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G. As mentioned in the Gravity and Time Machines feature box in this chapter, the film Interstellar has a lot
of black hole science in its plot and scenery. That’s because astrophysicist Kip Thorne at Caltech had a big
hand in writing the initial treatment for the movie, and later producing it. Get your group members
together (be sure you have popcorn) for a viewing of the movie and then try to use your knowledge of
black holes from this chapter to explain the plot. (Note that the film also uses the concept of a wormhole,
which we don’t discuss in this chapter. A wormhole is a theoretically possible way to use a large, spinning
black hole to find a way to travel from one place in the universe to another without having to go through
regular spacetime to get there.)
Exercises
Review Questions
1. How does the equivalence principle lead us to suspect that spacetime might be curved?
2. If general relativity offers the best description of what happens in the presence of gravity, why do physicists
still make use of Newton’s equations in describing gravitational forces on Earth (when building a bridge, for
example)?
3. Einstein’s general theory of relativity made or allowed us to make predictions about the outcome of several
experiments that had not yet been carried out at the time the theory was first published. Describe three
experiments that verified the predictions of the theory after Einstein proposed it.
4. If a black hole itself emits no radiation, what evidence do astronomers and physicists today have that the
theory of black holes is correct?
5. What characteristics must a binary star have to be a good candidate for a black hole? Why is each of these
characteristics important?
6. A student becomes so excited by the whole idea of black holes that he decides to jump into one. It has a
mass 10 times the mass of our Sun. What is the trip like for him? What is it like for the rest of the class,
watching from afar?
7. What is an event horizon? Does our Sun have an event horizon around it?
8. What is a gravitational wave and why was it so hard to detect?
9. What are some strong sources of gravitational waves that astronomers hope to detect in the future?
10. Suppose the amount of mass in a black hole doubles. Does the event horizon change? If so, how does it
change?
Thought Questions
11. Imagine that you have built a large room around the people in Figure 24.4 and that this room is falling at
exactly the same rate as they are. Galileo showed that if there is no air friction, light and heavy objects that
are dropping due to gravity will fall at the same rate. Suppose that this were not true and that instead
heavy objects fall faster. Also suppose that the man in Figure 24.4 is twice as massive as the woman. What
would happen? Would this violate the equivalence principle?
12. A monkey hanging from a tree branch sees a hunter aiming a rifle directly at him. The monkey then sees a
flash and knows that the rifle has been fired. Reacting quickly, the monkey lets go of the branch and drops
so that the bullet can pass harmlessly over his head. Does this act save the monkey’s life? Why or why
not? (Hint: Consider the similarities between this situation and that of Exercise 24.11.)
13. Why would we not expect to detect X-rays from a disk of matter about an ordinary star?
24 • Exercises 833
14. Look elsewhere in this book for necessary data, and indicate what the final stage of evolution—white
dwarf, neutron star, or black hole—will be for each of these kinds of stars.
A. Spectral type-O main-sequence star
B. Spectral type-B main-sequence star
C. Spectral type-A main-sequence star
D. Spectral type-G main-sequence star
E. Spectral type-M main-sequence star
15. Which is likely to be more common in our Galaxy: white dwarfs or black holes? Why?
16. If the Sun could suddenly collapse to a black hole, how would the period of Earth’s revolution about it
differ from what it is now?
17. Suppose the people in Figure 24.4 are in an elevator moving upward with an acceleration equal to g, but in
the opposite direction. The woman throws the ball to the man with a horizontal force. What happens to
the ball?
18. You arrange to meet a friend at 5:00 p.m. on Valentine’s Day on the observation deck of the Empire State
Building in New York City. You arrive right on time, but your friend is not there. She arrives 5 minutes late
and says the reason is that time runs faster at the top of a tall building, so she is on time but you were
early. Is your friend right? Does time run slower or faster at the top of a building, as compared with its
base? Is this a reasonable excuse for your friend arriving 5 minutes late?
19. You are standing on a scale in an elevator when the cable snaps, sending the elevator car into free fall.
Before the automatic brakes stop your fall, you glance at the scale reading. Does the scale show your real
weight? An apparent weight? Something else?
Figuring for Yourself
20. Look up G, c, and the mass of the Sun in Appendix E and calculate the radius of a black hole that has the
same mass as the Sun. (Note that this is only a theoretical calculation. The Sun does not have enough
mass to become a black hole.)
21. Suppose you wanted to know the size of black holes with masses that are larger or smaller than the Sun.
You could go through all the steps in Exercise 24.20, wrestling with a lot of large numbers with large
exponents. You could be clever, however, and evaluate all the constants in the equation once and then
simply vary the mass. You could even express the mass in terms of the Sun’s mass and make future
calculations really easy. Show that the event horizon equation is equivalent to saying that the radius of the
event horizon is equal to 3 km times the mass of the black hole in units of the Sun’s mass.
22. Use the result from Exercise 24.21 to calculate the radius of a black hole with a mass equal to: the Earth, a
B0-type main-sequence star, a globular cluster, and the Milky Way Galaxy. Look elsewhere in this text and
the appendixes for tables that provide data on the mass of these four objects.
23. Since the force of gravity a significant distance away from the event horizon of a black hole is the same as
that of an ordinary object of the same mass, Kepler’s third law is valid. Suppose that Earth collapsed to the
size of a golf ball. What would be the period of revolution of the Moon, orbiting at its current distance of
400,000 km? Use Kepler’s third law to calculate the period of revolution of a spacecraft orbiting at a
distance of 6000 km.
834 24 • Exercises
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Figure 25.1 Milky Way Galaxy. The Milky Way rises over Square Tower, an ancestral pueblo building at Hovenweep National
Monument in Utah. Many stars and dark clouds of dust combine to make a spectacular celestial sight of our home Galaxy. The
location has been designated an International Dark Sky Park by the International Dark Sky Association.
Chapter Outline
25.1 The Architecture of the Galaxy
25.2 Spiral Structure
25.3 The Mass of the Galaxy
25.4 The Center of the Galaxy
25.5 Stellar Populations in the Galaxy
25.6 The Formation of the Galaxy
Thinking Ahead
Today, we know that our Sun is just one of the many billions of stars that make up the huge cosmic island we
call the Milky Way Galaxy. How can we “weigh” such an enormous system of stars and measure its total mass?
One of the most striking features you can see in a truly dark sky—one without light pollution—is the band of
faint white light called the Milky Way, which stretches from one horizon to the other. The name comes from an
ancient Greek legend that compared its faint white splash of light to a stream of spilled milk. But folktales
differ from culture to culture: one East African tribe thought of the hazy band as the smoke of ancient
campfires, several Native American stories tell of a path across the sky traveled by sacred animals, and in
Siberia, the diffuse arc was known as the seam of the tent of the sky.
In 1610, Galileomade the first telescopic survey of the Milky Way and discovered that it is composed of a
multitude of individual stars. Today, we know that the Milky Way comprises our view inward of the huge
cosmic pinwheel that we call the Milky Way Galaxy and that is our home. Moreover, our Galaxy is now
recognized as just one galaxy among many billions of other galaxies in the cosmos.
The Milky Way Galaxy
25
25 • Thinking Ahead 835
25.1 The Architecture of the Galaxy
Learning Objectives
By the end of this section, you will be able to:
Explain why William and Caroline Herschel concluded that the Milky Way has a flattened structure
centered on the Sun and solar system
Describe the challenges of determining the Galaxy’s structure from our vantage point within it
Identify the main components of the Galaxy
The Milky Way Galaxy surrounds us, and you might think it is easy to study because it is so close. However,
the very fact that we are embedded within it presents a difficult challenge. Suppose you were given the task of
mapping New York City. You could do a much better job from a helicopter flying over the city than you could if
you were standing in Times Square. Similarly, it would be easier to map our Galaxy if we could only get a little
way outside it, but instead we are trapped inside and way out in its suburbs—far from the galactic equivalent
of Times Square.
Herschel Measures the Galaxy
In 1785, William Herschel (Figure 25.2) made the first important discovery about the architecture of the Milky
Way Galaxy. Using a large reflecting telescope that he had built, William and his sister Caroline counted stars
in different directions of the sky. They found that most of the stars they could see lay in a flattened structure
encircling the sky, and that the numbers of stars were about the same in any direction around this structure.
Herschel therefore concluded that the stellar system to which the Sun belongs has the shape of a disk or
wheel (he might have called it a Frisbee except Frisbees hadn’t been invented yet), and that the Sun must be
near the hub of the wheel (Figure 25.3).
Figure 25.2 William Herschel (1738–1822) and Caroline Herschel (1750–1848). William Herschel was a German musician who
emigrated to England and took up astronomy in his spare time. He discovered the planet Uranus, built several large telescopes, and
made measurements of the Sun’s place in the Galaxy, the Sun’s motion through space, and the comparative brightnesses of stars.
This painting shows William and his sister Caroline polishing a telescope lens. (credit: modification of work by the Wellcome Library)
To understand why Herschel reached this conclusion, imagine that you are a member of a band standing in
formation during halftime at a football game. If you count the band members you see in different directions
and get about the same number each time, you can conclude that the band has arranged itself in a circular
pattern with you at the center. Since you see no band members above you or underground, you know that the
circle made by the band is much flatter than it is wide.
836 25 • The Milky Way Galaxy
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Figure 25.3 Herschel’s Diagram of the Milky Way. Herschel constructed this cross section of the Galaxy by counting stars in
various directions.
We now know that Herschel was right about the shape of our system, but wrong about where the Sun lies
within the disk. As we saw in Between the Stars: Gas and Dust in Space, we live in a dusty Galaxy. Because
interstellar dust absorbs the light from stars, Herschel could see only those stars within about 6000 light-years
of the Sun. Today we know that this is a very small section of the entire 100,000-light-year-diameter disk of
stars that makes up the Galaxy.
Harlow Shapley: Mapmaker to the Stars
Until the early 1900s, astronomers generally accepted Herschel’s conclusion that the Sun is near the center
of the Galaxy. The discovery of the Galaxy’s true size and our actual location came about largely through
the efforts of Harlow Shapley. In 1917, he was studying RR Lyrae variable stars in globular clusters. By
comparing the known intrinsic luminosity of these stars to how bright they appeared, Shapley could
calculate how far away they are. (Recall that it is distance that makes the stars look dimmer than they would
be “up close,” and that the brightness fades as the distance squared.) Knowing the distance to any star in a
cluster then tells us the distance to the cluster itself.
Globular clusters can be found in regions that are free of interstellar dust and so can be seen at very large
distances. When Shapley used the distances and directions of 93 globular clusters to map out their
positions in space, he found that the clusters are distributed in a spherical volume, which has its center not
at the Sun but at a distant point along the Milky Way in the direction of Sagittarius. Shapley then made the
bold assumption, verified by many other observations since then, that the point on which the system of
globular clusters is centered is also the center of the entire Galaxy (Figure 25.4).
VOYAGERS IN ASTRONOMY
25.1 • The Architecture of the Galaxy 837
	Chapter 24 Black Holes and Curved Spacetime
	Exercises
	Chapter 25 The Milky Way Galaxy
	Thinking Ahead
	25.1 The Architecture of the Galaxy