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02 lecture outline
The document discusses patterns observed in the night sky from Earth and what was historically mysterious about planetary motions. Specifically: 1) Planets appear to normally move eastward among the stars but sometimes reverse to westward motion, known as retrograde motion. This was difficult to explain under the ancient Earth-centered model. 2) The ancient Greeks rejected the sun-centered explanation for planetary motion because they thought stellar parallax should be observable if the stars were actually very far away. 3) What appears as retrograde motion of planets is actually caused by Earth "lapping" other planets in their orbits around the sun.
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02 lecture outline
- 1. Chapter 2 Lecture ©2014 Pearson Education, Inc. The Cosmic Perspective Seventh Edition Discovering the Universe for Yourself
- 2. Discovering the Universefor Yourself
- 3. 2.1 Patterns inthe Night Sky • Our goals for learning: – What does the universe look like from Earth? – Why do stars rise and set? – Why do the constellations we see depend on latitude and time of year?
- 4. What does theuniverse look like from Earth? • With the naked eye, we can see more than 2000 stars as well as the Milky Way.
- 5. Constellations • A constellationis a region of the sky. • Eighty-eight constellations fill the entire sky.
- 6. Thought Question The brighteststars in a constellation A. all belong to the same star cluster. B. all lie at about the same distance from Earth. C. may actually be quite far away from each other.
- 7. Thought Question The brighteststars in a constellation A. all belong to the same star cluster. B. all lie at about the same distance from Earth. C. may actually be quite far away from each other.
- 8. The Celestial Sphere •Stars at different distances all appear to lie on the celestial sphere. • The 88 official constellations cover the celestial sphere.
- 9. The Celestial Sphere •The Ecliptic is the Sun's apparent path through the celestial sphere.
- 10. The Celestial Sphere •North celestial pole is directly above Earth's North Pole. • South celestial pole is directly above Earth's South Pole. • Celestial equator is a projection of Earth's equator onto sky.
- 11. The Milky Way •A band of light making a circle around the celestial sphere. What is it? • Our view into the plane of our galaxy.
- 12.
- 13. The Local Sky •An object's altitude (above horizon) and direction (along horizon) specify its location in your local sky.
- 14. The Local Sky •Meridian: line passing through zenith and connecting N and S points on horizon • Zenith: the point directly overhead • Horizon: all points 90° away from zenith
- 15. We measure thesky using angles.
- 16. Insert Figure 2.8 Insert Figure 2.8 AngularMeasurements • Full circle = 360º • 1º = 60′ (arcminutes) • 1′ = 60″ (arcseconds)
- 17. Thought Question The angularsize of your finger at arm's length is about 1°. How many arcseconds is this? A. 60 arcseconds B. 600 arcseconds C. 60 × 60 = 3600 arcseconds
- 18. The angular sizeof your finger at arm's length is about 1°. How many arcseconds is this? A. 60 arcseconds B. 600 arcseconds C. 60 × 60 = 3600 arcseconds Thought Question
- 19. Angular Size • Anobject's angular size appears smaller if it is farther away.
- 20. Why do starsrise and set? • Earth rotates from west to east, so stars appear to circle from east to west.
- 21. • Stars nearthe north celestial pole are circumpolar and never set. • We cannot see stars near the south celestial pole. • All other stars (and Sun, Moon, planets) rise in east and set in west. Our view from Earth:
- 22. Thought Question What isthe arrow pointing to in the photo below? A. the zenith B. the north celestial pole C. the celestial equator
- 23. Thought Question What isthe arrow pointing to in the photo below? A. the zenith B. the north celestial pole C. the celestial equator
- 24. Why do theconstellations we see depend on latitude and time of year? • They depend on latitude because your position on Earth determines which constellations remain below the horizon. • They depend on time of year because Earth's orbit changes the apparent location of the Sun among the stars.
- 25. Review: Coordinates onthe Earth • Latitude: position north or south of equator • Longitude: position east or west of prime meridian (runs through Greenwich, England)
- 26. The sky varieswith latitude but not with longitude.
- 27. Altitude of thecelestial pole = your latitude
- 28. Thought Question The NorthStar (Polaris) is 50° above your horizon, due north. Where are you? A. You are on the equator. B. You are at the North Pole. C. You are at latitude 50°N. D. You are at longitude 50°E. E. You are at latitude 50°N and longitude 50°E.
- 29. Thought Question The NorthStar (Polaris) is 50° above your horizon, due north. Where are you? A. You are on the equator. B. You are at the North Pole. C. You are at latitude 50°N. D. You are at longitude 50°E. E. You are at latitude 50°N and longitude 50°E.
- 30. The sky variesas Earth orbits the Sun • As the Earth orbits the Sun, the Sun appears to move eastward along the ecliptic. • At midnight, the stars on our meridian are opposite the Sun in the sky.
- 31. What have welearned? • What does the universe look like from Earth? – We can see over 2000 stars and the Milky Way with our naked eyes, and each position on the sky belongs to one of 88 constellations. – We can specify the position of an object in the local sky by its altitude above the horizon and its direction along the horizon. • Why do stars rise and set? – Because of Earth's rotation.
- 32. What have welearned? • Why do the constellations we see depend on latitude and time of year? – Your location determines which constellations are hidden by Earth. – The time of year determines the location of the Sun on the celestial sphere.
- 33. 2.2 The Reasonfor Seasons • Our goals for learning: – What causes the seasons? – How does the orientation of Earth's axis change with time?
- 34. Thought Question TRUE ORFALSE? Earth is closer to the Sun in summer and farther from the Sun in winter.
- 35. Thought Question TRUE ORFALSE? Earth is closer to the Sun in summer and farther from the Sun in winter. Hint: When it is summer in America, it is winter in Australia.
- 36. Thought Question TRUE ORFALSE! Earth is closer to the Sun in summer and farther from the Sun in winter. • Seasons are opposite in the N and S hemispheres, so distance cannot be the reason. • The real reason for seasons involves Earth's axis tilt.
- 37. • Seasons dependon how Earth's axis affects the directness of sunlight. What causes the seasons?
- 38. Direct light causesmore heating.
- 39. Axis tilt changesdirectness of sunlight during the year.
- 40. Sun's altitude alsochanges with seasons. • Sun's position at noon in summer: Higher altitude means more direct sunlight. • Sun's position at noon in winter: Lower altitude means less direct sunlight.
- 41. Summary: The RealReason for Seasons • Earth's axis points in the same direction (to Polaris) all year round, so its orientation relative to the Sun changes as Earth orbits the Sun. • Summer occurs in your hemisphere when sunlight hits it more directly; winter occurs when the sunlight is less direct. • AXIS TILT is the key to the seasons; without it, we would not have seasons on Earth.
- 42. Why doesn't distancematter? • Variation of Earth– Sun distance is small—about 3%; this small variation is overwhelmed by the effects of axis tilt. • Variation in any season of each hemisphere-Sun distance is even smaller!
- 43. How do wemark the progression of the seasons? • We define four special points: summer (June) solstice winter (December) solstice spring (March) equinox fall (September) equinox
- 44. We can recognizesolstices and equinoxes by Sun's path across sky: • Summer (June) solstice: highest path; rise and set at most extreme north of due east • Winter (December) solstice: lowest path; rise and set at most extreme south of due east • Equinoxes: Sun rises precisely due east and sets precisely due west.
- 45. Seasonal changes aremore extreme at high latitudes. • Path of the Sun on the summer solstice at the Arctic Circle
- 46. How does theorientation of Earth's axis change with time? • Although the axis seems fixed on human time scales, it actually precesses over about 26,000 years. ⇒ Polaris won't always be the North Star. ⇒ Positions of equinoxes shift around orbit; e.g., spring equinox, once in Aries, is now in Pisces! Earth's axis precesses like the axis of a spinning top
- 47. What have welearned? • What causes the seasons? – The tilt of the Earth's axis causes sunlight to hit different parts of the Earth more directly during the summer and less directly during the winter. – We can specify the position of an object in the local sky by its altitude above the horizon and its direction along the horizon. – The summer and winter solstices are when the Northern Hemisphere gets its most and least direct sunlight, respectively. The spring and fall equinoxes are when both hemispheres get equally direct sunlight.
- 48. What have welearned? • How does the orientation of Earth's axis change with time? – The tilt remains about 23.5° (so the season pattern is not affected), but Earth has a 26,000 year precession cycle that slowly and subtly changes the orientation of Earth's axis.
- 49. 2.3 The Moon,Our Constant Companion • Our goals for learning: – Why do we see phases of the Moon? – What causes eclipses?
- 50. Why do wesee phases of the Moon? • Lunar phases are a consequence of the Moon's 27.3-day orbit around Earth.
- 51. Phases of theMoon • Half of Moon is illuminated by Sun and half is dark. • We see a changing combination of the bright and dark faces as Moon orbits.
- 52. Phases of theMoon
- 53. Moon Rise/Set byPhase
- 54. Phases of theMoon: 29.5-day cycle Waxing • Moon visible in afternoon/evening • Gets "fuller" and rises later each day Waning • Moon visible in late night/morning • Gets "less full" and sets later each day
- 55. Thought Question It's 9a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? A. first quarter B. waxing gibbous C. third quarter D. half moon
- 56. Thought Question It's 9a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? A. first quarter B. waxing gibbous C. third quarter D. half moon
- 57. We see onlyone side of Moon • Synchronous rotation: the Moon rotates exactly once with each orbit. • That is why only one side is visible from Earth.
- 58. What causes eclipses? •The Earth and Moon cast shadows. • When either passes through the other's shadow, we have an eclipse.
- 59.
- 60. • Lunar eclipses canoccur only at full moon. • Lunar eclipses can be penumbral, partial, or total. When can eclipses occur?
- 61.
- 62. When can eclipsesoccur? • Solar eclipses can occur only at new moon. • Solar eclipses can be partial, total, or annular.
- 63. Why don't wehave an eclipse at every new and full moon? • The Moon's orbit is tilted 5° to ecliptic plane. • So we have about two eclipse seasons each year, with a lunar eclipse at new moon and solar eclipse at full moon.
- 64. Summary: Two conditionsmust be met to have an eclipse: 1. It must be full moon (for a lunar eclipse) or new moon (for a solar eclipse). AND 2. The Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes).
- 65. Predicting Eclipses • Eclipsesrecur with the 18-year, 11 1/3-day saros cycle, but type (e.g., partial, total) and location may vary.
- 66. What have welearned? • Why do we see phases of the Moon? – Half the Moon is lit by the Sun; half is in shadow, and its appearance to us is determined by the relative positions of Sun, Moon, and Earth. • What causes eclipses? – Lunar eclipse: Earth's shadow on the Moon – Solar eclipse: Moon's shadow on Earth – Tilt of Moon's orbit means eclipses occur during two periods each year.
- 67. 2.4 The AncientMystery of the Planets • Our goals for learning: – What was once so mysterious about planetary motion in our sky? – Why did the ancient Greeks reject the real explanation for planetary motion?
- 68. Planets Known inAncient Times • Mercury – difficult to see; always close to Sun in sky • Venus – very bright when visible; morning or evening "star" • Mars – noticeably red • Jupiter – very bright • Saturn – moderately bright
- 69. What was onceso mysterious about planetary motion in our sky? • Planets usually move slightly eastward from night to night relative to the stars. • But sometimes they go westward relative to the stars for a few weeks: apparent retrograde motion.
- 70. We see apparentretrograde motion when we pass by a planet in its orbit.
- 71. Explaining Apparent RetrogradeMotion • Easy for us to explain: occurs when we "lap" another planet (or when Mercury or Venus laps us). • But very difficult to explain if you think that Earth is the center of the universe! • In fact, ancients considered but rejected the correct explanation.
- 72. Why did theancient Greeks reject the real explanation for planetary motion? • Their inability to observe stellar parallax was a major factor.
- 73. 1. Stars areso far away that stellar parallax is too small to notice with the naked eye. 2. Earth does not orbit the Sun; it is the center of the universe. The Greeks knew that the lack of observable parallax could mean one of two things: With rare exceptions such as Aristarchus, the Greeks rejected the correct explanation (1) because they did not think the stars could be that far away. Thus, the stage was set for the long, historical showdown between Earth-centered and Sun- centered systems.
- 74. What have welearned? • What was so mysterious about planetary motion in our sky? – Like the Sun and Moon, planets usually drift eastward relative to the stars from night to night, but sometimes, for a few weeks or few months, a planet turns westward in its apparent retrograde motion. • Why did the ancient Greeks reject the real explanation for planetary motion? – Most Greeks concluded that Earth must be stationary, because they thought the stars could not be so far away as to make parallax undetectable.
Editor's Notes
- #6 Remind students that we often use the term "constellation" to describe a pattern of stars, such as the Big Dipper or the stars that outline Orion. However, technically a constellation is a region of the sky (and the patterns are sometimes called "asterisms"). A useful analogy for students: a constellation is to the sky as a state is to the United States. That is, wherever you point on a map of the U.S. you are in some state, and wherever you point into the sky you are in some constellation.
- #7 You can use this question both to check student understanding of the idea of a constellation and as a way of leading into the concept of the celestial sphere that follows.
- #8 Worth pointing out that two stars in the same constellation can actually be farther apart than stars on opposite sides of our sky, depending on their distances… E.g.,: Procyon and Alpha Centauri are much farther apart than Procyon and Betelgeuse; But in space, Alpha Cen and Procyon are both relatively nearby stars (their distances are 11.4 and 4.4 light-years, respectively) which means they are not more than about a dozen light-years apart, while Betelgeuse is several hundred light-years away from Procyon (distance to Betelgeuse is about 430 light-years).
- #9 The illusion of stars all lying at the same distance in the constellations allows us to define the celestial sphere. It doesn't really exist, but it's a useful applet for learning about the sky. When discussing this slide, be sure to explain: North celestial pole South celestial pole Celestial equator Ecliptic It's also very useful to bring a model of the celestial sphere to class and show these points/circles on the model.
- #10 If you do not have a model of the celestial sphere to bring to class, you might wish to use this slide; you will probably want to skip it if you have a model that you can discuss instead…
- #12 On the previous slide or your model, you can point out that the celestial sphere is also painted with the Milky Way. Many students may never have seen the Milky Way in the sky (especially if they live in a big city), so the photo here is also worth showing. Key points to emphasize: We use the term Milky Way in two ways: for the band of light in the sky and as the name of our galaxy. (2) The two meanings are closely related. We like to use the following analogy: Ask your students to imagine being a tiny grain of flour inside a very thin pancake (or crepe!) that bulges in the middle and a little more than halfway toward the outer edge. Ask, "What will you see if you look toward the middle?" The answer should be "dough." Then ask what they will see if they look toward the far edge, and they'll give the same answer. Proceeding similarly, they should soon realize that they'll see a band of dough encircling their location, but that if they look away from the plane, the pancake is thin enough that they can see to the distant universe. Additionally, it may be worth asking why the Milky Way appears curved in the image.
- #13 On the previous slide or your model, you can point out that the celestial sphere is also painted with the Milky Way. Many students may never have seen the Milky Way in the sky (especially if they live in a big city), so the photo here is also worth showing. Key points to emphasize: We use the term Milky Way in two ways: for the band of light in the sky and as the name of our galaxy. (2) The two meanings are closely related. We like to use the following analogy: Ask your students to imagine being a tiny grain of flour inside a very thin pancake (or crepe!) that bulges in the middle and a little more than halfway toward the outer edge. Ask, "What will you see if you look toward the middle?" The answer should be "dough." Then ask what they will see if they look toward the far edge, and they'll give the same answer. Proceeding similarly, they should soon realize that they'll see a band of dough encircling their location, but that if they look away from the plane, the pancake is thin enough that they can see to the distant universe.
- #14 Now we move from the celestial sphere to the local sky. The local sky looks like a dome because we see only half the celestial sphere. If we want to locate an object: It's useful to have some reference points. Students will probably already understand the horizon and the cardinal directions, but explain the zenith and the meridian; a simple way to define the meridian is as an imaginary half-circle stretching from the horizon due south, through the zenith, to the horizon due north. Now we can locate any object by specifying its altitude above the horizon and direction along the horizon. A good way to reinforce this idea is to pick an object located in your class room, tell students which way is north, and have them estimate its altitude and direction.
- #15 Now we move from the celestial sphere to the local sky. The local sky looks like a dome because we see only half the celestial sphere. If we want to locate an object: It's useful to have some reference points. Students will probably already understand the horizon and the cardinal directions, but explain the zenith and the meridian; a simple way to define the meridian is as an imaginary half-circle stretching from the horizon due south, through the zenith, to the horizon due north. Now we can locate any object by specifying its altitude above the horizon and direction along the horizon. A good way to reinforce this idea is to pick an object located in your class room, tell students which way is north, and have them estimate its altitude and direction.
- #16 Point out that in general we have no way of judging true (physical) sizes and distances of objects in the sky -- like the illusion of stars lying on the celestial sphere, this is due to our lack of depth perception in space. Thus, we can measure only angular sizes and distances. Use these diagrams as examples. Optional: You can show how angular sizes depend on distance by having students sitting at different distances from you in the class use their fists to estimate the angular size of a ball you are holding. Students in the back will measure a smaller angular size.
- #17 Use this slide if you want to review the definitions of arc minutes and arc seconds.
- #18 This is a quick test of whether students understand what we mean by arcseconds.
- #19 Now point out that 1 arc second is only about 1/3600 of the width of your finger against the sky --- yet modern telescopes routinely resolve features smaller than this….
- #21 The answer to the question is very simple if we look at the celestial sphere from the "outside." But of course, we are looking from our location on Earth, which makes the motions of stars look a little more complex…
- #22 Now explain the basic motion of the sky seen from Earth. (The arrow from "Your Horizon" should not point at the dot, but instead at the light blue/gray plane. )
- #23 This question will check whether students understand the pattern they see in this time exposure photograph.
- #24 This question will check whether students understand the pattern they see in this time exposure photograph.
- #25 These are the two basic reasons that the visible constellations vary; next we'll explore each one.
- #26 Use this for a brief review of latitude and longitude; it's also useful to bring in a real globe to class for this purpose. The photo at right is the entrance to the Old Royal Greenwich Observatory (near London); the line emerging from the door marks the Prime Meridian.
- #27 Use this interactive figure to explain the variation in the sky with latitude. Show how the altitude of the NCP equals your latitude (for N. hemisphere)…
- #28 Show students how to locate the NCP and SCP, and how the sky moves around them. (You might wish to repeat the time exposure photo of the sky at this point to re-emphasize what we see.) Can also ask students where they'd find the north celestial pole in their sky tonight…
- #29 This question just makes sure the students understand the altitude = latitude idea…
- #31 Use this interactive figure to explain how the constellations change with the time of year.
- #35 A good way to begin discussion of seasons is by posing this question about the most common season misconception.
- #36 This hint should make students realize that distance from the Sun CANNOT be the explanation for seasons: if it were, the entire Earth should experience the same seasons at the same time. Note: Some students think the axis tilt makes one hemisphere closer to the Sun than the other; you can show them why this is not the case by revisiting the 1-to-10 billion scale model solar system from Ch. 1. When you remind them that the ball point size Earth orbits 15 meters from the grapefruit size Sun, it's immediately obvious that the 2 hemispheres cannot have any significant difference in distance.
- #37 Now that you've answered the T/F question, we can go on to explore the real reason for seasons. Note: You might optionally mention that, in fact, Earth is closest to the Sun during N. hemisphere winter… Also, students who know of the Earth's axis tilt may think that the difference in distance between the Sun - Northern hemisphere and the Sun – Southern hemisphere is the key. What part of 150 Mkm is a 1000km?
- #38 Misconceptions about the cause of the seasons are so common that you may wish to go over the idea in more than one way. We therefore include several slides on this topic. This slide uses the interactive version of the figure that appears in the book; the following slides use frames from the Seasons tutorial on the MasteringAstronomy web site.
- #39 This applet is taken from the Seasons tutorial on the Mastering Astronomy. You can use it to reinforce the ideas from the previous slide. As usual, please encourage your students to try the tutorial for themselves.
- #40 This applet is taken from the Seasons tutorial on MasteringAstronomy.com. You can use it to reinforce the ideas from the previous slide. As usual, please encourage your students to try the tutorial for themselves.
- #41 This applet is taken from the Seasons tutorial on the MasteringAstronomy web site. You can use it to reinforce the ideas from the previous slide. As usual, please encourage your students to try the tutorial for themselves.
- #43 The two notes should be considered optional. If you cover the first note, you might point out that since Earth is closer to the Sun in S. hemisphere summer and farther in S. hemisphere winter, we might expect that the S. hemisphere would have the more extreme seasons, but it does not because the distance effect is overwhelmed by the geographical effect due to the distribution of oceans.
- #44 Here we focus in on just part of Figure 2.13 to see the four special points in Earth's orbit, which also correspond to moments in time when Earth is at these points.
- #45 Of course, the notes here are true for a N. hemisphere sky. You might ask students which part written above changes for S. hemisphere. (Answer: highest and lowest reverse above, but all the rest is still the same for the S. hemisphere; and remind students that we use names for the N. hemisphere, so that S. hemisphere summer actually begins on the winter solstice…)
- #46 Other points worth mentioning: Length of daylight/darkness becomes more extreme at higher latitudes. The four seasons are characteristic of temperate latitudes; tropics typically have rainy and dry seasons (rainy seasons when Sun is higher in sky). Equator has highest Sun on the equinoxes. Optional: explain Tropics and Arctic/Antarctic Circles.
- #47 Precession can be demonstrated in class in a variety of ways. Bring a top or gyroscope to class, or do the standard physics demonstration with a bicycle wheel and rotating platform. You may wish to go further with precession of the equinoxes, as in the Common Misconceptions box on "Sun Signs" --- this always surprises students, and helps them begin to see why astrology is questionable (to say the least!). Can also mention how Tropics of Cancer/Capricorn got their names from constellations of the solstices, even though the summer/winter solstices are now in Gemini/Sagittarius.
- #51 You may want to do an in-class demonstration of phases by darkening the room, using a lamp to represent the Sun, and giving each student a Styrofoam ball to represent the Moon. If your lamp is bright enough, the students can remain in their seats and watch the phases as they move the ball around their heads.
- #52 You may want to do an in-class demonstration of phases by darkening the room, using a lamp to represent the Sun, and giving each student a Styrofoam ball to represent the Moon. If you lamp is bright enough, the students can remain in their seats and watch the phases as they move the ball around their heads.
- #53 You can use this applet from the Phases of the Moon tutorial to present the idea behind phases in another way. As usual, please encourage your students to try the tutorial for themselves.
- #54 Use this applet from the Phases of the Moon tutorial to explain rise and set times for the Moon at various phases. As usual, please encourage your students to try the tutorial for themselves.
- #56 This will check whether students have grasped the key ideas about rise and set times.
- #57 If anyone chose "half moon," remind them that there is no phase with that name… (and that first and third quarter refer to how far through the cycle of phases we are…)
- #58 Use this applet from the Phases of the Moon tutorial to explain rise and set times for the Moon at various phases. As usual, please encourage your students to try the tutorial for themselves.
- #59 This slide starts our discussion of eclipses. Use the figure to explain the umbra/penumbra shadows.
- #60 This interactive applet goes through lunar eclipses. Use it instead of or in addition to the earlier slides on eclipses.
- #61 Use the interactive figure to show the conditions for the 3 types of lunar eclipse.
- #62 This interactive applet goes through the solar eclipses. Use it instead of or in addition to the earlier slides on eclipses.
- #63 Use the interactive figure to show the conditions for the 3 types of solar eclipse.
- #64 Use this pond analogy to explain what we mean by nodes and how we get 2 eclipse seasons each year (roughly). Note: You may wish to demonstrate the Moon's orbit and eclipse conditions as follows. Keep a model "Sun" on a table in the center of the lecture area; have your left fist represent the Earth, and hold a ball in the other hand to represent the Moon. Then you can show how the Moon orbits your "fist" at an inclination to the ecliptic plane, explaining the meaning of the nodes. You can also show eclipse seasons by "doing" the Moon's orbit (with fixed nodes) as you walk around your model Sun: the students will see that eclipses are possible only during two periods each year. If you then add in precession of the nodes, students can see why eclipse seasons occur slightly more often than every 6 months.
- #66 Point out that even though some ancient civilizations recognized the saros cycle, precise prediction still eluded them. Use the colored bands in the figure to illustrate the saros cycle (e.g., red bands for 2009 and 2027 eclipses are 18 yr, 11 1/3 days apart).
- #69 This slide explains what students can see of planets in the sky.
- #70 The diagram at left shows Jupiter's path with apparent retrograde motion in 2004-5. The photo composite shows Mars at 5-8 day intervals during the latter half of 2003.
- #71 We also recommend that you encourage students to try the apparent retrograde motion demonstration shown in the book in Figure 2.33a, since seeing it for themselves really helps remove the mystery…
- #74 In fact, the nearest stars have parallax angles less than 1 arcsecond, far below what the naked eye can see. Indeed, we CAN detect parallax today, offering direct proof that Earth really does go around the Sun…