. This means that the helium nucleus has less mass than the four initial protons. The difference in mass between the original protons and the helium nucleus produces the energy that we see shining from stars. The liberated energy is given by 2 E mc , in which m is the difference in mass. Even though this difference is only 0.7% of the mass of the four original protons, it is enough to create the observed luminosity. Let’s look in more detail at what happens in the nuclear reactions within stars, speci cally in the proton-proton chain that occurs in the Sun. The nucleus of a normal hydrogen atom is known as a proton, but hydrogen can occur in different isotopes, or types. For example, the proton could be bound to a neutron and become a deuteron. Two neutrons bound to a proton create a triton. Helium (with two protons) has two isotopes: the most common containing two neutrons, and the other (light helium), only one neutron. In the rst stage of nuclear reactions, two protons combine to form a deuteron, a positron, and a neutrino. This happens twice, forming two deuterons. Each of those deuterons can combine with a proton to form a nucleus of light helium. The two light helium nuclei fuse together to form the heavy, normal isotope of helium. In the process, two of the protons are liberated, so only two of the four protons in the two light helium nuclei are assimilated into the single nucleus of heavy helium. Thus, out of six protons, four are assimilated into the bound helium nucleus and two are left over. This proton-proton chain is the process by which fusion occurs in the core of the Sun and other low-mass main-sequence stars. Our Sun uses nearly 700 million tons of protons every second! This seems like a huge number, but the Sun is 70% hydrogen and its mass is enormous; thus, it has a lot of fuel. Even though only 10% to 15% of the Sun’s mass ever participates in nuclear reactions, we can calculate that the Sun’s main- sequence lifespan is about 10 billion years. The Sun, currently about 4.6 billion years old, is therefore only a middle-aged star. We can now see how more massive stars use up their energy more quickly: Their internal pressures and temperatures are higher in order to maintain hydrostatic equilibrium. Because the fusion rate increases sharply with increasing temperature, the fuel runs out more rapidly.
  • 247 All main-sequence stars convert hydrogen into helium in some way. The lower-mass stars (below about 1.1 to 1.2 solar masses) use the proton- proton chain. More massive stars use a process called the carbon-nitrogen- oxygen cycle (CNO). Basically, the stars begin with a carbon nucleus left over from some long-dead star. This fuses with a proton, forming nitrogen, which decays into another isotope of carbon, releasing a positron and a neutrino. The resulting carbon isotope combines with another proton to form a different nitrogen isotope than before. This combines with a proton to form an oxygen isotope, which decays into another isotope of nitrogen. That nitrogen can combine with a proton to form the most common isotope of carbon (having 6 protons and 6 neutrons) plus helium. The net effect is that the cycle began with a carbon nucleus and ended with a carbon nucleus, but four protons were turned into a helium nucleus plus energy. antiparticle: A particle whose charge (if not neutral) and certain other properties are opposite those of a corresponding particle of the same mass. An encounter between a particle and its antiparticle results in mutual annihilation and the production of high-energy photons. deuteron: A deuterium nucleus. fusion: The formation of heavier nuclei from lighter nuclei. neutrino: A nearly massless, uncharged fundamental particle that interacts exceedingly weakly with matter. There are three types: electron, muon, and tau neutrinos. positron: The antiparticle of an electron. proton-proton chain: A set of nuclear reactions by which four hydrogen nuclei (protons) combine to form one helium nucleus, with a resulting release of energy. protostar: A star still in the process of forming in a cloud of gas and dust, collapsing nearly in free fall. Important Terms
  • 248 Lecture48:HowStarsShine—Nature’sNuclearReactors solar mass: The mass of the Sun, 1.99 1033 grams, about 330,000 times the mass of the Earth. strong nuclear force: The strongest force, it binds protons and neutrons together in a nucleus. Actually, it is the residue of the even stronger color force that binds quarks together in a proton or neutron. Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Smith, The Origin of Stars. 1. Given that individual stars can live for millions or billions of years, how can observations taken at the present time tell us about stellar evolution? 2. At one time, it was thought that the source of the Sun’s energy is gravitational contraction. If this were true, however, the Sun could have a current age of only a few tens of millions of years. With what known facts about Earth would such a number con ict? 3. Why does nuclear fusion occur only in the central region of stars rather than near their surface? Suggested Reading Questions to Consider
  • 249 Solar Neutrinos—Probes of the Sun’s Core Lecture 49 “The detection of neutrinos and neutrino oscillations is one of the greatest achievements of the past few decades. It affects not just astrophysics, it also affects fundamental particle physics, throwing a giant wrench into the theory, and that’s really exciting.” I n the previous lecture, we learned that the Sun produces its energy through nuclear fusion. But we can’t actually conduct physical experiments on the core of the Sun, so how do we know nuclear fusion is occurring now? The Sun could not burn from chemical reactions, such as ames burning paper or wood, because such a reaction couldn’t produce enough energy to power the Sun. Also, we know that temperatures in the Sun are too high for chemical burning in the conventional sense. The Sun cannot burn through gravitational contraction because this process would allow the Sun to live only about 50 million years; the Sun has likely been shining at its present rate for at least 3 billion years. In addition, other studies prove that the Sun is not gravitationally contracting, at least not much. Physicists have concluded that nuclear fusion must be occurring now because there is no other source of energy for the Sun to use. Though earlier concepts about physics couldn’t account for nuclear fusion, the advent of quantum mechanics changed our perception of how particles behave and answered some questions about nuclear fusion in the Sun. Still, we cannot physically test the Sun for nuclear fusion reactions. We do know that photons emerge from the Sun, though this fact still doesn’t prove that nuclear fusion occurs. Why not? When a photon is produced in the middle of the Sun, it encounters an opaque gas on its way to the Sun’s surface (photosphere). This causes photons to move randomly on their way out, which on average, takes about 100,000 years. If nuclear fusion reactions in the Sun stopped right now, we wouldn’t know it for 100,000 years because photons are already on their way to the surface. Thus, we can’t rely on photons to tell us that nuclear fusion is occurring right now. We must rely on ghostly particles called neutrinos, which are produced during fusion reactions. Neutrinos have only a slight mass and hardly interact with other
  • 250 Lecture49:SolarNeutrinos—ProbesoftheSun’sCore matter. It takes about 2 seconds for a neutrino to go from the core of the Sun to its surface and another 8.3 minutes to reach Earth. If we could detect neutrinos coming in great numbers from the Sun, we could prove that nuclear fusion is occurring right now. Where do these neutrinos come from and how do they interact? Recall the rst step of the proton-proton chain, in which two protons combine to form a deuteron. In the process, one of the protons turns into a neutron, a positron—an antielectron—and a neutrino. The positron annihilates an electron and produces photons. In the proton-proton chain, the neutrino— called an electron neutrino because it is associated with processes that form electrons and antielectrons—simply exits the Sun at a high speed. Every square centimeter of the Earth, every second, is bathed by about 60 billion such neutrinos from the Sun. With such high concentrations of neutrinos all around us, surely some would react with earthly elements and we could detect them. In fact, neutrinos can combine with a neutron in an atomic nucleus, turning it into a proton and an electron. Speci cally, a nucleus of chlorine can occasionally absorb an electron neutrino, turning it into a radioactive form of argon, which can be detected with a Geiger counter or some other device that detects radioactivity. One such experiment was conducted by Ray Davis, whose amazingly precise methodology allowed for the detection of a single radioactive argon nucleus in a 100,000-gallon tank of dry-cleaning solution. Another experiment by Masatoshi Koshiba made a similar discovery. Koshiba could actually con rm that the neutrinos were coming from the Sun rather than some other source. The detection of neutrinos was a great breakthrough, but there was another puzzle. Davis’s experiment detected only about one-third of the expected number of neutrinos, suggesting that our theory about the Sun was incorrect or that something else was at work. For example, perhaps the temperature in the Sun’s core wasn’t quite as high as we thought. Or maybe the Sun simply wasn’t fusing much at all at the present time. Alternatively, perhaps the electron neutrinos turned into some other kind—of cially known as “ avor”—of neutrinos, such as muon neutrinos or tau neutrinos.
  • 251 A 1998 experiment measured muon neutrinos produced by the interaction of cosmic rays from space with molecules in the Earth’s atmosphere. The experiment detected muons coming from the direction just above the detector (close to the Earth’s surface), muons coming from the back side of Earth, and muons coming from other random directions. The number of neutrinos coming from the back side of Earth was smaller than that coming from close to the detector, suggesting that muon neutrinos passing through Earth turn into another avor of neutrino on the way. This was the rst real evidence that at least muon neutrinos can change their avor; therefore, perhaps electron neutrinos from the Sun could change, as well. Recent experiments in Canada showed that two types of reactions can occur when electron neutrinos travel through a certain form of heavy water (that is, water containing atoms of deuterium instead of normal hydrogen). In one reaction, sensitive only to electron neutrinos, a very energetic electron is formed. It travels through the water with a speed higher than the local speed of light (which is slower than that in a vacuum, due to an interaction of light with water), producing electromagnetic radiation called Cerenkov radiation, or Cerenkov light. This accounts for one-third of the expected number of neutrinos, as in previous experiments. A second type of reaction, however, was able to detect all three known avors of neutrinos: electron, muon, and tau. Remarkably, the total rate at which neutrinos were detected matched theoretical expectations! This essentially proves the hypothesis that the Sun’s source of energy is nuclear fusion. Electron neutrinos are produced in the Sun, but about two-thirds of them turn into other neutrino avors during their journey to the Earth. The three observed neutrino avors turn out to be different combinations of more fundamental neutrinos, called type 1, type 2, and type 3. For example (simpli ed to illustrate the physical principles), an electron neutrino might be a speci c combination of type 1 and type 2 neutrinos. The quantum mechanical waves of type 1 and 2 neutrinos can sometimes be in phase and sometimes out of phase, thus creating the different “In fundamental particle physics, neutrinos are supposed to be massless, and yet it turns out they cannot change avors if they’re massless.”
  • 252 Lecture49:SolarNeutrinos—ProbesoftheSun’sCore avors of observed neutrinos—electron, muon, and tau. Such neutrino oscillations (from one observed avor to another) imply that neutrinos have nonzero (but very small) mass. Previously, scientists thought that neutrinos had no mass at all. In order to change their avor, neutrinos must move slower than the speed of light—but to move slower than the speed of light, they must have mass. Particles with no mass have to travel at the speed of light; otherwise, they wouldn’t exist. This great discovery challenges previous theories about particle physics, which had asserted that neutrinos are massless. It affects our understanding of the ways in which particles fundamentally behave at the microscopic and submicroscopic scales. Cerenkov radiation: Electromagnetic radiation emitted by a charged particle traveling at greater than the speed of light in a transparent medium. The blue light emitted is the electromagnetic equivalent of a sonic boom heard when an aircraft exceeds the speed of sound. cosmic rays: High-energy protons and other charged particles, probably formed by supernovae and other violent processes. deuterium: An isotope of hydrogen that contains one proton and one neutron. particle physics: The study of the elementary constituents of nature. quantum mechanics: A 20th -century theory that successfully describes the behavior of matter on very small scales (such as atoms) and radiation. Golub and Pasachoff, Nearest Star: The Surprising Science of Our Sun. Institute for Advanced Study, School of Natural Sciences, John Bahcall, www.sns.ias.edu/~jnb/ (“popular articles” link). Important Terms Suggested Reading
  • 253 Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sudbury Neutrino Observatory (SNO), www.sno.phy.queensu.ca/. Sutton, Spaceship Neutrino. 1. Why do neutrinos give us different information about the Sun than light does? 2. Do you think astronomers were overly bold in predicting that the solar neutrino problem would be resolved by changes in our theories of fundamental particles, rather than by abandoning the standard model of solar energy production? 3. The solar neutrino experiments that preceded SNO were able to detect only electron neutrinos. Why was the ability to detect all avors of neutrinos so important in helping to resolve the solar neutrino problem? Questions to Consider
  • 254 Lecture50:BrownDwarfsandFree-FloatingPlanets Brown Dwarfs and Free-Floating Planets Lecture 50 “As we’ve seen, true stars are de ned by the fact that they produce nuclear fusion in their cores.” D eep in the core of the Sun, temperatures are so high that protons can fuse together through the proton-proton chain, forming helium nuclei. This nuclear fusion provides a long-term source of energy for the Sun and, presumably, for other stars. Pre-main-sequence stars release energy through gravitational contraction, replenishing the energy supply that is lost to surrounding space and heating up the gas. As contraction continues and the center of the star gets hotter, nuclear fusion begins to take place, providing a stable new source of energy and halting contraction. Thus, a star is born, having reached hydrostatic and thermal equilibrium. Some astronomical bodies cannot reach suf ciently high temperatures (at least 3 million K for the least massive stars; higher for more massive ones) to allow fusion to begin. Thus, contraction remains the only source of energy (except deuterium fusion; see below). Such bodies are called brown dwarfs, which some astronomers think of as failed stars. Brown dwarfs are cool, dim, and small, and they continue contracting until a new form of pressure takes over—electron degeneracy pressure. Electron degeneracy pressure is a strange quantum-mechanical pressure arising from the fact that electrons repel one another (not electrical repulsion but, rather, quantum mechanical). Electrons are a type of fundamental particle called fermions, which cannot occupy the same quantum state. Another fundamental particle is a boson. Unlike fermions, two or more bosons (e.g., photons) can be in the same quantum state. Eventually, the density becomes so high in a brown dwarf that the electrons start overlapping spatially. To be in different quantum states, their momenta and, hence, their energies must be different. Some of the electrons must have very high energies and momenta because all of the lower-energy and lower-momentum quantum states are already fully occupied. These high-energy electrons exert an extra pressure— degeneracy pressure—which helps support the contracting brown dwarf. Before a brown dwarf becomes degenerate, temperatures are suf ciently
  • 255 high and densities suf ciently low that electrons are spread more randomly and exert normal thermal pressure. Brown dwarfs are about the same size as Jupiter. Because they are cool and small, they are faint and dif cult to notice. What little light they do emit tends to be in the infrared wavelengths. Brown dwarfs were predicted many decades ago but weren’t found until the 1990s. Now, we know of at least 1000, the discoveries of which coincided with the explosive growth in studies of exoplanets. The spectrum of one of the rst brown dwarfs showed absorption bands of methane, which is similar to the spectra taken of Jupiter. This con rmed that the object was a very cool brown dwarf; the presence of methane means that the atmosphere is much colder than that of the least massive stars. Brown dwarfs with methane in their atmospheres are called T dwarfs, while hotter ones are called L dwarfs (but some L dwarfs are genuine stars). After the rst few discoveries, many more brown dwarfs were found. Sky surveys taken at infrared wavelengths reveal many brown dwarfs. Some of the brown dwarfs orbit nearby stars, but others appear to have formed in solitude. In order to truly know whether a star is a brown dwarf or an L-type main-sequence star, we need to know its mass. This tells us whether it’s capable of high enough temperatures for nuclear fusion to occur. Brown dwarf Gliese 229B as observed by Palomar Observatory (left) and the Hubble Space Telescope (right). (Note: The spike at right is an artifact of the telescope.) S.Kulkarni(Caltech),D.Golimowski(JHU)andNASA
  • 256 Lecture50:BrownDwarfsandFree-FloatingPlanets Some brown dwarfs are actually in binary systems, allowing us to measure their masses using Newton’s laws of motion and the law of universal gravitation. Just as there are exoplanets orbiting normal main-sequence stars, it is possible that exoplanets orbit some brown dwarfs. Debris discs have also been found around some brown dwarfs, which could potentially form small planets. Brown dwarfs do experience fusion, though not through the proton-proton chain, which requires temperatures over 3 million K. At lower temperatures, deuterium fusion can occur, essentially bypassing the dif cult rst step in the proton-proton chain. Brown dwarfs begin fusion with deuterium (normally formed in the proton-proton chain), which collides with protons to fuse into light helium nuclei. This type of fusion is short-lived and occurs in brown dwarfs between 13 and 75 Jupiter masses. Above 75 Jupiter masses, the normal proton-proton chain occurs. Astronomers disagree about whether or not brown dwarfs should be called true stars or failed stars. One solution is to simply recognize that brown dwarfs and normal stars are “fusers.” Normal stars undergo nuclear fusion of protons, whereas brown dwarfs fuse deuterium. Below 13 Jupiter masses, even deuterium fusion doesn’t occur. Thus, we call these bodies planets. Suppose we plot the distribution of the number of bodies discovered through the Doppler wobble technique (Lecture 38) against their derived masses. As we discussed when considering exoplanets, the Doppler wobble technique actually leads us to infer M sin i—rather than the actual mass, M—where i is the inclination angle between the orbital plane and our line of sight and sin denotes “sine.” Only the radial component of the total velocity is measured with the Doppler effect. Thus, if sin i is less than 1, the true mass (M) must be greater than the measured quantity, M sin i. Objects that are 12 or 13 Jupiter masses, minimum, are almost certainly brown dwarfs. Some with a minimum mass below 12 Jupiter masses are probably also brown dwarfs. Even a few objects having a rather low minimum mass (say, 4 Jupiter masses) might actually be brown dwarfs if their true mass exceeds 13 Jupiter masses. Nevertheless, most objects with an inferred minimum mass below about 6 Jupiter masses are probably planets, not brown dwarfs; they don’t experience fusion of any kind, even deuterium fusion.
  • 257 What would we call an object of less than 13 Jupiter masses, not fusing deuterium, and not orbiting a star? Most astronomers would call it a free- oating planet because it has a planetary mass and it is not undergoing fusion. Some free- oating planets were ejected from their planetary systems, while others simply formed on their own through gravitational contraction out of a cloud of gas—like normal stars. Some astronomers would like to call the result of the rst scenario a planet and the second scenario a brown dwarf, regardless of whether the object is massive enough for deuterium fusion to ever occur. Others don’t want to apply the term planet to objects that are not orbiting another star. Gibor Basri, of the University of California, Berkeley, has proposed that we call objects planemos (“planetary mass objects”) if they are at least massive enough to be spherical but not massive enough to be deuterium-fusing brown dwarfs. If a planemo happens to orbit a star, we call it a planet. Because we are nding more and more of these relatively low-mass objects through infrared studies of the skies, at some point, we will have to agree on the terminology and classi cation. Clearly, a range of masses can occur in the process of star and planet formation, from the most massive O-type stars to the least massive normal hydrogen-fusing stars, down to deuterium-fusing stars (brown dwarfs), and to planetary mass objects that don’t fuse at all. brown dwarf: A gravitationally bound object that is insuf ciently massive to ever be a main-sequence star but too massive for a planet. Generally, the mass range is taken to be 13 75 Jupiter masses. “All this is telling us is that, in the process of star and planet formation, there’s a range of masses that can occur. It’s all part of one continuum, one process that leaves the same sorts of objects, but having a continuum of masses.” Important Terms
  • 258 Lecture50:BrownDwarfsandFree-FloatingPlanets degenerate gas: A peculiar state of matter at high densities in which, according to the laws of quantum physics, the particles move very rapidly in well-de ned energy levels and exert tremendous pressure. California and Carnegie Planet Search, www.exoplanets.org. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What are the problems associated with requiring knowledge of an object’s formation history to classify it as a brown dwarf, a planet, or something else? 2. Under what circumstances can the true mass of a brown-dwarf candidate identi ed through the Doppler wobble technique be determined? 3. Do you consider brown dwarfs to be failed or genuine stars? Suggested Reading Questions to Consider
  • 259 Our Sun’s Brilliant Future Lecture 51 “Through observational studies of stars at different stages of their lives and using the physics of gases held together by gravity, astronomers can predict with accuracy how stars are likely to evolve.” T he laws of physics help us understand how stars will evolve based on the nuclear reactions that occur, pressures and temperatures in the core, and other factors. In this way, we can predict what will happen to our Sun as it evolves. For about 9 or 10 billion years, the Sun will remain on the main sequence—that is, it will fuse hydrogen into helium in its core through the proton-proton chain, releasing energy. At 4.6 billion years old, our Sun is about halfway through its normal main-sequence lifetime. As the Sun evolves, it will gradually brighten, because as it fuses hydrogen into helium, its core temperature necessarily has to rise, and the fusion rate will increase. For every four initial protons, only one helium nucleus will be produced. Therefore, the number of particles per unit volume in the middle of the Sun—that is, the number density—will gradually decrease. Pressure is proportional to the product of number density and temperature. If the number density decreases (because hydrogen is fusing to helium), the temperature has to rise to compensate and maintain the same pressure. In a few hundred million years, Earth will be substantially warmer because the Sun’s luminosity will have increased somewhat. In about half a billion to a billion years, the oceans will be gone, and the Earth will be like a scorching desert. It’s possible that some compensating effect will keep Earth’s temperatures lower than anticipated. We know that an inverse compensating effect must have occurred billions of years ago when the Sun’s luminosity was about 30% lower than it is now. Without such an effect, the Earth’s oceans would have been frozen, yet fossil evidence proves that certain life forms existed in relatively warm conditions. It’s possible that a more pronounced greenhouse effect was occurring on Earth at that time.
  • 260 Lecture51:OurSun’sBrilliantFuture What will happen in about 5 billion years when the Sun reaches the end of its main-sequence life? A similar future awaits other sun-like stars. Its helium core will increase to about 10% to 15% of the total mass. Remember, the core is the only part of the star where temperatures are high enough for nuclear fusion to be sustained. However, nuclear reactions in the core will stop because helium nuclei repel each other much more than protons do, and the temperature will not be high enough for helium nuclei to fuse into heavier elements. Heat will gradually diffuse out of the helium core, causing it to gravitationally contract in order to replenish the supply of energy lost to its surroundings. The energy released by the contracting helium core will heat the surrounding hydrogen-fusing shell. This will increase the fusion rate in that hydrogen shell, causing the star to become much more luminous than before. The energy liberated by the hydrogen- burning shell causes the surrounding layers (all the way out to the surface) to expand. Thus, contraction of the helium core leads to an expansion of much of the rest of the star. The expanding atmosphere of the star cools and its color shifts to more yellow, then orange (like that of a K-type star), and eventually, perhaps even somewhat red, because the peak of the spectrum shifts to longer and longer wavelengths. The Sun will become a red giant— perhaps 100 times more powerful than it is now—and much more luminous because of the vigorously burning hydrogen shell around the small helium core. The Sun will bloat to such a large size in its red-giant stage that it might extend to the orbit of Mercury. Contraction of the helium core will heat it up. Eventually, this slowly contracting helium core will reach temperatures of about 100 million K, suf cient for three helium nuclei to fuse, forming a carbon nucleus. The carbon nucleus can pick up another helium nucleus and turn into oxygen. Both of those reactions, the formation of carbon and the formation of oxygen, liberate still more energy. At that point, the Sun will have two sources of energy: the helium-fusing core surrounded by an inert helium shell and a hydrogen-burning shell around that. “Our Sun will probably form a spherically symmetrical planetary nebula. We don’t know exactly what it’ll look like, but I’m hoping that it’ll be really pretty, so that future aliens, looking at our dying Sun, will say, ‘Wow, that’s a real beauty.’ ”
  • 261 The fusion of helium into carbon and oxygen lasts only about 1 million years because the individual fusion reactions don’t produce much energy compared to the original proton fusion reactions. Yet because the star is very luminous, it produces a prodigious amount of energy quickly; therefore, helium is used up rather quickly, and a carbon-oxygen core forms. The carbon-oxygen core does not have high enough temperatures for fusion; thus, it begins to contract, just as its predecessor helium core had done. That contraction heats the carbon-oxygen core and liberates energy to a helium-fusing shell, which burns even faster, making the star’s luminosity rise. The hydrogen-burning shell also fuses at a faster rate, releasing even more energy. This extra energy pushes out the outer envelope of the star even more, causing it to become a still larger red giant, which in the case of the Sun, might encompass Earth’s orbit (or at least Venus’s orbit). Different stars have different red giant time phases, ranging from about 100 million years to a few billion years. The Sun’s red-giant stage will last about half a billion years. During the red-giant stage, our Sun will become unstable, and its outer layers will be ejected in a series of relatively nonviolent outbursts. At such a huge size, a star’s outer atmosphere is barely bound to the star; gravity is weak there because the gases are so far from the core. The star begins losing its outer atmosphere through a steady stellar wind (analogous to the current solar wind) as radiation pushes out the gases. The star also becomes unstable, oscillating in size, and some of these pulsations actually eject the outer parts of the star—10% to 20% of its mass—in a relatively nonviolent way, like a cosmic burp. When such material is ejected, the star becomes an expanding, glowing shell of ionized gas. The ejected shell can appear in the shape of a disk or a ring, called a planetary nebula, though it has nothing to do with planets. The term was derived in the 19th century before scientists knew that these nebulae were actually dying stars. Over a few tens of thousands of years, the nebula’s light spreads so much that it fades. The gas in a planetary nebula is ionized because many ultraviolet photons are emitted from the hot central star, whose surface used to be the core of the star (prior to the ejection of the outer atmosphere). The gas glows as the electrons recombine with positive ions. Also, electrons ying around in the gas hit other electrons bound in atoms, kicking them up to higher energy levels. These excited electrons subsequently jump back down to
  • 262 Lecture51:OurSun’sBrilliantFuture lower energy levels, thereby emitting light. Many interesting photographs have been taken of such light emitted from planetary nebulae, showing not only brilliant colors but some fascinating structures. Deep photographs can capture layers ejected long ago. Dying stars can also produce bipolar ejections—that is, ejections that occur along an axis, forming planetary nebulae that are not spherically symmetric but, rather, shaped somewhat like an hourglass. We think that bipolar ejections are formed in a binary system in which one star expands into a red giant and begins transferring material to its companion. The transferred material envelops the companion and the red giant. As the common envelope contracts, a disk forms, forcing the ejecta of the expanding nebula to be expelled predominantly along the plane of the rotating disk. planetary nebula: A shell of gas, expelled by a red-giant star near the end of its life (but before the white-dwarf stage), that glows because it is ionized by ultraviolet radiation from the star’s remaining core. Kippenhahn, 100 Billion Suns: The Birth, Life, and Death of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Do planets form directly from a planetary nebula? 2. How can we be so con dent in our theory of the Sun’s future evolution? 3. It is often said that we on Earth have about 5 billion years before we need to worry about the Sun’s death. Why is this incorrect? 4. Why doesn’t the helium core of a red giant immediately start fusing to heavier elements? Important Term Suggested Reading Questions to Consider
  • 263 White Dwarfs and Nova Eruptions Lecture 52 “By looking at more advanced stages of evolution of other Sun-like stars, and by using the laws of physics—in particular, the physics of hot gases—we have deduced that, in about 5 or 6 billion years, our Sun will expand greatly and then eject its outer envelope of gases, becoming a beautiful, glowing planetary nebula.” I n this lecture, we will examine what happens when relatively low-mass solitary stars (such as the Sun) die at the end of their lives. Stars with initial sizes of between 0.08 and 8 solar masses and, perhaps, up to 10 solar masses eventually expel their outer atmosphere of gases during the planetary nebula stage and cease all nuclear fusion to become white dwarfs. The Sun is a representative star in this range. After the Sun becomes a red giant and then a planetary nebula, the remaining star (what used to be the core of the red giant) consists of carbon and oxygen. The nuclei repel each other so strongly that fusion cannot take place. Even in the helium shell around the carbon and oxygen core, temperatures are too low for fusion to be maintained. The core continues to contract as the star loses energy, increasing its density. Electron degeneracy pressure keeps the star from contracting inde nitely; it eventually reaches an equilibrium size. Heat is still liberated from the dying star by electrons moving to the lowest energy levels and from positively charged atomic nuclei. Yet no new energy is created because nuclear reactions and gravitational contraction have stopped. White dwarfs are about the size of Earth. The radius of a white dwarf is proportional to its mass raised to the 1/3 power: R M–1/3 . As mass increases, radius decreases because of the high compression of electrons by gravity. A tablespoon of white dwarf material would weigh several tons. “At the ends of their lives, stars can do a variety of interesting things: from the surface explosions of white dwarfs, to instabilities in more-massive stars that cause them to brighten and fade occasionally.”
  • 264 Lecture52:WhiteDwarfsandNovaEruptions 264 The atomic nuclei of a white dwarf are not degenerate; they can still lose energy, because although the electrons are all in their lowest energy states, the nuclei are not. Thus, white dwarfs can be thought of as “retired stars.” Their light comes from the supply of thermal energy built up in the nuclei over the star’s lifetime. A white dwarf gradually becomes dimmer and dimmer as the atomic nuclei cool down. After tens of billions of years, white dwarfs are no longer visible, and they become black dwarfs—though there is no sharp dividing line between white dwarfs and black dwarfs, and some astronomers avoid this term. Black dwarfs are still supported by electron degeneracy pressure, but the positive ions inside have cooled to low temperatures. If we could touch a very cold white dwarf (black dwarf), it wouldn’t burn you, despite the fact that many electrons are moving at very high speeds. All of the electrons are already in the lowest energy states possible. In other words, the electrons can’t transfer energy to a touching hand because they can’t move to lower energy levels and give off excess energy. Now let’s review what we have learned about the post-main sequence, or after-main sequence, evolution of a Sun-like star. We’ll also add some details and examine the physical properties of white dwarfs. The position of a star on the temperature-luminosity diagram is dependent on its mass. A main-sequence star remains nearly unchanged in luminosity and surface temperature for a long time. (It grows somewhat brighter with time, but to a rst approximation, we can ignore this.) Once a star’s core hydrogen is used up, the helium core contracts and the star transforms into a red giant. The helium then fuses to carbon and oxygen. Contraction of the carbon- oxygen core turns the star into an even larger red giant. The red giant’s outer atmosphere becomes unstable and is dispersed through winds and gentle ejections. The temperature of the central star’s surface increases as its outer layers are peeled away. This pattern of degeneration to a white dwarf is what happens in general to all stars between about 0.08 and 8 solar masses and, perhaps, up to 10 solar masses, following their long period of stability as main-sequence stars. It turns out that what happens in detail to a star as it dies depends on its mass at birth. Regardless of its initial mass (up to 8 solar masses), those stars that
  • 265 become white dwarfs will always be less than 1.1 solar masses in the white dwarf stage. Our Sun will end up as a roughly 0.6-solar-mass white dwarf. Stars with initial mass below 0.45 solar masses will consist of helium in the white dwarf stage; those stars never achieve a suf ciently high temperature for helium to undergo fusion into carbon and oxygen. A star with an initial mass between 8 and 10 solar masses fuses carbon and oxygen to form oxygen, neon, and magnesium in its core. Though we don’t know for sure, such a star could turn into an oxygen-neon-magnesium white dwarf having a mass perhaps somewhat larger than 1.1 solar masses. Other calculations say that such stars explode at the end of their lives. We are not yet certain what will happen. Stars initially greater than 10 solar masses eventually explode, which we’ll discuss in Lecture 53. White dwarfs have a theoretical maximum mass of 1.4 solar masses. This is known as the Chandrasekhar limit, named for a great Indian astrophysicist who derived it. The limit occurs because as a white dwarf accumulates material, its radius shrinks. Eventually, the radius is so small and the electrons are squeezed into such a tiny volume, that their speeds approach the speed of light, and their ability to exert more pressure diminishes. A star in a gravitationally bound binary system can change its mass by accreting material from its companion. Thus, stars whose initial masses were low can increase in mass—and, hence, core pressure—causing them to behave like more-massive stars, which in turn, speeds up their evolution. In a binary system in which one star is already a white dwarf and its companion star begins “feeding” it material through an accretion disk, a sudden brightening can occur, called a nova. The eruption is caused when accreting material forms clumps that fall onto the white dwarf’s surface, releasing gravitational energy. The white dwarf can brighten by a factor of 100, sometimes even more, for a few weeks. Or the material can accumulate on the surface and undergo an uncontrolled chain of nuclear reactions, releasing even larger amounts of energy and making the white dwarf up to a million times brighter for a short time.
  • 266 Lecture52:WhiteDwarfsandNovaEruptions In addition to white dwarfs, other stars can undergo such rapid eruptions, though the physical mechanisms may differ. One example is Eta Carina, in the southern hemisphere, a massive star that sometimes brightens considerably. Clearly, at the end of their lives, stars exhibit a variety of interesting phenomena, from the surface explosions of white dwarfs to instabilities in more massive stars that cause them to occasionally brighten and fade. Chandrasekhar, Subrahmanyan (1910 1995). Indian-born American astrophysicist. Awarded the Nobel Prize in Physics in 1983 for his work on the physical understanding of stars, especially the upper mass limit of white dwarfs. Chandrasekhar limit: The maximum stable mass of a white dwarf or the iron core of a massive star, above which degeneracy pressure is unable to provide suf cient support; about 1.4 solar masses. Kippenhahn, 100 Billion Suns: The Birth, Life, and Death of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. If you compare a photograph of a nearby planetary nebula taken 100 years ago with one taken now, how would you expect them to differ? 2. Why is the surface of a star hotter after the star sheds a planetary nebula? Name to Know Important Term Suggested Reading Questions to Consider
  • 267 3. What forces balance to make a white dwarf? 4. If you wanted to prove that a nova must be a binary star system, what kinds of observations might you make?
  • 268 Lecture53:ExplodingStars—CelestialFireworks! Exploding Stars—Celestial Fireworks! Lecture 53 In the last lecture, we saw that most stars die rather quietly, becoming red giants, planetary nebulae (gentle ejections of matter), and white dwarfs. A small minority of stars, however, ends their lives with catastrophic explosions: supernovae. A supernova can increase a star’s luminosity to as much as 10 billion Suns. At its peak, a supernova can rival the brightness of an entire galaxy of stars. The star’s gases may be ejected at speeds greater than 10,000 kilometers per second, which we can determine by examining the spectra of supernovae, as we’ll see in the next lecture. Supernovae heat the interstellar medium—the gases between the stars—causing winds to blow out of entire galaxies. They also give rise to compact remnants in some cases, such as neutron stars and bizarre black holes. Supernovae accelerate charged particles to very high speeds, creating cosmic rays that cause at least some of the mutations that led to the evolution of life. From the human perspective, the most important aspect of supernovae is that they create and disperse into the cosmos the very elements of which life is made. Though the hot, dense, early Universe (the so-called Big Bang, to be studied in future lectures) produced hydrogen and helium, all the heavier elements were created inside stars. If some stars didn’t explode, those heavy elements would remain forever locked up inside white dwarfs, unavailable as the raw material from which new stars, new planets, and even life could form. Indeed, all of the elements in the upper part of the periodic table, such as silver and gold, were produced from such “stardust.” In addition, iron, calcium, carbon, and oxygen, ejected by exploding stars, are essential for life on Earth. We can look at the spectra of supernova remnants and see those elements, which weren’t present when the star rst formed. After tens of thousands of years, nebulae expand even more, gradually merging with other existing clouds of gas and dust within galaxies to form new stars, new planets, and even life. DNA, the basis of life itself, owes its existence to previous
  • 269 generations of stars. The ejection of the heavy elements into the cosmos, and the production of the elements themselves, is the most centrally important aspect of supernovae. Is our Sun, then, a second-generation star? From what supernova did we come? In reality, our Solar System was formed from a mixture of exploding stars in which debris from many explosions coalesced. In other words, many different generations of stars gave rise to the cloud of gas from which our Solar System formed over a vast time scale. Let’s discuss some speci c supernovae. The most famous supernova remnant is the Crab Nebula, an expanding set of gases created by a supernova that occurred in A.D. 1054, rst seen on July 4 by Chinese astronomers. The supernova was alleged to be visible during the day for 23 days. In A.D. 1006, another supernova left a bright remnant recently photographed with the Chandra X-ray Observatory and other telescopes. A clear supernova was last seen in 1604 in our own Milky Way Galaxy by Johannes Kepler, of which we can see the remnant. Kepler’s mentor, Tycho Brahe, also witnessed a supernova in 1572 that has produced an expanding remnant. Supernovae are rare; in a big galaxy like our own, they might occur a few times per century. The reason we may not have seen a bright supernova since 1604 is that some may be hidden by the extensive gas and dust in the plane of our Galaxy. One supernova occurred in the 1670s in the constellation Cassiopeia, but only one person possibly noticed it. However, today, we clearly see its remnant and can even detect a neutron star in the middle. Ironically, supernovae are easier to nd than other galaxies. Because they are so rare, we have a better chance of nding one by looking at many galaxies over time to observe changes. The Lick Observatory’s Katzman Automatic Imaging Telescope (KAIT), owned and operated by my research group, is programmed to take pictures Supernova remnant, Cassiopeia A. NASAandTheHubbleHeritageTeam(STScI/AURA) usingdatacollectedbyPrincipalAstronomerRobFesen (DartmouthU.)andcollaboratorsandtheHubbleHeritage team(STScI/AURA)
  • 270 Lecture53:ExplodingStars—CelestialFireworks! (CCD images) of more than 1000 galaxies over the course of a single night in search of supernovae. Each week, new images of 7000 or 8000 galaxies can be compared with previous images to see if anything new appears. The computer software automatically makes the comparisons and identi es supernova candidates; then, undergraduate students examine them to determine which ones are likely to be genuine supernovae. My group has discovered more than 600 relatively nearby supernovae during the past decade, about half of all the bright supernovae that have occurred during this interval. We are the world’s leaders in nding such objects. Supernovae are named in the order of discovery in any given calendar year. For example, the rst supernova of 2000 is named SN 2000A, the second is named SN 2000B, and so on, up through SN 2000Z. The next two after that are SN 2000aa and SN 2000ab, and so on. Though this is not scienti cally important, my group even found both SN 2000A and SN 2001A— the rst supernova of the new millennium, regardless of one’s de nition of the new millennium (Jan. 1, 2000, or Jan. 1, 2001). We now study nearby supernovae in great detail for a better understanding of how stars explode. Amateur astronomers have discovered many supernovae by making similar observations. Rev. Robert Evans, who lives in Australia, was the rst amateur astronomer to systematically nd bright supernovae. He conducted visual observations of galaxies through his telescope and found about 40 supernovae over the course of a few decades. Inspired in part by the success of Evans and in part by our KAIT search at the Lick Observatory, several amateur astronomers have now found more than 100 supernovae each by repeatedly taking CCD images of galaxies and comparing them to look for new objects. For this reason, amateurs are important in our studies of the heavens. Amateur astronomers in general contribute to our study of the stars, helping to increase our chances of discovering interesting celestial phenomena. “You want to spend your time with the Keck telescopes and others studying the supernovae, not searching for them. It’s really a great form of cooperation between professionals and amateurs.”
  • 271 interstellar medium: The space between the stars, lled to some extent with gas and dust. supernova remnant: The cloud of chemically enriched gases ejected into space by a supernova. Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Harvard-Smithsonian Center for Astrophysics, Supernova, www-cfa.harvard.edu/oir/Research/supernova/SNlinks.html. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Does the fact that you are made of stardust give you a sense of unity with the cosmos? 2. Why do we think that the Crab Nebula is a supernova remnant? 3. If one or two supernovae occur in a typical galaxy every century, how many galaxies would you need to monitor to nd 20 supernovae each year? Important Terms Suggested Reading Questions to Consider
  • 272 Lecture54:WhiteDwarfSupernovae—StealingtoExplode White Dwarf Supernovae—Stealing to Explode Lecture 54 Inthepreviouslecture,welookedatsupernovae,catastrophicexplosions of a small minority of stars at the ends of their lives. We begin this lecture by discussing the two main kinds of exploding stars. A s we have seen, spectra of stars provide us with information about the stars’ chemical compositions. Similarly, spectra of stellar explosions can tell us a tremendous amount about the stars from which the supernovae arise and about the explosions themselves. There are two main types of exploding stars. Those that show hydrogen in their spectra are called Type II; those that do not show hydrogen in their spectra are called Type I. The Type I class is further divided into subclasses Type Ia, Ib, and Ic, based on the details of the optical spectra. Type Ia supernovae were formerly known simply as Type I before the other two subclasses were recognized. Type Ia supernovae reach their peak brightness over the course of about 3 weeks, then decline for many months or years. Type II supernovae reach their peak brightness in just a day or two, then maintain that brightness for up to 3 months before quickly declining. Type Ia supernovae occur in all kinds of galaxies, including elliptical ones that consist only of old stars. Type II supernovae, as well as Types Ib and Ic, tend to occur in the arms of spiral galaxies and those galaxies where young stars are forming. This suggests that Types II, Ib, and Ic are somehow related to the deaths of massive stars. The spectra of supernovae show evidence for the rapid ejection of gases at speeds sometimes exceeding 10,000 kilometers per second. We can deduce this by plotting their brightness against wavelength and seeing how the absorption lines are blueshifted relative to the emission line. The invention of robotic technology and computer software allows us to examine supernovae in great detail. For example, we can obtain the spectra and compare the light curves of many such events, teaching us about the physics of explosions.
  • 273 We can also study the rates at which different kinds of supernovae occur (that is, how many per century per galaxy, on average) and in what types of galaxies. This information is important because different types of supernovae produce different kinds of chemical elements, and they infuse their galaxies with that material. If certain kinds of galaxies produce more Type Ia supernovae than Type II, the chemical evolution of those galaxies will be different from the galaxies that produce more Type II supernovae, for example. The data can also help us determine the rate of formation of neutron stars and pulsars, as well as how quickly the gas between the stars is heated by these explosions. What produces a Type Ia supernova? Traditional Type Ia supernovae don’t show hydrogen in their spectra, which means that there’s very little or no hydrogen present in their ejecta. This is signi cant because hydrogen is by far the most common element in the Universe. In addition, as we said earlier, Type Ia supernovae tend to occur in galaxies that have only old stars. Further, all supernovae of this type have nearly the same observed properties—similar light curves and similar peak power. These characteristics suggest that Type Ia supernovae arise from carbon-oxygen white dwarfs, perhaps surrounded by a thin helium layer, but possibly with little or no hydrogen. Such a white dwarf in a binary system can sometimes accrete hydrogen from a companion star that is on its way to becoming a red giant. The accreted material increases the white dwarf’s mass. If the accretion rate is just right, the star can avoid nova-like surface explosions that prevent the mass of the white dwarf from growing substantially. Instead, its mass increases. Once the white dwarf reaches its limiting mass, the Chandrasekhar limit of about 1.4 solar masses, it becomes unstable, setting off a runaway chain of nuclear reactions (starting with the fusion of carbon and oxygen) that releases tremendous energy and completely obliterates the star. “An understanding of Type Ia supernovae and how they occur will be very important in our studies of cosmology, the overall structure and evolution of the Universe.”
  • 274 Lecture54:WhiteDwarfSupernovae—StealingtoExplode About half of the white dwarf’s mass fuses to a radioactive isotope of nickel. This nickel-56 decays into radioactive cobalt-56, then into stable iron-56. The decay process emits gamma rays, which are extremely energetic photons. Those gamma rays bounce around inside the exploding star, gradually being converted into optical light. The optical radiation escapes from the expanding gases, giving rise to the optical display of light that we see for a few months or a few years. If radioactive nuclei had not been produced, the explosion would not be visible because all of the released energy would have been used up in the star’s expansion. We are not certain about the details of such explosions. For example, what happens if we incorporate rotation and magnetic elds? How, exactly, is the thermonuclear runaway initiated, and how does it proceed? Although we think that only carbon-oxygen white dwarfs in binary systems can accrete enough material to reach the Chandrasekhar limit and explode in the observed manner, we don’t exactly know which kinds of binary systems are suitable and how the white dwarfs reach this limit. Main-sequence stars are generally much smaller than their Roche lobes—the region within which a star’s gravity dominates—and, therefore, are not capable of spilling material onto their companion white dwarfs. On the other hand, if a red giant is spilling material onto a white dwarf, we would expect the explosion to rip some of the gas away from the envelope of the red giant, causing the hydrogen to glow and show up in the spectrum. Yet it doesn’t. Some physicists have proposed the existence of sub-Chandrasekhar white dwarfs—with masses of less than 1.4 solar masses yet still explosive. For example, an explosion can be initiated at the boundary between the helium envelope and the carbon-oxygen core. The problem is that the spectra and light curves from such models don’t agree with what is observed. Some physicists have proposed that two white dwarfs in a binary system will gradually spiral together and merge, causing an explosion. However, we know of too few binary white dwarfs in our own Galaxy to account for the observed number of Type Ia supernovae in a typical galaxy. We don’t really know how a star reaches the Chandrasekhar limit, but this question offers a great opportunity for future astronomers to discover the fundamental mechanism by which white dwarfs reach their explosive stage.
  • 275 neutron star: The compact endpoint in stellar evolution in which typically 1.4 solar masses of material is compressed into a small (diameter = 20 30 km) sphere supported by neutron degeneracy pressure. pulsar: An astronomical object detected through pulses of radiation (usually radio waves) having a short, extremely well-de ned period; thought to be a rotating neutron star with a very strong magnetic eld. Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Harvard-Smithsonian Center for Astrophysics, Supernova, www-cfa.harvard. edu/oir/Research/supernova/SNlinks.html. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Distinguish between what goes on in novae and Type Ia supernovae. 2. Do you think the observed widths of emission and absorption lines in the spectra of supernovae give some indication of the speed of the ejected gas? 3. Most white dwarfs have a mass of about 0.5 to 0.6 times the mass of the Sun. Does this pose a problem for the hypothesis that most Type Ia supernovae arise from the explosion of a merged white dwarf binary whose mass reaches the Chandrasekhar limit? Important Terms Suggested Reading Questions to Consider
  • 276 Lecture54:WhiteDwarfSupernovae—StealingtoExplode 4. Given that the nuclear reactions at the surface of a white dwarf undergoing a nova explosion release enough energy to eject the material accreted from the companion star, why do you think it is important for a white dwarf to avoid the nova process if it is to eventually become a supernova?
  • 277 Core-Collapse Supernovae—Gravity Wins Lecture 55 In previous lectures, we’ve seen how some white dwarfs reach an unstable mass, the Chandrasekhar limit, causing them to explode. In this lecture, we will look at another kind of mechanism for stellar explosions in Type II supernovae and related subclasses. T ype II supernovae appear in spiral galaxies, usually in or near spiral arms, where lots of massive stars are forming or have recently formed. Red supergiants are most likely to become supernovae, and these stars typically have masses initially at least 10 times that of our Sun. A cross- section of such a star would show an iron core with shells of progressively lighter elements surrounding it: silicon and sulfur; oxygen, neon, and magnesium; carbon and oxygen; helium; and nally, hydrogen. Most of the volume, however, is hydrogen. Red supergiants have this onion-like layering because the ashes of one set of nuclear reactions become the fuel for the next set. Hydrogen fuses to helium; helium fuses to carbon and oxygen; and carbon and oxygen fuse to neon, magnesium, and so on, all the way up to iron. Each set of reactions liberates energy because the products are more and more tightly bound compared to the reactants; the binding energy is released during nuclear fusion. Iron and other elements of similar mass—nickel and cobalt, for example—are the most tightly bound elements. For this reason, their fusion does not produce energy; rather, it requires energy. Very heavy elements (such as uranium) can undergo ssion, or break up, into lighter elements, releasing energy. Per nucleon (proton or neutron), the binding energy of the products is higher than the binding energy of the very heavy elements. However, this is not what occurs in a red supergiant. We mention ssion of very heavy elements simply to stress that iron-group elements are the most tightly bound (that is, have the highest binding energy per nucleon). Thus, as a red supergiant undergoes successive stages of nuclear burning, iron eventually forms in the core, with a silicon-sulfur- fusing shell surrounding it.
  • 278 Lecture55:Core-CollapseSupernovae—GravityWins As the iron core gains mass, it eventually reaches the Chandrasekhar limit of roughly 1.4 solar masses. At its mass limit, the iron core collapses due to gravity, to a radius of only about 10 kilometers, liberating a tremendous amount of gravitational energy. Microscopically, the electrons and protons combine to form neutrons and neutrinos. The pressure support, previously provided mostly by the electrons, disappears until the star is just a ball of neutrons—a neutron star. During the core’s collapse, it rebounds from itself because its constituent particles repel one another when they get too close together. Because material surrounding the core is no longer supported by pressure, it collapses, but then it collides with the rebounding core and is propelled outward at high speeds. But this prompt mechanism, or rebounding effect, is not enough to completely eject the material into space. The gravity of the central neutron star pulls it back; thus, a stronger force is needed to give the material an extra push and create the full visual effect that we see in an exploding star. When the star collapses, its protons and electrons combine to form neutrons and neutrinos. Far more neutrinos are produced simply because of the fact that the young neutron star has an extremely high temperature, about 100 billion K; neutrinos are ef ciently produced at such temperatures. Some of the released neutrinos can hit the surrounding layers of gas and eject them into space, creating a successful supernova explosion. During the explosion, elements even heavier than iron can form, generally through the sequential capture of many neutrons (followed by radioactive decay of some of them into protons). In this process, we get the rich periodic table of the elements, of which we and other Earth-like, rocky planets consist. It is dif cult to know precisely when a red supergiant will explode because we can’t tell what the core is doing, and there are different time scales associated with the various stages of nuclear burning. For example, because Betelgeuse is a red supergiant, we know that it’s at least in the helium-burning stage, which lasts 500,000 years. (For comparison, the main-sequence stage lasted perhaps 7 million years.) It might be in the carbon-burning stage, which lasts only 600 years, or it might even be in the silicon-burning stage, which lasts only a day. Most likely, it’ll explode sometime in the next half a million years. In the last few stages of a red supergiant’s life—oxygen fusing to silicon and sulfur, and silicon fusing to iron—the temperatures are so high
  • 279 that many neutrinos are formed, which escape from the star immediately at speeds close to the speed of light. If we could develop a highly sensitive neutrino detector, we might be able to predict more accurately when a star is about to explode. Red supergiants are not the only stars that can explode in this way, as core- collapse supernovae. Several other subclasses of stars belong to this category. Most core-collapse supernovae have a hydrogen shell, formally making them Type II supernovae, but some massive stars lose this shell before exploding. Such a progenitor star has a helium envelope and other elements (carbon, oxygen, and so on) in its core, ending with iron at the center. These stars explode as Type Ib supernovae. The progenitor stars of Type Ic supernovae have lost both their hydrogen and helium outer layers, leaving an envelope of carbon and oxygen, with shells of successively heavier elements inside. These subclasses of stars are important because we now recognize that not all Type I supernovae obliterate themselves and produce a large amount of iron ( rst in the form of radioactive nickel), as Type Ia supernovae do. Instead, Type Ib and Ic supernovae form compact neutron stars and eject large quantities of intermediate-mass elements, such as oxygen, calcium, magnesium, and sulfur. Thus, Type Ib and Ic supernovae affect the chemical evolution of galaxies in a way that differs from that of Type Ia supernovae. How does the envelope of hydrogen—and, in some cases, helium—get stripped away from a star? Some massive stars experience winds and gentle ejections, where the pressure of photons expels the envelope. Stars in a binary system can also transfer part of their gas atmospheres onto a companion star. In some cases, only partial stripping of the hydrogen envelope occurs, creating a low-mass shell of hydrogen. We call the subsequent explosion a Type IIb supernova. Thus, core-collapse supernovae come in a number of varieties: Type II, the hydrogen-rich and most common kind, and Types Ib and Ic, classi ed according to whether or not they have “It looks like gravity is ultimately victorious in all these stars, all these massive stars, regardless of how much of an envelope they still retain.”
  • 280 Lecture55:Core-CollapseSupernovae—GravityWins helium envelopes. Regardless of how much of a hydrogen envelope they have, their iron cores ultimately collapse to form neutron stars. progenitor: In the case of a supernova, the star that will eventually explode. stripped massive stars: Stars that have lost their hydrogen and helium envelopes, either through stellar winds or through transfer of gas to a companion star; thought to be the progenitors for gamma-ray bursts. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. ———, “A Supernova with an Identity Crisis,” Sky & Telescope, Dec. 1993. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. What are the observational and physical differences between Type Ia and Type II supernovae? Which kinds of stars explode, and how do they explode? 2. In a supernova explosion of a 15-solar-mass star, about how much material is ejected (blown away)? 3. Do you expect Type Ib and Ic supernovae to produce a burst of neutrinos, just as a Type II supernova does? Important Terms Suggested Reading Questions to Consider
  • 281 The Brightest Supernova in Nearly 400 Years Lecture 56 The brightest supernova in nearly 400 years was studied in great detail. It occurred in the Large Magellanic Cloud, a satellite galaxy of the Milky Way, only 170,000 light years away from Earth. T hough astronomers have never directly witnessed the explosion of a visible white dwarf as a Type Ia supernova, we have seen some very massive stars explode as Type II supernovae. One in particular, SN 1987A, was observed in great detail, both before and after the explosion. Supernova 1987A, the rst supernova to be witnessed in the year 1987, was the brightest supernova in nearly 400 years. It occurred in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy. The Large Magellanic Cloud is about 170,000 light years away, which means that the explosion occurred about 170,000 years ago, just about the time of early hominids on Earth. The supernova was discovered by Ian Shelton, a student working at Las Campanas Observatory in Chile. Using a small telescope, he took numerous photographs of the Large Magellanic Cloud in his study of the variable brightnesses of stars. One of Shelton’s photographs indicated an extra point of light that hadn’t appeared in previous photographs. The supernova appeared near the Tarantula Nebula and was visible to the naked eye. Other astronomers, both amateur and professional, had also witnessed the same supernova from other parts of the world, though Shelton is credited with its discovery. SN 1987A was a Type II supernova; that is, it had an envelope of hydrogen. But it was a peculiar object. For example, SN 1987A faded much more rapidly than it should have at ultraviolet wavelengths. Moreover, it didn’t brighten as much as astronomers had expected. Being so bright and nearby, SN 1987A was studied with a broad range of telescopes, allowing us to test our theories of Type II supernovae. By examining pre-explosion photographic plates, we discovered that the progenitor star (the star that exploded) was a blue supergiant with an initial massofabout20solarmasses.Bluesupergiantshaveaboutthesameluminosity
  • 282 Lecture56:TheBrightestSupernovainNearly400Years as red ones, but blue supergiants have much higher surface temperatures. Previously, astronomers didn’t think blue supergiants could explode because we thought they were on their way to becoming red supergiants and would not yet have been able to build up their iron cores. The supernova showed peculiar characteristics, such as the rapid decline of ultraviolet light and a much dimmer than expected appearance. Its apparent magnitude began at about 4.5, then gradually grew to only 2.5 (remember, the lower the magnitude, the brighter the object). Thus, it was visible to the naked eye, but it should have been much brighter than what was actually seen. The de cit of light is consistent with the star being a blue supernova because such stars are smaller than red supergiants. The smaller size translates to less radiating area; thus, the star could not become as bright as a larger star would. The discovery of SN 1987Ataught us that under some conditions, blue supergiants can develop an iron core and explode. The mechanism is unclear, but it is possible that, because the Large Magellanic Cloud is de cient in heavy elements relative to our own Galaxy, stars de cient in heavy elements have a different structure in their envelopes (outer layers), allowing them to explode as hotter but smaller stars—blue supergiants. Some astronomers think that the star was a blue supergiant when it exploded because it could have been part of a binary system and perhaps swallowed its companion star prior to the explosion, changing its outer structure. Another theory tested was whether multitudes of neutrinos are emitted when a Type II supernova occurs. Indeed, neutrinos were detected by at least two underground tanks of water that had originally Supernova 1987A rings, taken by the Hubble Space Telescope. Dr.ChristopherBurrows,ESA/STScIandNASA
  • 283 been designed to search for the decay of protons. Calculations showed us that the total energy emitted by SN 1987A, in roughly a few seconds, was comparable to the total amount of energy emitted by all the normal stars in the rest of the observable Universe during those few seconds. Aside from the Big Bang itself, this type of explosion is about the biggest we can get. More than 99% of the explosion energy was in the form of neutrinos. Most of the other 1% was the kinetic energy of the ejected gases. Only about 0.01% of the energy was emitted as optical radiation. Thus, even though SN 1987A was a bright, naked-eye supernova, the visible light constituted only 1/10,000 of the true energy emitted by the explosion. When neutrinos are emitted by a supernova and hit Earth, they generally don’t indicate from which direction they came. In other words, how did we know that the neutrinos detected around the time of SN 1987A came from that star? One obvious factor was that the neutrinos were detected at about the same time as the supernova was discovered. Two reactions can occur when neutrinos released from an exploding star interact with material on Earth. First, neutrinos can scatter off electrons, propelling the electrons forward in roughly the same direction from the supernova. These electrons produce Cerenkov light cones, which can then be detected by a light detector and tell us from which direction the neutrinos came. However, a second reaction—and far more common—is for antineutrinos to combine with protons, forming energetic positrons and neutrons. In such a case, positrons can go in any direction with nearly equal probability (described by the term isotropic); thus, they do not indicate where in the sky the supernova occurred. In general, if a supernova were to occur in our Galaxy (that is, close by), it would produce enough detectable neutrinos (scattering off electrons) to allow us to know in which direction the supernova was likely to become visible within a day. The neutrinos would reach Earth before the light of the exploding star, telling us where to look for the impending supernova “I’m sure that in the next decade or two, Supernova 1987A will have additional secrets to tell us.”
  • 284 Lecture56:TheBrightestSupernovainNearly400Years light. Although neutrinos don’t quite travel at the speed of light, they get a “head start” over the photons from the surface of the exploding star (which are formed only after the shock wave coming from the star’s central region reaches the surface, traveling at about 1/10 the speed of light). Another theory con rmed by SN 1987A was that heavy elements are synthesized by supernova explosions. Electromagnetic radiation from such elements was detected by gamma-ray telescopes and other instruments launched above the Earth’s atmosphere after SN 1987A was discovered. Gamma rays were detected arising from speci c radioactive elements. The explosion formed radioactive nickel, which quickly decays into cobalt, which—on a longer time scale—decays into iron. These radioactive elements could have been produced only by SN 1987A. Because they are short-lived, they would not have remained in the star at the time of its death had they been present in the material from which the star was rst formed, millions of years earlier. Supernova 1987A is surrounded by rings of gas released before the actual explosion. These rings can be used to study the progenitor star’s behavior during the last few thousand years before its death. Ejected gases from the supernova explosion itself are now colliding with the external rings, which are consequently beginning to increase in brightness. During the next few years, the supernova will experience a renaissance, appearing substantially brighter than it is now. isotropic: The same in all directions (that is, no preferred alignment). Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Goldsmith, Supernova! The Exploding Star of 1987. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Important Term Suggested Reading
  • 285 Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Is it surprising that SN 1987A occurred near a giant cloud of gas (called the Tarantula Nebula) where massive stars have been produced for the past few tens of millions of years? 2. If only 10 neutrinos from SN 1987A were detected by each of two underground tanks containing several thousand tons of water and if a typical human consists of 100 pounds of water, what are the odds that your body directly detected a neutrino from SN 1987A (assuming that you were alive in Feb. 1987)? 3. How compelling do you nd the arguments that we are made of stardust? Questions to Consider
  • 286 Lecture57:TheCorpsesofMassiveStars The Corpses of Massive Stars Lecture 57 In the previous lecture, we saw how supernova 1987A helped con rm our basic ideas about supernovae but showed that we also needed to re ne some of our ideas. Though the progenitor star of the peculiar SN 1987A was a blue supergiant, other, more typical Type II supernovae have been found to come from red supergiant stars. A s recently as 2005, the Hubble Space Telescope observed a supernova in M51, the Whirlpool Galaxy. The progenitor of SN 2005cs was a red supergiant of about 12 solar masses, and the supernova had a more normal—or expected—spectrum than that exhibited by SN 1987A. The data for SN 2005cs strengthened the evidence that the cores of red supergiants implode and the outer parts get ejected. In most cases, an imploding core forms a neutron star, a very dense ball of neutrons maintained by neutron degeneracy pressure, similar to the electron degeneracy pressure experienced by white dwarfs. A neutron star 1.5 times the mass of the Sun can be only about 20 kilometers in diameter. A teaspoonful of material from such a star would weigh about 1 billion tons. A neutron star is similar to a white dwarf in that it is made of degenerate material crammed into a very small space. The pressure exerted by degenerate neutrons prevents the star from collapsing. Neutron stars were predicted by Fritz Zwicky and Walter Baade in 1933. They also predicted that neutron stars were produced during cataclysmic explosions of massive stars. Neutron stars weren’t actually discovered until 1967, when Jocelyn Bell detected one in the form of a pulsar; these objects generally can’t be seen clearly, but they emit regular pulses of radio radiation. The rst pulsar Bell detected had a periodicity of 1.3373011 seconds. The spacing of the pulsar’s blips was regular, although the intensity, or brightness, varied considerably with time. At rst, it was suggested that pulsars might be extraterrestrial communications. Shortly thereafter, however, several more regular series of pulses were found coming from other parts of the sky but with different periodicities. It was deemed unlikely that a network of intelligent species, all communicating in a similar manner, was present in our Galaxy. Moreover, there was no evidence of a periodically changing Doppler
  • 287 shift, indicating that the pulsars were not coming from another planet or object that was orbiting a star. Through an interesting process of elimination, astrophysicists quickly determined that pulsars probably emanated from rapidly rotating, highly magnetized neutron stars. One clue was that most of the pulsars originated from the plane of the Milky Way Galaxy, where many of the more massive stars are concentrated. Pulsars can’t arise from oscillating (vibrating) normal stars or white dwarfs, whose periodicity is too slow. In contrast, the expected vibration period of neutron stars is too fast. Two normal stars or white dwarfs cannot orbit each other so quickly, either. Two neutron stars can have such a tight orbit, but they would rapidly lose energy, and the orbital period would decrease—yet pulsar periods were observed to be very stable. The surface of such a rapidly rotating normal star would exceed the speed of light. Similarly, a white dwarf is disrupted if its rotation period is less than about 0.3 seconds, too slow for the rapid pulsars. Neutron stars, on the other hand, are capable of rotating about their axes at speeds that are consistent with the observed pulsar rates. We now have additional, more direct evidence that pulsars are rapidly rotating neutron stars. Let’s look at some of the characteristics of pulsars and their causes. We don’t really know the details of why pulsars shine, but this characteristic is undoubtedly related to their magnetic elds. Neutron stars have magnetic elds within and surrounding them, the axes of which generally differ from the stars’ axes of rotation, forming conical patterns as they rotate. The magnetic axis rst points in one direction, then in another direction. This rotation can create electric elds that are strong enough to accelerate electrons to speeds close to that of light. Accelerating charged particles emit radiation along their direction of acceleration, creating (by methods still not fully understood) two oppositely directed beams of light that are visible from Earth—with their associated periodicity—as the star rotates. The effect is similar to that of a lighthouse: It is on all the time, but you see a ash only when the rotating lamp is pointing at you. We think that the magnetic eld is a trillion times as strong as Earth’s magnetic eld. (The unit of magnetism is a gauss, and the Earth’s magnetic
  • 288 Lecture57:TheCorpsesofMassiveStars eld is about 1 gauss.) It is possible that the strong magnetic eld is a result of the star’s collapse, forcing the star’s magnetic eld into such a small space that its strength increases dramatically. Why does a neutron star rotate so quickly? All stars rotate to some extent, and as they collapse, the spin rate must increase in order to conserve angular momentum. Very young pulsars shine not only at radio wavelengths but at optical and x-ray wavelengths and at other wavelengths. As the stars get older, the high- energy forms of radiation subside; what remains are low-energy forms of radiation, such as radio waves. We have observed that one particular pulsar in the Crab Nebula, the remnant of the supernova of A.D. 1054, creates a wind, as well as jets of material, energizing the Crab Nebula and causing it to glow brightly. Over time, this neutron star has been losing energy through the production of its light beams and jets of material, slowing its pulsation rate. Quantitatively, the rate of energy gain in the Crab Nebula is equal to the rate of energy loss of the rotating neutron star, providing strong support for our basic model of pulsars. We expect pulsars to remain turned on for only about a few million years before their rotation rates (and, perhaps, the strength of their magnetic elds) diminish so much so that light beams are no longer produced. Every pulsar is a neutron star, but not every neutron star will be visible as a pulsar. Some will have died, or some might have axes of rotation oriented in such a way that they don’t allow the beams of light to cross Earth’s line of sight. Typically, pulsars spin about once per second, or 10 times per second, or maybe once every 10 seconds. But some spin hundreds of times per second—these are called millisecond pulsars. Converting the frequencies at which these pulsars spin to audible signals will produce corresponding musical notes. Some astronomers have written musical pieces with the notes of known millisecond pulsars. We think these pulsars spin so fast because they previously accreted material from a companion star orbiting them. In 1991, one millisecond pulsar was discovered to have at least three planets orbiting it. The key to this discovery was that, sometimes, the pulses arrived sooner than expected and, other times, they arrived later than expected. This slight deviation from perfect periodicity is caused by orbiting planets; the
  • 289 planets and the neutron star orbit their common center of mass, so the neutron star is sometimes slightly closer to Earth, and sometimes slightly farther away. These “planets” are quite different from those in our Solar System, though they happen to be comparable in size to the terrestrial planets. In addition, these “planets” could not have existed before the supernova that gave rise to the pulsar because the planets would have been destroyed in the supernova explosion. Therefore, it’s likely that they formed from a disk of debris around the neutron star that remained after the explosion. In the last decade, astronomers have learned some interesting things about neutron stars. Some neutron stars have magnetic elds up to 1015 gauss units; these are called magnetars, the strongest magnets in the Universe. Magnetars sometimes emit tremendous amounts of energy because, apparently, the structure of their crust changes such that it creates a kind of “starquake.” Furthermore, the magnetic eld changes, also releasing a tremendous amount of energy. One such magnetar was observed on December 27, 2004, in the constellation Sagittarius, creating the brightest are ever seen from outside our Solar System. The eruption was so bright that it ionized Earth’s atmosphere and activated the sensors on several satellites. Satellites transmitted the information to radio telescopes on the ground, which immediately moved to begin observing that location of the sky. These telescopes detected debris emanating from the magnetar and moving at speeds close to the speed of light. We believe this was a restructuring of the surface layers of a neutron star. After the main burst of energy, alternating ashes of light from the neutron star’s north and south poles became visible as the star rotated. We believe that this type of neutron star, which gives rise to a magnetar, has an interior of liquid neutrons and other particles with a generally solid crust. The crust essentially buckles or cracks, changing the magnetic eld con guration, as well. We know that magnetars survive this basic burst because some of these events have been seen to repeat after a few years. “Magnetars are exciting, but don’t get anywhere near one—especially if you have a pacemaker, because it’ll de nitely mess it up.”
  • 290 Lecture57:TheCorpsesofMassiveStars Zwicky, Fritz (1898 1974). Swiss-American astronomer; proposed that supernovae result from the collapse of the cores of massive stars, producing neutron stars and energetic particles (cosmic rays). Compiled an extensive atlas of galaxy clusters and showed that many such clusters must contain dark matter in order to be gravitationally bound. lighthouse model: The explanation of a pulsar as a spinning neutron star whose beam we see as it comes around and points toward us. magnetar: Spinning neutron star with an extraordinarily powerful magnetic eld that occasionally releases a burst of gamma rays when the crust of the star undergoes a sudden restructuring (a “star quake”). Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 1. Can you nd any loopholes in the process-of-elimination argument used to conclude that pulsars are rotating neutron stars? 2. How did studies of the Crab Nebula pin down the explanation of pulsars? 3. Calculate the density (mass per unit volume) of a neutron star having a mass of 1.4 solar masses and a radius of 10 kilometers. Compare this with the density of a neutron or a proton (each of which has a radius of about 10–15 m and a mass of about 1.67 10–24 g). Name to Know Important Terms Suggested Reading Questions to Consider
  • 291 Einstein’s General Theory of Relativity Lecture 58 Based on the idea that there is no difference between a uniform acceleration and a uniform gravitational eld, Einstein’s theory postulates that gravity is a manifestation of the warping of space and time produced by matter and energy; objects follow their natural trajectory through curved space-time. I n our understanding of the physical properties of neutron stars—in particular, their immense density—we need to consider Einstein’s general theory of relativity. Though Newton’s famous laws of motion and of universal gravitation were tremendous breakthroughs in science, the laws break down when we consider objects traveling at very high speeds or in strong gravitational elds. Einstein’s special theory of relativity accounted for high speeds, as discussed in Lecture 42. Moreover, Newton never fully understood how gravity worked, and Einstein also knew that standard Newtonian gravity was inconsistent with his special theory of relativity. The fundamental problem with Newton’s theory of gravity is revealed in a thought experiment, in which Einstein tried to predict what would happen to the Earth if the Sun were to simply vanish, leaving no gravitational forces to affect Earth. Because Newtonian gravity invokes instantaneous “action at a distance,” the moment the Sun disappeared, the Earth would sail along the tangent to its trajectory, no longer in orbit. With no forces acting upon Earth, it would continue moving in a straight line at a constant speed, according to Newton’s rst law of motion. Thus, Einstein knew that Newton’s law of gravitation violated his own special theory of relativity because relativity claims that no information can travel faster than the speed of light. How can the Earth instantaneously “know” that the Sun’s mass vanished? Einstein worked on this problem for more than a decade and came up with the general theory of relativity, which deals with accelerations and gravitational elds. The theory is based on the idea that there’s no fundamental difference between a uniform acceleration and a uniform gravitational eld. Recall that special relativity is based on the idea that there is no difference in the laws of
  • 292 Lecture58:Einstein’sGeneralTheoryofRelativity physics experienced in laboratories at rest and in uniform motion (constant speed and direction). This is a more restricted theory than general relativity. Let’s look at another thought experiment of Einstein’s for general relativity. A person standing in a windowless elevator that suddenly accelerates upward would momentarily feel heavier. From the person’s perspective, either the elevator accelerated up or a large mass was temporarily placed beneath the elevator, increasing the gravitational eld and creating that momentary heavy feeling. Einstein theorized, then, that a person in an elevator moving with a constant speed would see light travel in a straight line, because that is what happens in elevators at rest. However, that person in an elevator accelerating upward would theoretically see light travel in a path that curved downward, because the light cannot “know” that the elevator is accelerating. Because accelerations and gravitational elds are equivalent, according to the general theory, light must therefore also bend in a gravitational eld. As Einstein further formulated general relativity, he found that the paths of light and particles in a gravitational eld can be represented by their natural paths in curved space-time. Gravity is a manifestation of the warping of space and time; effectively, objects move along their natural paths in an intrinsically warped space. This space-time warping, or curvature, is caused by mass or energy. The warping occurs in some fourth spatial dimension, which we cannot see and to which we have no physical access. The denser and more massive the object, the more it bends the space-time around it. For example, the Sun produces a warping that causes Earth to go around it, but Earth has a little warp around it as well, so the Moon follows its natural path around Earth. Can we actually test Einstein’s theory? We know that the orbits of objects are not closed ellipses; rather, their long axis shifts, or precesses, with time. The rate of shift increases in stronger gravitational elds, as was rst seen with the orbit of Mercury (compared with that of Venus or Earth). Many perturbations of Mercury’s orbit can be explained by effects from the large planet Jupiter and other smaller in uences. However, Mercury’s orbit shifts by 43 arc seconds per century, which is not caused by Jupiter’s gravity. Einstein explained the shift using his general theory of relativity. We also know that light from stars moving past the Sun is shifted, proving that gravity can bend light. Quasars are central regions in distant galaxies where we think a giant
  • 293 black hole is swallowing material. We can measure shifts in the quasars’ positions relative to the Sun’s position, indicating that their light bends through space. Finally, we know that light emerging from a gravitational eld is redshifted as the photons lose energy. This has been seen even in weak elds, such as Earth’s, though the effect is very subtle. Einstein also predicted that time is warped by gravitational elds. We can actually measure this on Earth by using global positioning system (GPS) units. GPS satellites must have atomic clocks that are slower by 38 microseconds per day compared to clocks on Earth’s surface in order for the system to work on Earth. Hawking, The Universe in a Nutshell. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Wolfson, Simply Einstein: Relativity Demysti ed. 1. If you were immersed in a gravitational eld that is not uniform, how might you distinguish this from an acceleration? 2. According to the elevator thought experiment showing that light is bent by a gravitational eld, does the amount of bending depend on the wavelength of light? 3. Why do the special relativistic and general relativistic corrections to GPS satellite clocks go in opposite directions? “The global positioning system is a great practical application of relativity. If it didn’t work, it wouldn’t get you to the right place at the right time.” Suggested Reading Questions to Consider
  • 294 Lecture59:WarpingofSpaceandTime Warping of Space and Time Lecture 59 Another effect of general relativity is the bending of light through space, also a measurable phenomenon that can help us detect the presence of brown dwarfs and black holes. I n the previous lecture, we looked at Einstein’s general theory of relativity and mentioned how it applies to the global positioning system (GPS). Let’s consider this in more detail to see how relativity works quantitatively and, at least in this one case, affects our everyday lives. Timing is crucial; in order for a GPS device to work, we must know exactly how far away each of the GPS satellites is. We can gure this out by measuring when a satellite’s signal was emitted and how long it takes to reach Earth. The speed of light is about 1 foot per nanosecond (1 billionth of a second). But the relativistic effect in time difference between the satellites and our unique position on Earth is 38 nanoseconds. Such a difference, though seemingly small, would accumulate to large errors over the course of a month. If GPS designers did not take relativity into account, then after a few days, a GPS unit would begin providing quite inaccurate information. Thus, a GPS satellite’s atomic clock is programmed to run at a rate that exactly compensates for both the special relativistic effect, a slowdown of 7 microseconds per day, and the general relativistic effect, an increase of 45 microseconds per day. The net effect is a compensation of 38 microseconds per day. Today, lasers, computers, and other electronic devices depend on our understanding of quantum mechanics. Thus, who knows in the future what other technological inventions will have to take into account the effects of general relativity? Let’s review Einstein’s thought experiment in which the Sun’s mass suddenly vanished. Then, we will consider other ways that we can test for Einstein’s general theory. As we saw in Lecture 58, according to Newton’s law of gravitation, at the moment the Sun disappeared, Earth would be thrown off its orbit along the tangent of its trajectory. However, Einstein claimed that Earth would not experience the Sun’s disappearance until 8.3 minutes later. Thus, information about the Sun’s disappearance would travel via gravitational waves at the speed of light, according to theory (the speed has never actually
  • 295 been measured). Once this information reached Earth, 8.3 minutes later, our planet would then travel along the tangent to its trajectory. An analogy would be tossing a ball into a calm swimming pool. The ball sends out concentric waves, but someone at the pool’s edge wouldn’t experience those waves until they reached the edge. Likewise, the removal of the Sun would create a disturbance in the warping of space, a disturbance that travels at the speed of light through the Solar System. The warp that the Sun used to produce no longer exists; space would be at there instead, though it wouldn’t happen instantaneously. Recall that the rst historical test of relativity was the con rmation that Mercury’s extra precession, 43 seconds of arc per century, could be quantitatively explained through general relativity. That was a great triumph, but 43 arc seconds per century is a small amount. We now have much better evidence through our study of two neutron stars, discovered (in 1974) to be orbiting each other in just 8 hours. One of the stars is a pulsar; thus, the system was dubbed a binary pulsar, even though only one star is visible as a pulsar. The precession of the pulsar’s elliptical trajectory is 4 degrees per year, much greater than Mercury’s orbital precession of 43 arc seconds per century. Each star forms a warp in space, creating a ripple, or gravitational wave, that propagates through space at the speed of light. As these ripples travel and the stars continue to orbit around their common center of mass, energy is removed from their system. The removal of energy forces the stars to move closer to each other, due to gravity, which in turn, increases the stars’ orbital speed and decreases their orbital periods. As the stars’ orbital period decreased over time, the pulsar signal also changed. The cumulative measurement of the pulsar’s change over time exactly corresponded to what general relativity predicts. In 2003, an even more closely spaced binary pulsar was found, with an orbital period of just 2.5 hours, in which both of the neutron stars have visible pulsars. “We think that on large scales the theory of relatively is correct quantitatively. But it’s always possible that it is false. Any new experimental test is welcome with open arms.”
  • 296 Lecture59:WarpingofSpaceandTime Astronomers have determined that the stars’orbits shrink by 7 millimeters per day. This system, as well, strongly con rms quantitatively the predictions of general relativity. A related effect of this warping of space occurs in a process called gravitational lensing. We’ve already encountered this in our discussion of the de ection of starlight by the Sun and other massive objects. As we’ve seen in a previous lecture, if we observe the light of a distant star, our Sun de ects—bends—the star’s light. If we look at an intrinsically point-like light, we might actually see what is called an Einstein ring. Such rings have been photographed at visible wavelengths by the Hubble Space Telescope. The ring appears in perfectly symmetrical situations, such as when a black hole passes between our line of sight and a distant galaxy. In this case, the galaxy’s light is actually bent such that it appears as a ring of light. If the focusing effect is caused by a foreground star, rather than by a galaxy, we call it gravitational microlensing. Usually, small deviations from symmetry cause a ring to break up into smaller units, such as partial arcs or even point-like images: We can see several images of the background object that is lensed by the foreground object. Each image is a mirage; for example, quasars often become imaged into several discrete mirages when a galaxy appears in the foreground and gravitationally lenses the light from the background quasar. If the clarity of the images is not enough to show distinct mirages, we would still see an apparent brightening of the object due to the focusing of light rays toward us. The cumulative brightness of the ring, or the mirages, is increased through the gravitational focusing of light. This brightening effect can be used to detect the presence of foreground gravitationally lensing objects, even if they aren’t directly noticeable. For example, if a brown dwarf or a black hole passes along our line of sight to a background star, the focusing effect still occurs, revealing the presence of an otherwise hard-to-see object. Some brown dwarfs and wandering black holes have been detected through this process. Even a few isolated, free- oating planets have been detected by their gravitational microlensing of a background star. In 2005, a small planet (about 5 Earth masses) was
  • 297 discovered through this effect, which also has the potential to reveal many more exoplanets having relatively small masses. Finally, using one more emerging test for general relativity, we are hoping to demonstrate that a rotating object drags space around it; that is, space itself rotates around a rotating object. Data gathered in 2006 from a satellite called Gravity Probe B are now being analyzed. The experiment involves a complex technique and the orientation of gyroscopes within the satellite. This dragging effect, which has never been measured, is believed to occur at a rotation of 0.042 arc seconds per year at the location of the satellite. By measuring the orientation of the satellite’s gyroscopes, we should be able to demonstrate the effect, if general relativity is correct. binary pulsar: A pulsar in a binary system. Often, this term is used for systems in which the pulsar’s companion is another neutron star. gravitational lens: In the gravitational lens phenomenon, a massive body changes the path of light passing near it so as to make a distorted image of the object. gravitational waves: Waves thought to be a consequence of changing distributions of mass. relativistic: Having a speed that is such a large fraction of the speed of light that the special theory of relativity must be applied. Hawking, The Universe in a Nutshell. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy. Important Terms Suggested Reading
  • 298 Lecture59:WarpingofSpaceandTime Will, Was Einstein Right? Putting General Relativity to the Test. Wolfson, Simply Einstein: Relativity Demysti ed. 1. Suppose you nd several closely spaced quasars that you think are the gravitationally lensed images of a single quasar. How might you test your hypothesis? 2. Because of time dilation in the special theory of relativity, an observer on Earth sees a rapidly moving twin in a spaceship aging more slowly than he does. After returning to Earth, the traveling twin will be younger than the one who stayed on Earth. But consider this: The traveling twin thinks that he is at rest and the Earth twin is moving—in which case, the Earth twin would be younger than the spaceship twin. How do you think this famous twin paradox is resolved? (Hint: What does the traveling twin have to do in order to return to Earth? Does this allow the two frames of reference to be distinguished from one another? Is this similar to being placed in a gravitational eld?) 3. If a speci c observer sees an apparent brightening of an object due to the focusing of light rays during an episode of gravitational lensing, will this object appear fainter than expected from some other lines of sight at that same time? Questions to Consider
  • 299 Black Holes—Abandon Hope, Ye Who Enter Lecture 60 Our discussion of general relativity is motivated in part by the existence of neutron stars, very dense stars that form when a massive star collapses. But there exists a phenomenon that is even stranger than a neutron star—a black hole. A black hole is a region of space where material is compressed to such a high density and the local gravitational eld is so strong that nothing—not even light—can escape. If we could shine a light on a black hole, nothing would be re ected; also, no light is emitted from within a black hole. To understand how black holes form, we must recall that a neutron star, held up by neutron degeneracy pressure, can have only a certain maximum mass before it collapses. We don’t know the exact limiting mass for a neutron star because we don’t yet fully understand the structure of matter at nuclear densities. The limiting gure could be 2 to 3 solar masses. If we consider rotation, a neutron star could be stable at up to about 5 solar masses. Beyond 5 solar masses, barring the existence of some yet unknown form of matter, a typical rotating neutron star would collapse to form a black hole. The most massive star whose mass has been reliably measured has about 60 solar masses. Some stars may be as large as 100 solar masses; beyond this point, the radiation pressure of a star itself would tear it apart and prevent its formation. Yet the most massive stars have strong winds, so their outer layers essentially evaporate away. These stars (and others) can also lose mass through transfer of matter to companion stars if they are in binary systems. Therefore, it is possible that the most massive stars do not give rise to black holes because much of their mass is easily lost and they end up with relatively small cores that become neutron stars instead. It is also possible that a massive star’s core could collapse to form a black hole. Some astronomers believe that stars having initial mass between 20 and 40 solar masses are the most likely to form black holes. Below 20 and above 40 solar masses, a neutron star is more likely to form at the end of a star’s life. There is some evidence to support this hypothesis.
  • 300 Lecture60:BlackHoles—AbandonHope,YeWhoEnter Let’s look at why an object compressed at a high density would appear black, as well as some characteristics of a black hole. Newton’s law of gravity states that F = GM1 M2 /d2 , in which F is force, G is Newton’s constant of universal gravitation, M1 and M2 are the masses of two objects, and d is the distance between them (more precisely, the distance between their centers of mass). From this, we can derive an object’s escape velocity—that is, the speed at (or above) which a projectile would have to travel in order to completely escape from the object. If the radius of the object is compressed but its mass remains the same, then the escape velocity increases. That is, the projectile would have to travel even faster to fully escape from the object. Such an argument was proposed in the late 18th century independently by John Mitchell and Pierre-Simon de Laplace to suggest that there may be objects in the Universe that are so dense that not even light can escape—black holes. This is an example of a Newtonian plausibility argument. The Newtonian argument provides a formula for determining the radius to which an object would have to be compressed in order for its escape velocity to reach the speed of light: RS = 2GM/c2 . The derivation is not rigorously correct, but fortuitously, it agrees with the result from the general theory of relativity. The relativistic calculation was done by the German physicist Karl Schwarzschild in 1916, and this radius is now known as the Schwarzschild radius in his honor. The Schwarzschild radius of the object is directly proportional to its mass. The more massive the object, the larger the minimum radius to which it would have to be compressed in order to become a black hole. For example, the Schwarzschild radius for a 10-solar-mass star is 30 kilometers; thus, if the star were compressed to a radius of 30 kilometers or less, it would form a black hole. What would the Earth’s radius have to be in order to form a black An artist’s rendition of a black hole. NASA/GoddardSpaceFlightCenter
  • 301 hole? Of course, this isn’t possible, but for the sake of illustration, Earth would have to be compressed to a radius of about 1 centimeter.A60-kilogram person would have to be compressed to a radius of 10–23 centimeters, 10 orders of magnitude smaller than a proton, in order to become a black hole! The event horizon of a non-rotating black hole is the imaginary spherical surface with a radius equal to the Schwarzschild radius. It is called an event horizon because we cannot see events that occur beyond it, and nothing can escape from within it. Once matter is inside a black hole, gravity still acts on it, and thus, that matter continues to collapse. Theoretically, the matter would reach a point of in nite density, called a singularity. However, quantum mechanical effects will surely modify this, which we will discuss later when we talk about string theory. Despite the correct equation for the Schwarzschild radius given by the Newtonian argument, the only way we can truly understand black holes is through general relativity. The Newtonian formula, F = GM1 M2 /d2 , obviously breaks down where black holes are concerned because light doesn’t have mass. Thus, light is not trapped by the “gravitational force” but, rather, by the extreme curvature of space-time around a dense object. Recall our example of a ball distorting a rubber sheet, making the sheet (or space) bulge. As the ball (or celestial object) increases in density, the bulge increases in its depth, making it more dif cult for light to escape that depth. Indeed, light coming from a strong gravitational eld is bent and redshifted. For example, light shining tangent to the surface of a collapsed star having a radius of 1.5 Schwarzschild radii, can be bent so much that it actually goes into orbit around the star, creating a photon sphere. If the star were to contract even more, most of the light would be bent so much that it would be absorbed back into the star. Only a small amount of light could escape in a narrow beam, called the exit cone, which has a certain opening angle. Once the star was suf ciently contracted (to a radius equal “It’s possible that there are types of stars that are smaller and denser than a classical neutron star, yet not truly a black hole, not smaller than the event horizon.”
  • 302 Lecture60:BlackHoles—AbandonHope,YeWhoEnter to the Schwarzschild radius), the exit cone’s opening angle would shrink to zero and no light could escape. Far from a black hole, the properties of space are basically normal; the idea that black holes are giant cosmic vacuum cleaners, sucking up everything around them, is a misconception. Once a black hole has reached equilibrium— after the star has fully collapsed—its properties are simple. According to the famous no hair theorem, a black hole is described completely by its mass, electric charge, and angular momentum (total spin). The nature of the objects thrown into the black hole is irrelevant. Some physicists have suggested the possible existence of material on a stellar scale even denser than that of neutron stars, yet that is not an actual black hole. There is some tentative observational evidence for this, but nothing conclusive. event horizon: The boundary of a black hole from within which nothing can escape. photosphere: The visible surface of the Sun (or another star) from which light escapes into space. Schwarzschild radius: The radius to which a given mass must be compressed to form a nonrotating black hole. Also, the radius of the event horizon of a nonrotating black hole. singularity: A mathematical point of zero volume associated with in nite values for physical parameters, such as density. Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Ferguson, Prisons of Light—Black Holes. Important Terms Suggested Reading
  • 303 Kaufmann, Black Holes and Warped Spacetime. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy. Will, Was Einstein Right? Putting General Relativity to the Test. 1. How would the gravitational force at the surface of a star change if the star contracted to 1/5 of its previous diameter without losing any of its mass? 2. Why doesn’t the pressure from electrons or neutrons prevent a suf ciently massive star from becoming a black hole? 3. If someone close to (but not inside) a black hole were shining a blue ashlight beam outward, how would the color that you see be affected if you are far from the black hole? 4. The average density of an object is its mass per unit volume. If the volume of a non-rotating black hole is proportional to the cube of its Schwarzschild radius, show that its average density is inversely proportional to the square of its mass. (Of course, all of the mass in a black hole is actually concentrated at the singularity—either the classical or the quantum variety.) Questions to Consider
  • 304 Lecture61:TheQuestforBlackHoles The Quest for Black Holes Lecture 61 A major prediction of general relativity is the physical possibility of a black hole, a region of space where there’s so much material in such a small volume that the space-time curvature is suf ciently strong to trap everything, even light. But if we can’t see black holes, how do we know they exist? W e don’t see black holes directly, but we can detect them through their gravitational in uence on other objects. Recall a binary system, in which two stars orbit their common center of mass. If one star is more massive than the other, that star is closer to the common center of mass than the less-massive star. We can detect the stars’ orbits and deduce their masses. If the larger object isn’t visible, we can still detect its mass by measuring the wobble in the smaller star’s spectrum. Recall that this method is used to detect the presence of extrasolar planets orbiting suns. If we have a wobbling star and the cause of that wobble (the other object) is not visible, we might conclude that the other object is a black hole if its mass exceeds a certain amount. For example, if the object shows no absorption lines in the spectrum, is not visible, and is 10 solar masses (a star this size would be visible), we might conclude that it is a black hole. Other observations would verify whether the object really is a black hole. The best place to look for black holes is in a spectroscopic binary system. Owing to the number of such systems, how can we narrow down our search to those that might yield black holes? Observations at x-ray wavelengths can provide such a clue. If a black hole or a neutron star is orbiting around another star, it can steal material from the other star. This material would glow as it settled into an accretion disk; the accretion disk’s gases come so close to the compact object—either a neutron star or black hole—that they heat up in the strong gravitational eld. One such object found with x-ray telescopes is Cygnus X-1, the brightest x-ray source in the constellation Cygnus the Swan. This object appears to be a star orbiting a black hole, creating an accretion disk that glows at x-ray wavelengths. The black hole is at least 7 solar masses, but it could be as large as 16 solar masses. If it
  • 305 were a star, it would be easily visible, but it’s not. The problem that arises