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- 1. History of Astronomy
- 2. Geocentric Universe <ul><li>The idea that the earth is at the center of the universe and all things fall around her is the simplest and longest lasting universal view that we have had. </li></ul>
- 3. What the Geocentric Universe is made of <ul><li>Sun </li></ul><ul><li>Moon </li></ul><ul><li>Stars </li></ul><ul><li>5 Planets </li></ul><ul><ul><li>Mercury </li></ul></ul><ul><ul><li>Venus </li></ul></ul><ul><ul><li>Mars </li></ul></ul><ul><ul><li>Jupiter </li></ul></ul><ul><ul><li>Saturn </li></ul></ul><ul><ul><ul><li>How did they discover the existence of these planets? </li></ul></ul></ul>
- 4. Geocentric Universe <ul><li>M uch of what we know about Greek astronomy comes to us through Claudius Ptolemy (c. 100-170). But he is most famous for advancing the first general theory of cosmology—“the study of the structure and motions of the universe”—although his work drew heavily on that of perhaps the greatest Greek astronomer, Hipparchus . </li></ul>
- 5. PTOLEMY’S UNIVERSE <ul><li>Ptolemy placed Earth at the center of the universe, with the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn circling our planet. </li></ul><ul><li>Ptolemy designed a geocentric, or Earth-centered, model that held sway for 1400 years. </li></ul>
- 7. Assumptions about the Universe <ul><li>1. The earth is the center of all motion. </li></ul><ul><li>2. The earth does not move. </li></ul><ul><li>3. The earth is flat. </li></ul><ul><li>4. Planets move in circular orbit. </li></ul><ul><li>5. Stars are immutable. </li></ul>
- 8. Astronomers during the Geocentric Era <ul><li>Pythagoras – all celestial objects are spherical in shape and the first person to suggest that the earth revolves around the sun. </li></ul><ul><li>Aristotle – he discovered moon’s phases and eclipses </li></ul><ul><li>Plato – suggest that all motion in the sky follows a uniform circular motion. </li></ul><ul><li>Philolaus – introduced the idea that the earth is in motion around an invisible fire </li></ul><ul><li>Aristarchus – proposed that the earth is round because of the other objects observed in the sky and attempted to calculate the distance of the earth from the moon and the sun </li></ul><ul><li>Eratosthenes – he determined the size of the earth through mathematical calculations. </li></ul>
- 9. Hipparchus <ul><li>Hipparchus – classified stars according to magnitude and discovered the motion of the earth called precession. </li></ul>
- 10. <ul><li>The idea of Copernicus was not really new! A sun-centered Solar System had been proposed as early as about 200 B.C. by Aristarchus of Samos (Samos is an island off the coast of what is now Turkey). However, it did not survive long under the weight of Aristotle's influence and "common sense": </li></ul><ul><li>If the Earth actually spun on an axis, why didn't objects fly off the spinning Earth? </li></ul><ul><li>If the Earth was in motion around the sun, why didn't it leave behind the birds flying in the air? </li></ul><ul><li>If the Earth were actually on an orbit around the sun, why wasn't a parallax effect observed? </li></ul>
- 11. <ul><li>In the 3rd century B.C., Aristarchus of Samos hypothesized that the observed motions of the stars and planets could be explained if Earth revolved around the Sun. No one knows why he made this conceptual leap, although he had made a crude calculation showing the Sun to be much larger than Earth, and perhaps he felt it made more sense for the bigger object to lie at the center. </li></ul><ul><li>T he man who first measured the world, the Greek astronomer Eratosthenes He noticed that on the first day of summer in Syene (now Aswan), Egypt, the Sun appeared directly overhead at noon. At the same time in Alexandria, however, the Sun appeared slightly south (about 7 degrees) of the zenith. Knowing the distance between Syene and Alexandria and assuming that the Sun’s rays were parallel when they struck the curved Earth, he calculated the size of our planet using simple geometry. His result, about 25,000 miles for the circumference, proved remarkably accurate. </li></ul>
- 12. The Heliocentric System <ul><li>In a book called On the Revolutions of the Heavenly Bodies (that was published as Copernicus lay on his deathbed), Copernicus proposed that the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system . The ordering of the planets known to Copernicus in this new system, which we recognize as the modern ordering of those planets making him the FATHER of MODERN DAY ASTRONOMY </li></ul>
- 13. The Copernican Model: A Sun-Centered Solar System <ul><li>In this new ordering the Earth is just another planet (the third outward from the Sun), and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction. </li></ul>
- 14. Retrograde Motion and Varying Brightness of the Planets <ul><li>The Copernican system by banishing the idea that the Earth was the center of the Solar System, immediately led to a simple explanation of both the varying brightness of the planets and retrograde motion </li></ul><ul><li>The planets in such a system naturally vary in brightness because they are not always the same distance from the Earth. </li></ul><ul><li>The retrograde motion could be explained in terms of geometry and a faster motion for planets with smaller orbits, as illustrated in the following animation. </li></ul>
- 16. Copernicus and the Need for Epicycles <ul><li>There is a common misconception that the Copernican model did away with the need for epicycles. </li></ul><ul><li>This is not true, because Copernicus was able to rid himself of the long-held notion that the Earth was the center of the Solar system, but he did not question the assumption of uniform circular motion . </li></ul><ul><li>Thus, in the Copernican model the Sun was at the center , but the planets still executed uniform circular motion about it. </li></ul>
- 17. We noted earlier that 3 incorrect ideas held back the development of modern astronomy from the time of Aristotle until the 16th and 17th centuries: <ul><li>(1) the assumption that the Earth was the center of the Universe, </li></ul><ul><li>(2) the assumption of uniform circular motion in the heavens, and </li></ul><ul><li>(3) the assumption that objects in the heavens were made from a perfect, unchanging substance not found on the Earth. </li></ul>
- 18. <ul><li>As we shall see later, the orbits of the planets are not circles, they are actually ellipses. </li></ul><ul><li>As a consequence, the Copernican model, with it assumption of uniform circular motion, still could not explain all the details of planetary motion on the celestial sphere without epicycles. </li></ul><ul><li>The difference was that the Copernican system required many fewer epicycles than the Ptolemaic system because it moved the Sun to the center. The Copernican Revolution </li></ul>
- 19. The Observations of Tycho Brahe <ul><li>A Danish nobleman, Tycho Brahe (1546-1601), made important contributions by devising the most precise instruments available before the invention of the telescope for observing the heavens. </li></ul><ul><li>The instruments of Brahe allowed him to determine more precisely than had been possible the detailed motions of the planets. </li></ul>
- 20. Summary of Brahe's Contributions <ul><li>He made the most precise observations that had yet been made by devising the best instruments available before the invention of the telescope. </li></ul><ul><li>His observations of planetary motion, particularly that of Mars, provided the crucial data for later astronomers like Kepler to construct our present model of the solar system. </li></ul><ul><li>He made observations of a supernova in 1572, we now know that a supernova is an exploding star. This was a "star" that appeared suddenly where none had been seen before, and was visible for about 18 months before fading from view. This was early evidence against the immutable nature of the heavens . </li></ul>
- 21. <ul><li>He made the best measurements that had yet been made in the search for stellar parallax. Upon finding no parallax for the stars, he (correctly) concluded that either </li></ul><ul><ul><li>The earth was motionless at the center of the Universe, </li></ul></ul><ul><ul><li>The stars were so far away that their parallax was too small to measure. </li></ul></ul><ul><li>Not for the only time in human thought, a great thinker formulated a pivotal question correctly, but then made the wrong choice of possible answers: Brahe did not believe that the stars could possibly be so far away and so concluded that the Earth was the center of the Universe and that Copernicus was wrong. </li></ul>
- 22. Brahe’s Cosmology <ul><li>Brahe proposed a model of the Solar System that was intermediate between the Ptolemaic and Copernican models. It proved to be incorrect, but was the most widely accepted model of the Solar System for a time. </li></ul><ul><li>Thus, Brahe's ideas about his data were not always correct, but the quality of the observations themselves was central to the development of modern astronomy. </li></ul>
- 23. Johannes Kepler: The Laws of Planetary Motion <ul><li>The next great development in the history of astronomy was the theoretical intuition of Johannes Kepler (1571-1630), a German who went to Prague to become Brahe's assistant. </li></ul>
- 24. Kepler and the Elliptical Orbits <ul><li>Unlike Brahe, Kepler believed firmly in the Copernican system. In retrospect, the reason that the orbit of Mars was particularly difficult was that Copernicus had correctly placed the Sun at the center of the Solar System, but had erred in assuming the orbits of the planets to be circles. </li></ul><ul><li>Thus, in the Copernican theory epicycles were still required to explain the details of planetary motion. </li></ul>
- 25. <ul><li>It fell to Kepler to provide the final piece of the puzzle: after a long struggle, in which he tried mightily to avoid his eventual conclusion, Kepler was forced finally to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" that geometers call ellipses </li></ul>
- 26. Some Properties of Ellipses
- 27. The Laws of Planetary Motion <ul><li>Utilizing the voluminous and precise data of Brahe, Kepler was eventually able to build on the realization that the orbits of the planets were ellipses to formulate his Three Laws of Planetary Motion . </li></ul>
- 28. <ul><li>The amount of "flattening" of the ellipse is termed the eccentricity . Thus, in the following figure the ellipses become more eccentric from left to right. </li></ul>
- 29. Kepler's First Law: <ul><li>I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. </li></ul><ul><li>Known as “The Law of Ellipses” </li></ul>
- 30. Kepler's Second Law: <ul><li>The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse. </li></ul><ul><li>Known as “The Law of Equal Areas” </li></ul>
- 32. Calculations Using Kepler's Third Law <ul><li>A convenient unit of measurement for periods is in Earth years, and a convenient unit of measurement for distances is the average separation of the Earth from the Sun, which is termed an astronomical unit and is abbreviated as AU. If these units are used in Kepler's 3rd Law, the denominators in the preceding equation are numerically equal to unity and it may be written in the simple form </li></ul><ul><li>This equation may then be solved for the period P of the planet, given the length of the semimajor axis, </li></ul><ul><li>or for the length of the semimajor axis, given the period of the planet, </li></ul>
- 33. Kepler's Third Law: <ul><li>III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes. </li></ul><ul><li>In this equation P represents the period of revolution for a planet and R represents the length of its semimajor axis. The subscripts "1" and "2" distinguish quantities for planet 1 and 2 respectively. The periods for the two planets are assumed to be in the same time units and the lengths of the semimajor axes for the two planets are assumed to be in the same distance units. </li></ul>
- 34. Galileo: the Telescope & the Laws of Dynamics <ul><li>Galileo Galilei (1564-1642) was a pivotal figure in the development of modern astronomy, both because of his contributions directly to astronomy, and because of his work in physics and its relation to astronomy. </li></ul><ul><li>He provided the crucial observations that proved the Copernican hypothesis, and also laid the foundations for a correct understanding of how objects moved on the surface of the earth (dynamics) and of gravity. </li></ul>
- 35. The Telescope <ul><li>Galileo did not invent the telescope (Dutch spectacle makers receive that credit – Hans Leppershey ), but he was the first to use the telescope to study the heavens systematically. His little telescope was poorer than even a cheap modern amateur telescope, but what he observed in the heavens rocked the very foundations of Aristotle's universe and the theological-philosophical worldview that it supported. </li></ul><ul><li>It is said that what Galileo saw was so disturbing for some officials of the Church that they refused to even look through his telescope; they reasoned that the Devil was capable of making anything appear in the telescope, so it was best not to look through it. </li></ul>
- 36. Sunspots <ul><li>Galileo observed the Sun through his telescope and saw that the Sun had dark patches on it that we now call sunspots (he eventually went blind, perhaps from damage suffered by looking at the Sun with his telescope). Furthermore, he observed motion of the sunspots indicating that the Sun was rotating on an axis. </li></ul><ul><li>These "blemishes" on the Sun were contrary to the doctrine of an unchanging perfect substance in the heavens, and the rotation of the Sun made it less strange that the Earth might rotate on an axis too, as required in the Copernican model . Both represented new facts that were unknown to Aristotle and Ptolemy. </li></ul>
- 37. The Moons of Jupiter <ul><li>Galileo observed 4 points of light that changed their positions with time around the planet Jupiter. He concluded that these were objects in orbit around Jupiter. Indeed, they were the 4 brightest moons of Jupiter, which are now commonly called the Galilean moons . </li></ul><ul><li>One of the arguments against the Copernican system (and the original heliocentric idea of Aristarchus) had been that if the moon were in orbit around the Earth and the Earth in orbit around the Sun, the Earth would leave the Moon behind as it moved around its orbit. </li></ul>
- 38. The Phases of Venus <ul><li>The crucial point is the empirical fact that Venus is never very far from the Sun in our sky. Thus, as the following diagrams indicate, in the Ptolemaic system Venus should always be in crescent phase as viewed from the Earth because as it moves around its epicycle it can never be far from the direction of the sun, but in the Copernican system Venus should exhibit a complete set of phases over time as viewed from the Earth because it is illuminated from the center of its orbit. </li></ul>
- 41. Myriad Observations Showing Phenomena Unknown to Aristotle <ul><li>Galileo made many other observations that undermined the authority on which the Ptolemaic universe was built. Some of these included </li></ul><ul><ul><li>Showing that the planets were disks, not points of light, as seen through the telescope. </li></ul></ul><ul><ul><li>Showing that the great "cloud" called the Milky Way (which we now know to be the disk of our spiral galaxy) was composed of enormous numbers of stars that had not been seen before. </li></ul></ul><ul><ul><li>Observing that the planet Saturn had "ears". We now know that Galileo was observing the rings of Saturn, but his telescope was not good enough to show them as more than extensions on either side of the planet. </li></ul></ul><ul><ul><li>Showing that the Moon was not smooth, as had been assumed, but was covered by mountains and craters. </li></ul></ul>
- 42. Sir Isaac Newton and the Unification of Physics & Astronomy <ul><li>Sir Isaac Newton (1642-1727) was by many standards the most important figure in the development of modern science. Many would credit him and Einstein with being the most original thinkers in science development. </li></ul>
- 43. We shall concentrate on three developments of most direct relevance to our discussion: <ul><li>(1) Newton's Three Laws of Motion, </li></ul><ul><li>(2) the Theory of Universal Gravitation, and </li></ul><ul><li>(3) the demonstration that Kepler's Laws follow from the Law of Gravitation. </li></ul>
- 44. Newton's Three Laws of Motion <ul><li>"Law of Inertia". </li></ul><ul><li>I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. </li></ul>
- 45. Newton's Second Law of Motion: <ul><li>II. The relationship between an object's mass m , its acceleration a, and the applied force F is F = ma . </li></ul><ul><li>Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. </li></ul><ul><li>Law of acceleration </li></ul>
- 46. Newton's Third Law of Motion: <ul><li>III. For every action there is an equal and opposite reaction. </li></ul><ul><li>Law of Interaction </li></ul>
- 47. Sir Isaac Newton: The Universal Law of Gravitation <ul><li>There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation. As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened. </li></ul>
- 48. What Really Happened with the Apple?
- 49. Albert Einstein and the Theory of Relativity <ul><li>Motion is relative not absolute. </li></ul><ul><li>Other striking consequences are associated with the dependence of space and time on velocity: at speeds near that of light, space itself becomes contracted in the direction of motion and the passage of time slows. Although these seem bizarre ideas (because our everyday experience typically does not include speeds near that of light), many experiments indicate that the Special Theory of Relativity is correct and our "common sense" (and Newton's laws) are incorrect near the speed of light. </li></ul>
- 50. SUMMARY Earth is the center of motion Earth is does not move Earth IS flat Planets move in circular orbits Stars are immutable Galileo Galilean satellites Phases of Venus Universal Law of Gravitation Newton Laws of Motion Einstein Theory of Relativity Kepler Laws of Planetary Motion Brahe Supernova
- 51. <ul><li>End of Discussion.. </li></ul><ul><li>Exam next meeting…. </li></ul><ul><li>THANK YOU VERY MUCH! </li></ul>
- 53. http://csep10.phys.utk.edu/astr161/lect/index.html <ul><li>The first two objections were not valid because they represent an inadequate understanding of the physics of motion that would only be corrected in the 17th century. The third objection is valid, but failed to account for what we now know to be the enormous distances to the stars. As illustrated in the following figure, the amount of parallax decreases with distance. </li></ul><ul><li>The parallax effect is there, but it is very small because the stars are so far away that their parallax can only be observed with very precise instruments. Indeed, the parallax of stars was not measured conclusively until the year 1838. Thus, the heliocentric idea of Aristarchus was quickly forgotten and Western thought stagnated for almost 2000 years as it waited for Copernicus to revive the heliocentric theory. </li></ul>

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