OpenStax Astronomy 2e Instructor Answer Guide
,OpenStax Astronomy 2e Instructor Answer Guide
Chapter 1: Science and the Universe
No assessments for this chapter.
This file is copyright 2022, Rice University. All Rights Reserved.
,OpenStax Astronomy 2e Instructor Answer Guide
Chapter 2: Observing the Sky: The Birth of Astronomy
Review Questions
1. From where on Earth could you observe all of the stars during the course of the year?
What fraction of the sky can be seen from the North Pole?
Answer
You can observe all of the stars from the equator over the course of a year, although
high-declination stars will be difficult to see so close to the horizon. Only half the sky
can be seen from the North Pole, and that half does not change throughout the year.
2. Give four ways to demonstrate that Earth is spherical.
Answer
The shadow cast on the Moon is always round in shape. Ships sailing away on the
ocean appear to sink into the ocean due to the curvature of Earth’s surface, rather than
simply getting smaller and smaller. Orbiting satellites taking photographs of Earth show
that Earth looks round from every direction. The Sun is at different altitudes in the sky
for different longitudes (it would be in the same place for everyone if Earth were flat, for
example), and the Sun’s position in the sky depends upon the time.
3. Explain, according to both geocentric and heliocentric cosmologies, why we see
retrograde motion of the planets.
Answer
In the geocentric model, Mars orbits outside of the Sun on its deferent path, but it also
moves in a circular motion on its epicycle as it follows the deferent. If the planet moves
faster “backward” on the epicycle than it moves forward on the deferent, then it can
appear to move in a retrograde manner while still retaining the overall pattern of
prograde motion in the sky. In the heliocentric model, Mars moves somewhat slower
than Earth. During periods of time when Earth passes Mars, Mars appears to move
backward on the sky relative to the background stars. This is confirmed by the fact that
Mars appears at its brightest during this motion (due to it being at its closest approach
to Earth) and is also on the opposite side of the sky from the Sun during retrograde
motion.
4. In what ways did the work of Copernicus and Galileo differ from the views of the
ancient Greeks and of their contemporaries?
Answer
Copernicus and Galileo believed that Earth spins on its axis and revolves around the
Sun as one of the planets, both contradicting the idea that Earth is motionless at the
center of the solar system. In addition, Galileo thought that the best way to understand
nature is through experiments, rather than just pure thought, as the ancient Greeks did.
Galileo also had a telescope with which to examine the heavens, which the ancient
Greeks did not have.
5. What were four of Galileo’s discoveries that were important to astronomy?
Answer
His observation of the phases of Venus, which supported the heliocentric model; his
observations of Jupiter’s moons, which showed not everything orbits Earth; his
observations of features on the surface of the Moon, which showed it has similarities to
Earth; and his discovery that the Milky Way is simply a mass of unresolved stars.
6. Explain the origin of the magnitude designation for determining the brightness of
stars. Why does it seem to go backward, with smaller numbers indicating brighter stars?
,OpenStax Astronomy 2e Instructor Answer Guide
Answer
The system originated with Hipparchus, who ranked the brightest stars as being “first
magnitude,” fainter stars being of the “second magnitude,” then “third magnitude,” and
so on as the stars grew progressively fainter.
7. Ursa Minor contains the pole star, Polaris, and the asterism known as the Little
Dipper. From most locations in the Northern Hemisphere, all of the stars in Ursa Minor
are circumpolar. Does that mean these stars are also above the horizon during the day?
Explain.
Answer
Yes, they are always above the horizon; but during the day, the sunlight makes them
invisible to us.
8. How many degrees does the Sun move per day relative to the fixed stars? How many
days does it take for the Sun to return to its original location relative to the fixed stars?
Answer
The Sun moves about 1° per day. It takes about 360 days (actually 365.25 days) to
return to its original location.
9. How many degrees does the Moon move per day relative to the fixed stars? How
many days does it take for the Moon to return to its original location relative to the fixed
stars?
Answer
The Moon moves about 12° per day. It takes the Moon about 30 days to return to its
original position relative to the fixed stars (actually 27.3 days).
10. Explain how the zodiacal constellations are different from the other constellations.
Answer
These constellations intersect with the ecliptic, the Sun’s apparent annual path in the
sky. So from Earth, the Sun appears to move through the zodiacal constellations, but
not the others.
11. The Sun was once thought to be a planet. Explain why.
Answer
In the geocentric system, all of the objects that moved in the sky relative to the fixed
stars were considered to be “wanderers,” and the Sun was no exception, so it was
classified as a planet.
12. Is the ecliptic the same thing as the celestial equator? Explain.
Answer
The celestial equator is the projection of Earth’s equator onto the sky whereas the
ecliptic is the Sun’s apparent annual path in the sky. These two circles are separated by
an angle of 23.5° (see Figure 2.7 The Celestial Tilt).
13. What is an asterism? Can you name an example?
Answer
An asterism is a small, easily recognizable group of stars within a larger constellation.
Examples include the Little Dipper inside Ursa Minor and the Big Dipper inside Ursa
Major.
14. Why did Pythagoras believe that Earth should be spherical?
Answer
He believed circles and spheres were perfect forms and that Earth should, naturally,
take one of these shapes.
,OpenStax Astronomy 2e Instructor Answer Guide
15. How did Aristotle deduce that the Sun is farther away from Earth than the Moon?
Answer
He noticed during solar eclipses that the Moon passes in front of the Sun, and the
opposite case never happens.
16. What are two ways in which Aristotle deduced that Earth is spherical?
Answer
He noticed that the shadow Earth casts on the Moon during a lunar eclipse is always
circular, which is only possible if a spherical body casts the shadow. He also noted that
as travelers go farther south, fewer stars are circumpolar and more stars are visible to
them overall.
17. How did Hipparchus discover the wobble of Earth’s axis, known as precession?
Answer
He compared his careful observations of the stars with those of earlier observers and
noticed that the positions of the fixed stars had changed slightly and systematically over
the course of about 150 years, consistent with the direction of the celestial pole
changing relative to the stars.
18. Why did Ptolemy have to introduce multiple circles of motion for the planets instead
of a single, simple circle to represent the planet’s motion around the Earth?
Answer
He had to account for the observed occasional retrograde motion of the planets.
19. Why did Copernicus want to develop a completely new system for predicting
planetary positions? Provide two reasons.
Answer
He wanted to improve upon the predictions of planetary positions because the
geocentric model often gave inaccurate results. He also thought his system was simpler
and more elegant—that the existing system was needlessly and implausibly
complicated.
20. What two factors made it difficult, at first, for astronomers to choose between the
Copernican heliocentric model and the Ptolemaic geocentric model?
Answer
Both gave inaccurate predictions of planetary positions and motions from complicated
models. In those days, little weight was given to observational experimental methods of
validating one model or the other.
21. What phases would Venus show if the geocentric model were correct?
Answer
Venus would only show crescent phases because the illuminated side would only ever
partially be visible from Earth.
Thought Questions
22. Describe a practical way to determine in which constellation the Sun is found at any
time of the year.
Answer
Use a star chart to determine which zodiacal constellation rises at sunset (or, if it is
easier, which zodiacal constellation crosses the meridian near midnight). Then, the
constellation on the opposite side of the sky (with dates 6 months different from the
constellation you observed) is likely the constellation in which the Sun will be found.
,OpenStax Astronomy 2e Instructor Answer Guide
23. What is a constellation as astronomers define it today? What does it mean when an
astronomer says, “I saw a comet in Orion last night?”
Answer
A constellation is a well-defined area of the sky with borders, much like states have
borders on a map of the United States. Seeing a comet in Orion means the comet was
seen in the sky within the defined borders of the constellation Orion.
24. Draw a picture that explains why Venus goes through phases the way the Moon
does, according to the heliocentric cosmology. Does Jupiter also go through phases as
seen from Earth? Why?
Answer
Refer to Figure 2.18 Phases of Venus for the picture of Venus going through its phases.
Jupiter, which is farther from the Sun than Earth is, does not experience phases
because it is always fully illuminated as seen from Earth.
25. Show with a simple diagram how the lower parts of a ship disappear first as it sails
away from you on a spherical Earth. Use the same diagram to show why lookouts on
old sailing ships could see farther from the masthead than from the deck. Would there
be any advantage to posting lookouts on the mast if Earth were flat? (Note that these
nautical arguments for a spherical Earth were quite familiar to Columbus and other
mariners of his time.)
Answer
For the observer at the flag, the horizontal dashed line indicates the horizon. Two ships
are shown at different distances. The closer ship still has a part of the hull visible
whereas the farther ship only has the crow’s nest visible. Someone in the crow’s nest
can see much farther around the curvature of Earth. For the farther ship, the flag is
visible from the crow’s nest, but not from the main deck. If Earth were flat, elevation
would not matter in terms of what is visible from the ship, so there would be no
advantage to posting a lookout on the mast of the ship. Note that the size of the ship is
greatly exaggerated in this drawing.
26. Parallaxes of stars were not observed by ancient astronomers. How can this fact be
reconciled with the heliocentric hypothesis?
Answer
The parallax is the shift of an object in the sky when seen from two separated vantage
points. It depends inversely on the distance to the object. Stars are so far away,
compared to the size of Earth’s orbit, that their parallax angle could not be measured to
the necessary precision attainable at the time.
27. Why do you think so many people still believe in astrology and spend money on it?
What psychological needs does such a belief system satisfy?
Answer
,OpenStax Astronomy 2e Instructor Answer Guide
Student answers will vary. One concept is that people are comforted by the idea of a
higher power controlling some aspects of their lives or fate so they don’t have to take
full responsibility. Also, such a “cosmic” system can give meaning to everyday triumphs
and challenges; it can explain events in life that people find confusing, unfair, or difficult.
28. Consider three cosmological perspectives—the geocentric perspective, the
heliocentric perspective, and the modern perspective—in which the Sun is a minor star
on the outskirts of one galaxy among billions. Discuss some of the cultural and
philosophical implications of each point of view.
Answer
The geocentric perspective implies that humanity holds some kind of special or
privileged place in the cosmos—that the universe is centered on us somehow. In the
heliocentric perspective, our system of planets is still the center of things, with the Sun
the center of that and not Earth. Earth thus becomes only one planet among the others.
Our modern understanding shows that our solar system, our planet, and all of us do not
exist in a particularly special or privileged location and, further, there really is no such
location.
29. The north celestial pole appears at an altitude above the horizon that is equal to the
observer’s latitude. Identify Polaris, the North Star, which lies very close to the north
celestial pole. Measure its altitude. (This can be done with a protractor. Alternatively,
your fist, extended at arm’s length, spans a distance approximately equal to 10°.)
Compare this estimate with your latitude. (Note that this experiment cannot be
performed easily in the Southern Hemisphere because Polaris itself is not visible in the
south and no bright star is located near the south celestial pole.)
Answer
Student answers will vary based on their actual latitude, but they should be able to show
their measurement and determine how close that measurement is to the actual figure.
30. What were two arguments or lines of evidence in support of the geocentric model?
Answer
We do not feel any motion. There is no wind or vibration indicating that Earth is moving.
Also, because we do not see stellar parallax, the simplest explanation is that there is no
movement of Earth around the Sun.
31. Although the Copernican system was largely correct to place the Sun at the center
of all planetary motion, the model still gave inaccurate predictions for planetary
positions. Explain the flaw in the Copernican model that hindered its accuracy.
Answer
Copernicus assumed all motion must be uniform circular motion. Because planets orbit
the Sun in elliptical paths with varying speeds, there is no way to reproduce that motion
faithfully with the planets in circular motion at constant speed around the Sun.
32. During a retrograde loop of Mars, would you expect Mars to be brighter than usual
in the sky, about average in brightness, or fainter than usual in the sky? Explain.
Answer
Retrograde motion is seen due to the faster-moving Earth passing Mars in orbit, so the
two planets must be next to each other (closer to each other than usual). Thus, Mars
should appear brighter than usual.
33. The Great Pyramid of Giza was constructed nearly 5000 years ago. Within the
pyramid, archaeologists discovered a shaft leading from the central chamber out of the
,OpenStax Astronomy 2e Instructor Answer Guide
pyramid, oriented for favorable viewing of the bright star Thuban. Thinking about Earth’s
precession, explain why Thuban might have been an important star to the ancient
Egyptians.
Answer
Five thousand years ago, Thuban occupied a position in the sky very close to the north
celestial pole, so for the ancient Egyptians, it served a purpose similar to the one Polaris
serves for us.
34. Explain why more stars are circumpolar for observers at higher latitudes.
Answer
Circumpolar stars tend to be higher declination stars that move in very small circles in
the sky centered on the celestial poles. At higher latitudes, when the celestial pole is
higher in the sky, these small circular paths are more likely to be completely above the
horizon. As latitude increases and the altitude of the pole above the horizon increases,
so does the size of the circular motion for stars that will remain above the horizon, and
so more stars are circumpolar from higher latitudes.
35. What is the altitude of the north celestial pole in the sky from your latitude? If you do
not know your latitude, look it up. If you are in the Southern Hemisphere, answer this
question for the south celestial pole, since the north celestial pole is not visible from
your location.
Answer
Student answers will vary; however, the altitude of the north or south celestial pole
should be equal to students’ latitude.
36. If you were to drive to some city south of your current location, how would the
altitude of the celestial pole in the sky change?
Answer
If you are in the Northern Hemisphere, the north celestial pole should be lower in
altitude. In the Southern Hemisphere, the south celestial pole should be higher in
altitude.
37. Hipparchus could have warned us that the dates associated with each of the natal
astrology sun signs would eventually be wrong. Explain why.
Answer
The precession of Earth changes the dates for which the Sun crosses through each of
the zodiacal constellations over the course of 26,000 years.
38. Explain three lines of evidence that argue against the validity of astrology.
Answer
There are no known forces that could explain why the positions of planets should affect
a person’s personality or fate. The dates that supposedly correspond to a person’s natal
astrology sun sign have shifted significantly since the first astrological charts, and no
corrections or adjustments have been made to the predictive methods, implying that
they are not logical or true. Statistical tests of astrology, such as seeing whether people
in certain occupations were
born in just one or two sun signs, show that people are distributed randomly in their
astrological characteristics.
39. What did Galileo discover about the planet Jupiter that cast doubt on exclusive
geocentrism?
Answer
,OpenStax Astronomy 2e Instructor Answer Guide
He discovered four visible moons orbiting Jupiter, meaning that Earth clearly is not the
central focus of all motion in the universe. He showed the moons can orbit Jupiter while
Jupiter moves around the Sun, so it is possible that our Moon can orbit Earth as Earth
revolves around the Sun.
40. What did Galileo discover about Venus that cast doubt on geocentrism?
Answer
He discovered that Venus shows a full range of phases, from new to crescent to
gibbous, and these phases are only possible if Venus orbits so that sometimes it is on
the near side of the Sun with respect to us and sometimes on the far side of the Sun
(where he presumed it went to full phase, although he could not see it). Thus, Venus
must orbit the Sun and not Earth.
Figuring for Yourself
41. Suppose Eratosthenes had found that, in Alexandria, at noon on the first day of
summer, the line to the Sun makes an angle 30° with the vertical. What, then, would he
have found for Earth’s circumference?
Answer
Because 30° is 1/12 of 360°, he would have found that Earth’s circumference was 12
times the distance between the two cities.
42. Suppose Eratosthenes’ results for Earth’s circumference were quite accurate. If the
diameter of Earth is 12,740 km, what is the length of his stadium in kilometers?
Answer
Because his answer was 250,000 stadia and the circumference of Earth is 3.14 ×
12,740 = 40,000 km, we divide to find
43. Suppose you are on a strange planet and observe, at night, that the stars do not rise
and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000
miles, and at your new location on the planet, you find that all stars rise straight up in
the east and set straight down in the west, perpendicular to the horizon. How could you
determine the circumference of the planet without any further observations? What is the
circumference, in miles, of the planet?
Answer
You could deduce that you have walked 1/4 of the way around the planet, from the pole
to the equator, so you could multiply 4 by the distance you traveled to determine the
circumference: 4 × 8000 miles = 32,000 miles.
This file is copyright 2022, Rice University. All Rights Reserved.
, OpenStax Astronomy 2e Instructor Answer Guide
Chapter 3: Orbits and Gravity
Review Questions
1. State Kepler’s three laws in your own words.
Answer
Kepler’s first law says that all planetary orbits are ellipses with the Sun at one focus. Kepler’s
second law says that planets sweep out equal areas of their orbits in equal amounts of time.
Kepler’s third law says that the square of the average distance a planet is from the Sun is
proportional to the period of its orbit cubed.
2. Why did Kepler need Tycho Brahe’s data to formulate his laws?
Answer
In science, laws of nature are often developed by carefully analyzing data collected from
observations of various phenomena. In this case, Kepler used Brahe’s data regarding the
observed positions of the planet Mars in order to determine that Mars moved in an elliptical, not
circular, orbit.
3. Which has more mass: an armful of feathers or an armful of lead? Which has more volume: a
kilogram of feathers or a kilogram of lead? Which has higher density: a kilogram of feathers or a
kilogram of lead?
An armful of lead would have more mass. A kilogram of feathers would have a greater volume.
A kilogram of lead would have a higher density.
4. Explain how Kepler was able to find a relationship (his third law) between the orbital periods
and distances of the planets that did not depend on the masses of the planets or the Sun.
Answer
Since all the planets orbit the Sun, the Sun’s mass is the same for all the planets in Kepler’s third
law. The individual masses for each of the planets, M2, are so small (even Jupiter’s) compared to
the Sun that they are insignificant in calculating and can be treated as if
they were zero and not significantly change the answer.
5. Write out Newton’s three laws of motion in terms of what happens with the momentum of
objects.
Answer
Newton’s first law says that the momentum of an object remains constant in both magnitude and
direction unless acted upon by a force. Newton’s second law says that the rate of change of the
momentum of an object is equal to the force that produced that change. Newton’s third law says
that momentum is conserved when two or more objects interact with each other.
6. Which major planet has the largest . . .
A. semimajor axis?
B. average orbital speed around the Sun?
C. orbital period around the Sun?
D. eccentricity?
Answer
A. Neptune; B. Mercury; C. Neptune; D. Mercury. (This question asked only about planets, not
dwarf planets, just in case Pluto or Eris fans are objecting.)
7. Why do we say that Neptune was the first planet to be discovered through the use of
mathematics?
Answer
Careful observations of Uranus showed that the planet was not exactly where Newton’s laws
predicted it to be in the night sky from day to day. Using mathematics, Kepler’s laws, and
,OpenStax Astronomy 2e Instructor Answer Guide
Chapter 1: Science and the Universe
No assessments for this chapter.
This file is copyright 2022, Rice University. All Rights Reserved.
,OpenStax Astronomy 2e Instructor Answer Guide
Chapter 2: Observing the Sky: The Birth of Astronomy
Review Questions
1. From where on Earth could you observe all of the stars during the course of the year?
What fraction of the sky can be seen from the North Pole?
Answer
You can observe all of the stars from the equator over the course of a year, although
high-declination stars will be difficult to see so close to the horizon. Only half the sky
can be seen from the North Pole, and that half does not change throughout the year.
2. Give four ways to demonstrate that Earth is spherical.
Answer
The shadow cast on the Moon is always round in shape. Ships sailing away on the
ocean appear to sink into the ocean due to the curvature of Earth’s surface, rather than
simply getting smaller and smaller. Orbiting satellites taking photographs of Earth show
that Earth looks round from every direction. The Sun is at different altitudes in the sky
for different longitudes (it would be in the same place for everyone if Earth were flat, for
example), and the Sun’s position in the sky depends upon the time.
3. Explain, according to both geocentric and heliocentric cosmologies, why we see
retrograde motion of the planets.
Answer
In the geocentric model, Mars orbits outside of the Sun on its deferent path, but it also
moves in a circular motion on its epicycle as it follows the deferent. If the planet moves
faster “backward” on the epicycle than it moves forward on the deferent, then it can
appear to move in a retrograde manner while still retaining the overall pattern of
prograde motion in the sky. In the heliocentric model, Mars moves somewhat slower
than Earth. During periods of time when Earth passes Mars, Mars appears to move
backward on the sky relative to the background stars. This is confirmed by the fact that
Mars appears at its brightest during this motion (due to it being at its closest approach
to Earth) and is also on the opposite side of the sky from the Sun during retrograde
motion.
4. In what ways did the work of Copernicus and Galileo differ from the views of the
ancient Greeks and of their contemporaries?
Answer
Copernicus and Galileo believed that Earth spins on its axis and revolves around the
Sun as one of the planets, both contradicting the idea that Earth is motionless at the
center of the solar system. In addition, Galileo thought that the best way to understand
nature is through experiments, rather than just pure thought, as the ancient Greeks did.
Galileo also had a telescope with which to examine the heavens, which the ancient
Greeks did not have.
5. What were four of Galileo’s discoveries that were important to astronomy?
Answer
His observation of the phases of Venus, which supported the heliocentric model; his
observations of Jupiter’s moons, which showed not everything orbits Earth; his
observations of features on the surface of the Moon, which showed it has similarities to
Earth; and his discovery that the Milky Way is simply a mass of unresolved stars.
6. Explain the origin of the magnitude designation for determining the brightness of
stars. Why does it seem to go backward, with smaller numbers indicating brighter stars?
,OpenStax Astronomy 2e Instructor Answer Guide
Answer
The system originated with Hipparchus, who ranked the brightest stars as being “first
magnitude,” fainter stars being of the “second magnitude,” then “third magnitude,” and
so on as the stars grew progressively fainter.
7. Ursa Minor contains the pole star, Polaris, and the asterism known as the Little
Dipper. From most locations in the Northern Hemisphere, all of the stars in Ursa Minor
are circumpolar. Does that mean these stars are also above the horizon during the day?
Explain.
Answer
Yes, they are always above the horizon; but during the day, the sunlight makes them
invisible to us.
8. How many degrees does the Sun move per day relative to the fixed stars? How many
days does it take for the Sun to return to its original location relative to the fixed stars?
Answer
The Sun moves about 1° per day. It takes about 360 days (actually 365.25 days) to
return to its original location.
9. How many degrees does the Moon move per day relative to the fixed stars? How
many days does it take for the Moon to return to its original location relative to the fixed
stars?
Answer
The Moon moves about 12° per day. It takes the Moon about 30 days to return to its
original position relative to the fixed stars (actually 27.3 days).
10. Explain how the zodiacal constellations are different from the other constellations.
Answer
These constellations intersect with the ecliptic, the Sun’s apparent annual path in the
sky. So from Earth, the Sun appears to move through the zodiacal constellations, but
not the others.
11. The Sun was once thought to be a planet. Explain why.
Answer
In the geocentric system, all of the objects that moved in the sky relative to the fixed
stars were considered to be “wanderers,” and the Sun was no exception, so it was
classified as a planet.
12. Is the ecliptic the same thing as the celestial equator? Explain.
Answer
The celestial equator is the projection of Earth’s equator onto the sky whereas the
ecliptic is the Sun’s apparent annual path in the sky. These two circles are separated by
an angle of 23.5° (see Figure 2.7 The Celestial Tilt).
13. What is an asterism? Can you name an example?
Answer
An asterism is a small, easily recognizable group of stars within a larger constellation.
Examples include the Little Dipper inside Ursa Minor and the Big Dipper inside Ursa
Major.
14. Why did Pythagoras believe that Earth should be spherical?
Answer
He believed circles and spheres were perfect forms and that Earth should, naturally,
take one of these shapes.
,OpenStax Astronomy 2e Instructor Answer Guide
15. How did Aristotle deduce that the Sun is farther away from Earth than the Moon?
Answer
He noticed during solar eclipses that the Moon passes in front of the Sun, and the
opposite case never happens.
16. What are two ways in which Aristotle deduced that Earth is spherical?
Answer
He noticed that the shadow Earth casts on the Moon during a lunar eclipse is always
circular, which is only possible if a spherical body casts the shadow. He also noted that
as travelers go farther south, fewer stars are circumpolar and more stars are visible to
them overall.
17. How did Hipparchus discover the wobble of Earth’s axis, known as precession?
Answer
He compared his careful observations of the stars with those of earlier observers and
noticed that the positions of the fixed stars had changed slightly and systematically over
the course of about 150 years, consistent with the direction of the celestial pole
changing relative to the stars.
18. Why did Ptolemy have to introduce multiple circles of motion for the planets instead
of a single, simple circle to represent the planet’s motion around the Earth?
Answer
He had to account for the observed occasional retrograde motion of the planets.
19. Why did Copernicus want to develop a completely new system for predicting
planetary positions? Provide two reasons.
Answer
He wanted to improve upon the predictions of planetary positions because the
geocentric model often gave inaccurate results. He also thought his system was simpler
and more elegant—that the existing system was needlessly and implausibly
complicated.
20. What two factors made it difficult, at first, for astronomers to choose between the
Copernican heliocentric model and the Ptolemaic geocentric model?
Answer
Both gave inaccurate predictions of planetary positions and motions from complicated
models. In those days, little weight was given to observational experimental methods of
validating one model or the other.
21. What phases would Venus show if the geocentric model were correct?
Answer
Venus would only show crescent phases because the illuminated side would only ever
partially be visible from Earth.
Thought Questions
22. Describe a practical way to determine in which constellation the Sun is found at any
time of the year.
Answer
Use a star chart to determine which zodiacal constellation rises at sunset (or, if it is
easier, which zodiacal constellation crosses the meridian near midnight). Then, the
constellation on the opposite side of the sky (with dates 6 months different from the
constellation you observed) is likely the constellation in which the Sun will be found.
,OpenStax Astronomy 2e Instructor Answer Guide
23. What is a constellation as astronomers define it today? What does it mean when an
astronomer says, “I saw a comet in Orion last night?”
Answer
A constellation is a well-defined area of the sky with borders, much like states have
borders on a map of the United States. Seeing a comet in Orion means the comet was
seen in the sky within the defined borders of the constellation Orion.
24. Draw a picture that explains why Venus goes through phases the way the Moon
does, according to the heliocentric cosmology. Does Jupiter also go through phases as
seen from Earth? Why?
Answer
Refer to Figure 2.18 Phases of Venus for the picture of Venus going through its phases.
Jupiter, which is farther from the Sun than Earth is, does not experience phases
because it is always fully illuminated as seen from Earth.
25. Show with a simple diagram how the lower parts of a ship disappear first as it sails
away from you on a spherical Earth. Use the same diagram to show why lookouts on
old sailing ships could see farther from the masthead than from the deck. Would there
be any advantage to posting lookouts on the mast if Earth were flat? (Note that these
nautical arguments for a spherical Earth were quite familiar to Columbus and other
mariners of his time.)
Answer
For the observer at the flag, the horizontal dashed line indicates the horizon. Two ships
are shown at different distances. The closer ship still has a part of the hull visible
whereas the farther ship only has the crow’s nest visible. Someone in the crow’s nest
can see much farther around the curvature of Earth. For the farther ship, the flag is
visible from the crow’s nest, but not from the main deck. If Earth were flat, elevation
would not matter in terms of what is visible from the ship, so there would be no
advantage to posting a lookout on the mast of the ship. Note that the size of the ship is
greatly exaggerated in this drawing.
26. Parallaxes of stars were not observed by ancient astronomers. How can this fact be
reconciled with the heliocentric hypothesis?
Answer
The parallax is the shift of an object in the sky when seen from two separated vantage
points. It depends inversely on the distance to the object. Stars are so far away,
compared to the size of Earth’s orbit, that their parallax angle could not be measured to
the necessary precision attainable at the time.
27. Why do you think so many people still believe in astrology and spend money on it?
What psychological needs does such a belief system satisfy?
Answer
,OpenStax Astronomy 2e Instructor Answer Guide
Student answers will vary. One concept is that people are comforted by the idea of a
higher power controlling some aspects of their lives or fate so they don’t have to take
full responsibility. Also, such a “cosmic” system can give meaning to everyday triumphs
and challenges; it can explain events in life that people find confusing, unfair, or difficult.
28. Consider three cosmological perspectives—the geocentric perspective, the
heliocentric perspective, and the modern perspective—in which the Sun is a minor star
on the outskirts of one galaxy among billions. Discuss some of the cultural and
philosophical implications of each point of view.
Answer
The geocentric perspective implies that humanity holds some kind of special or
privileged place in the cosmos—that the universe is centered on us somehow. In the
heliocentric perspective, our system of planets is still the center of things, with the Sun
the center of that and not Earth. Earth thus becomes only one planet among the others.
Our modern understanding shows that our solar system, our planet, and all of us do not
exist in a particularly special or privileged location and, further, there really is no such
location.
29. The north celestial pole appears at an altitude above the horizon that is equal to the
observer’s latitude. Identify Polaris, the North Star, which lies very close to the north
celestial pole. Measure its altitude. (This can be done with a protractor. Alternatively,
your fist, extended at arm’s length, spans a distance approximately equal to 10°.)
Compare this estimate with your latitude. (Note that this experiment cannot be
performed easily in the Southern Hemisphere because Polaris itself is not visible in the
south and no bright star is located near the south celestial pole.)
Answer
Student answers will vary based on their actual latitude, but they should be able to show
their measurement and determine how close that measurement is to the actual figure.
30. What were two arguments or lines of evidence in support of the geocentric model?
Answer
We do not feel any motion. There is no wind or vibration indicating that Earth is moving.
Also, because we do not see stellar parallax, the simplest explanation is that there is no
movement of Earth around the Sun.
31. Although the Copernican system was largely correct to place the Sun at the center
of all planetary motion, the model still gave inaccurate predictions for planetary
positions. Explain the flaw in the Copernican model that hindered its accuracy.
Answer
Copernicus assumed all motion must be uniform circular motion. Because planets orbit
the Sun in elliptical paths with varying speeds, there is no way to reproduce that motion
faithfully with the planets in circular motion at constant speed around the Sun.
32. During a retrograde loop of Mars, would you expect Mars to be brighter than usual
in the sky, about average in brightness, or fainter than usual in the sky? Explain.
Answer
Retrograde motion is seen due to the faster-moving Earth passing Mars in orbit, so the
two planets must be next to each other (closer to each other than usual). Thus, Mars
should appear brighter than usual.
33. The Great Pyramid of Giza was constructed nearly 5000 years ago. Within the
pyramid, archaeologists discovered a shaft leading from the central chamber out of the
,OpenStax Astronomy 2e Instructor Answer Guide
pyramid, oriented for favorable viewing of the bright star Thuban. Thinking about Earth’s
precession, explain why Thuban might have been an important star to the ancient
Egyptians.
Answer
Five thousand years ago, Thuban occupied a position in the sky very close to the north
celestial pole, so for the ancient Egyptians, it served a purpose similar to the one Polaris
serves for us.
34. Explain why more stars are circumpolar for observers at higher latitudes.
Answer
Circumpolar stars tend to be higher declination stars that move in very small circles in
the sky centered on the celestial poles. At higher latitudes, when the celestial pole is
higher in the sky, these small circular paths are more likely to be completely above the
horizon. As latitude increases and the altitude of the pole above the horizon increases,
so does the size of the circular motion for stars that will remain above the horizon, and
so more stars are circumpolar from higher latitudes.
35. What is the altitude of the north celestial pole in the sky from your latitude? If you do
not know your latitude, look it up. If you are in the Southern Hemisphere, answer this
question for the south celestial pole, since the north celestial pole is not visible from
your location.
Answer
Student answers will vary; however, the altitude of the north or south celestial pole
should be equal to students’ latitude.
36. If you were to drive to some city south of your current location, how would the
altitude of the celestial pole in the sky change?
Answer
If you are in the Northern Hemisphere, the north celestial pole should be lower in
altitude. In the Southern Hemisphere, the south celestial pole should be higher in
altitude.
37. Hipparchus could have warned us that the dates associated with each of the natal
astrology sun signs would eventually be wrong. Explain why.
Answer
The precession of Earth changes the dates for which the Sun crosses through each of
the zodiacal constellations over the course of 26,000 years.
38. Explain three lines of evidence that argue against the validity of astrology.
Answer
There are no known forces that could explain why the positions of planets should affect
a person’s personality or fate. The dates that supposedly correspond to a person’s natal
astrology sun sign have shifted significantly since the first astrological charts, and no
corrections or adjustments have been made to the predictive methods, implying that
they are not logical or true. Statistical tests of astrology, such as seeing whether people
in certain occupations were
born in just one or two sun signs, show that people are distributed randomly in their
astrological characteristics.
39. What did Galileo discover about the planet Jupiter that cast doubt on exclusive
geocentrism?
Answer
,OpenStax Astronomy 2e Instructor Answer Guide
He discovered four visible moons orbiting Jupiter, meaning that Earth clearly is not the
central focus of all motion in the universe. He showed the moons can orbit Jupiter while
Jupiter moves around the Sun, so it is possible that our Moon can orbit Earth as Earth
revolves around the Sun.
40. What did Galileo discover about Venus that cast doubt on geocentrism?
Answer
He discovered that Venus shows a full range of phases, from new to crescent to
gibbous, and these phases are only possible if Venus orbits so that sometimes it is on
the near side of the Sun with respect to us and sometimes on the far side of the Sun
(where he presumed it went to full phase, although he could not see it). Thus, Venus
must orbit the Sun and not Earth.
Figuring for Yourself
41. Suppose Eratosthenes had found that, in Alexandria, at noon on the first day of
summer, the line to the Sun makes an angle 30° with the vertical. What, then, would he
have found for Earth’s circumference?
Answer
Because 30° is 1/12 of 360°, he would have found that Earth’s circumference was 12
times the distance between the two cities.
42. Suppose Eratosthenes’ results for Earth’s circumference were quite accurate. If the
diameter of Earth is 12,740 km, what is the length of his stadium in kilometers?
Answer
Because his answer was 250,000 stadia and the circumference of Earth is 3.14 ×
12,740 = 40,000 km, we divide to find
43. Suppose you are on a strange planet and observe, at night, that the stars do not rise
and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000
miles, and at your new location on the planet, you find that all stars rise straight up in
the east and set straight down in the west, perpendicular to the horizon. How could you
determine the circumference of the planet without any further observations? What is the
circumference, in miles, of the planet?
Answer
You could deduce that you have walked 1/4 of the way around the planet, from the pole
to the equator, so you could multiply 4 by the distance you traveled to determine the
circumference: 4 × 8000 miles = 32,000 miles.
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, OpenStax Astronomy 2e Instructor Answer Guide
Chapter 3: Orbits and Gravity
Review Questions
1. State Kepler’s three laws in your own words.
Answer
Kepler’s first law says that all planetary orbits are ellipses with the Sun at one focus. Kepler’s
second law says that planets sweep out equal areas of their orbits in equal amounts of time.
Kepler’s third law says that the square of the average distance a planet is from the Sun is
proportional to the period of its orbit cubed.
2. Why did Kepler need Tycho Brahe’s data to formulate his laws?
Answer
In science, laws of nature are often developed by carefully analyzing data collected from
observations of various phenomena. In this case, Kepler used Brahe’s data regarding the
observed positions of the planet Mars in order to determine that Mars moved in an elliptical, not
circular, orbit.
3. Which has more mass: an armful of feathers or an armful of lead? Which has more volume: a
kilogram of feathers or a kilogram of lead? Which has higher density: a kilogram of feathers or a
kilogram of lead?
An armful of lead would have more mass. A kilogram of feathers would have a greater volume.
A kilogram of lead would have a higher density.
4. Explain how Kepler was able to find a relationship (his third law) between the orbital periods
and distances of the planets that did not depend on the masses of the planets or the Sun.
Answer
Since all the planets orbit the Sun, the Sun’s mass is the same for all the planets in Kepler’s third
law. The individual masses for each of the planets, M2, are so small (even Jupiter’s) compared to
the Sun that they are insignificant in calculating and can be treated as if
they were zero and not significantly change the answer.
5. Write out Newton’s three laws of motion in terms of what happens with the momentum of
objects.
Answer
Newton’s first law says that the momentum of an object remains constant in both magnitude and
direction unless acted upon by a force. Newton’s second law says that the rate of change of the
momentum of an object is equal to the force that produced that change. Newton’s third law says
that momentum is conserved when two or more objects interact with each other.
6. Which major planet has the largest . . .
A. semimajor axis?
B. average orbital speed around the Sun?
C. orbital period around the Sun?
D. eccentricity?
Answer
A. Neptune; B. Mercury; C. Neptune; D. Mercury. (This question asked only about planets, not
dwarf planets, just in case Pluto or Eris fans are objecting.)
7. Why do we say that Neptune was the first planet to be discovered through the use of
mathematics?
Answer
Careful observations of Uranus showed that the planet was not exactly where Newton’s laws
predicted it to be in the night sky from day to day. Using mathematics, Kepler’s laws, and
