Discovering the Universe for Yourself

Discovering the Universe for Yourself
© 2014 Pearson Education, Inc. 1

Discovering the Universe for Yourself
© 2014 Pearson Education, Inc.

2.1 Patterns in the 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? © 2014 Pearson Education, Inc.

What does the universe look like from Earth?
With the naked eye, we can see more than 2000 stars as well as the Milky Way. © 2014 Pearson Education, Inc.

Constellations A constellation is a region of the sky.
Eighty-eight constellations fill the entire sky. 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. © 2014 Pearson Education, Inc.

Thought Question The brightest stars in a constellation
all belong to the same star cluster. all lie at about the same distance from Earth. may actually be quite far away from each other. 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. © 2014 Pearson Education, Inc.

Thought Question The brightest stars in a constellation
all belong to the same star cluster. all lie at about the same distance from Earth. may actually be quite far away from each other. 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). © 2014 Pearson Education, Inc.

The Celestial Sphere Stars at different distances all appear to lie on the celestial sphere. The 88 official constellations cover the celestial sphere. 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. © 2014 Pearson Education, Inc.

The Celestial Sphere The Ecliptic is the Sun's apparent path through the celestial sphere. 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… © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

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. 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. © 2014 Pearson Education, Inc.

The Milky Way 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. © 2014 Pearson Education, Inc.

The Local Sky An object's altitude (above horizon) and direction (along horizon) specify its location in your local sky. 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. © 2014 Pearson Education, Inc.

The Local Sky Meridian: line passing through zenith and connecting N and S points on horizon 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. Zenith: the point directly overhead Horizon: all points 90° away from zenith © 2014 Pearson Education, Inc.

We measure the sky using angles.
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. © 2014 Pearson Education, Inc.

Angular Measurements Full circle = 360º 1º = 60 (arcminutes)
1 = 60 (arcseconds) Use this slide if you want to review the definitions of arc minutes and arc seconds. Insert Figure 2.8 © 2014 Pearson Education, Inc.

Thought Question The angular size of your finger at arm's length is about 1°. How many arcseconds is this? 60 arcseconds 600 arcseconds 60  60 = 3600 arcseconds This is a quick test of whether students understand what we mean by arcseconds. © 2014 Pearson Education, Inc.

Thought Question The angular size of your finger at arm's length is about 1°. How many arcseconds is this? 60 arcseconds 600 arcseconds 60  60 = 3600 arcseconds 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…. © 2014 Pearson Education, Inc.

Why do stars rise and set?
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… Earth rotates from west to east, so stars appear to circle from east to west. © 2014 Pearson Education, Inc.

Our view from Earth: Stars near the 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. 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. ) © 2014 Pearson Education, Inc.

Thought Question What is the arrow pointing to in the photo below? A. the zenith B. the north celestial pole C. the celestial equator This question will check whether students understand the pattern they see in this time exposure photograph. © 2014 Pearson Education, Inc.

Why do the constellations 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. These are the two basic reasons that the visible constellations vary; next we'll explore each one. © 2014 Pearson Education, Inc.

Review: Coordinates on the Earth
Latitude: position north or south of equator Longitude: position east or west of prime meridian (runs through Greenwich, England) 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. © 2014 Pearson Education, Inc.

The sky varies with latitude but not with longitude.
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)… © 2014 Pearson Education, Inc.

Altitude of the celestial pole = your latitude
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… © 2014 Pearson Education, Inc.

Thought Question The North Star (Polaris) is 50° above your horizon, due north. Where are you? You are on the equator. You are at the North Pole. You are at latitude 50°N. You are at longitude 50°E. You are at latitude 50°N and longitude 50°E. This question just makes sure the students understand the altitude = latitude idea… © 2014 Pearson Education, Inc.

Thought Question The North Star (Polaris) is 50° above your horizon, due north. Where are you? You are on the equator. You are at the North Pole. You are at latitude 50°N. You are at longitude 50°E. You are at latitude 50°N and longitude 50°E. © 2014 Pearson Education, Inc.

The sky varies as 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. Use this interactive figure to explain how the constellations change with the time of year. © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

2.2 The Reason for Seasons Our goals for learning:
What causes the seasons? How does the orientation of Earth's axis change with time? © 2014 Pearson Education, Inc.

Thought Question TRUE OR FALSE? Earth is closer to the Sun in summer and farther from the Sun in winter. A good way to begin discussion of seasons is by posing this question about the most common season misconception. © 2014 Pearson Education, Inc.

Thought Question TRUE OR FALSE? 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. 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. © 2014 Pearson Education, Inc.

Thought Question TRUE OR FALSE! 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. 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? © 2014 Pearson Education, Inc.

What causes the seasons?
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. Seasons depend on how Earth's axis affects the directness of sunlight. © 2014 Pearson Education, Inc.

Direct light causes more heating.
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. © 2014 Pearson Education, Inc.

Axis tilt changes directness of sunlight during the year.
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. © 2014 Pearson Education, Inc.

Sun's altitude also changes 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. 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. © 2014 Pearson Education, Inc.

Summary: The Real Reason 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. © 2014 Pearson Education, Inc.

Why doesn't distance matter?
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! 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. © 2014 Pearson Education, Inc.

How do we mark the progression of the seasons?
We define four special points: summer (June) solstice winter (December) solstice spring (March) equinox fall (September) equinox 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. © 2014 Pearson Education, Inc.

We can recognize solstices 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. 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…) © 2014 Pearson Education, Inc.

Seasonal changes are more extreme at high latitudes.
Path of the Sun on the summer solstice at the Arctic Circle 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. © 2014 Pearson Education, Inc.

How does the orientation 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 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. © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

2.3 The Moon, Our Constant Companion
Our goals for learning: Why do we see phases of the Moon? What causes eclipses? © 2014 Pearson Education, Inc.

Why do we see phases of the Moon?
Lunar phases are a consequence of the Moon's 27.3-day orbit around Earth. 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. © 2014 Pearson Education, Inc.

Phases of the Moon 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. 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. © 2014 Pearson Education, Inc.

Phases of the Moon 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. © 2014 Pearson Education, Inc.

Moon Rise/Set by Phase 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. © 2014 Pearson Education, Inc.

Phases of the Moon: 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 © 2014 Pearson Education, Inc.

Thought Question It's 9 a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? first quarter waxing gibbous third quarter half moon This will check whether students have grasped the key ideas about rise and set times. © 2014 Pearson Education, Inc.

Thought Question It's 9 a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? first quarter waxing gibbous third quarter half moon 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…) © 2014 Pearson Education, Inc.

We see only one side of Moon
Synchronous rotation: the Moon rotates exactly once with each orbit. That is why only one side is visible from Earth. 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. © 2014 Pearson Education, Inc.

What causes eclipses? The Earth and Moon cast shadows.
When either passes through the other's shadow, we have an eclipse. This slide starts our discussion of eclipses. Use the figure to explain the umbra/penumbra shadows. © 2014 Pearson Education, Inc.

When can eclipses occur?
Lunar eclipses can occur only at full moon. Lunar eclipses can be penumbral, partial, or total. Use the interactive figure to show the conditions for the 3 types of lunar eclipse. © 2014 Pearson Education, Inc.

When can eclipses occur?
Solar eclipses can occur only at new moon. Solar eclipses can be partial, total, or annular. Use the interactive figure to show the conditions for the 3 types of solar eclipse. © 2014 Pearson Education, Inc.

Why don't we have 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. 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. © 2014 Pearson Education, Inc.

Summary: Two conditions must be met to have an eclipse:
It must be full moon (for a lunar eclipse) or new moon (for a solar eclipse). AND The Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes). © 2014 Pearson Education, Inc.

Predicting Eclipses Eclipses recur with the 18-year, 11 1/3-day saros cycle, but type (e.g., partial, total) and location may vary. 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). © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

2.4 The Ancient Mystery 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? © 2014 Pearson Education, Inc.

Planets Known in Ancient 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 This slide explains what students can see of planets in the sky. © 2014 Pearson Education, Inc.

What was once so 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. The diagram at left shows Jupiter's path with apparent retrograde motion in The photo composite shows Mars at 5-8 day intervals during the latter half of 2003. © 2014 Pearson Education, Inc.

We see apparent retrograde motion when we pass by a planet in its orbit.
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… © 2014 Pearson Education, Inc.

Explaining Apparent Retrograde Motion
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. © 2014 Pearson Education, Inc.

Why did the ancient Greeks reject the real explanation for planetary motion?
Their inability to observe stellar parallax was a major factor. © 2014 Pearson Education, Inc.

The Greeks knew that the lack of observable parallax could mean one of two things:
Stars are so far away that stellar parallax is too small to notice with the naked eye. Earth does not orbit the Sun; it is the center of the universe. 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. 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… © 2014 Pearson Education, Inc.

What have we learned? 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. © 2014 Pearson Education, Inc.

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