OpenStax Astronomy 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?
Answer
,OpenStax Astronomy Instructor Answer Guide
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.
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
,OpenStax Astronomy Instructor Answer Guide
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.
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?
, OpenStax Astronomy Instructor Answer Guide
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
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
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?
Answer
,OpenStax Astronomy Instructor Answer Guide
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.
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
,OpenStax Astronomy Instructor Answer Guide
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.
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?
, OpenStax Astronomy Instructor Answer Guide
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
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
