57) Besides mass, what else can be determined about the stars in an eclipsing binary system by
observing their light curve?
A) their luminosities
B) their temperatures
C) their radii
D) none of the above
12.2 True/False Questions
1) The apparent brightness of a star depends only on its luminosity.
2) If the distance between us and a star is doubled, its apparent brightness will decrease by a
factor of four.
3) The more distant a star, the smaller its parallax.
4) We can measure the parallax of most stars in our galaxy.
5) Imagine that the size of the Earth’s orbit is doubled. This will allow the parallaxes of more
distant stars to be measured.
6) The spectral type, surface temperature, and color of a star are all related.
7) Some stars are cool enough to have molecules in their atmosphere.
8) A star with an apparent magnitude of 10 appears fainter than a star with an apparent
magnitude of 9.
9) The faintest stars visible to the naked eye have an apparent magnitude of about 6.
10) It is impossible for a star to have a negative apparent magnitude, such as -1.
11) We can measure the radii of eclipsing binary stars from the light curve of the system.
12) Two stars have the same spectral type. Star X is in luminosity class III, while Star Y is in
luminosity class V. Star X must be larger in radius than Star Y.
13) Two stars have the same luminosity. Star X is spectral type F, while Star Y is spectral type
K. Star X must be larger in radius than Star Y.
14) Two stars both lie on the main sequence. Star X is spectral type A, while Star Y is spectral
type G. Star X must be more massive than Star Y.
15) A 10 solar mass star is about ten times more luminous than a 1 solar mass star.
16) Blue stars are always more luminous than red stars.
17) Most stars on the main sequence fuse hydrogen into helium in their cores, but some do not.
18) All stars spend approximately the same amount of time on the main sequence.
19) Blue stars are always hotter than red stars.
20) Some 10 solar mass main-sequence stars have much shorter lifetimes than other 10 solar
mass main-sequence stars.
21) Main-sequence stars are all about the same radius as the Sun.
22) Main-sequence stars have radii ranging from about 0.03 solar radius to 30 solar radius.
23) White dwarfs are all about the same size.
12.3 Process of Science Questions
1) Our Sun, An Average Star: Often in science it is helpful to talk about a representative example
of the objects or phenomena being studied. However, you must always keep in mind that the
average case is not always representative. For example, our Sun is often described as an
“average” star in the Milky Way. In what sense is this statement true? In what sense is this
statement seriously misleading? Do you think it is useful to characterize the stars in the Milky
Way by simply citing our “average” Sun?
2) Confusing Terminology in Science: Scientists’ love of jargon and acronyms often confounds
the public and makes it impossible for them to read scientific literature. Use the example of
spectral types introduced in this chapter (i.e., the Sun is a “G2” star) as a case study in jargon.
What is the historical origin of the spectral types? Why are the letters in a confusing, non-
alphabetical order? Why do you think astronomers persist in using spectral types? Do you think
astronomers should drop this notation, and, if so, what should replace it?
3) Observing Stellar Evolution: Stars evolve on timescales of millions to billions of years,
making it impossible for astronomers to follow the life-cycle of any individual star. Explain how
astronomers overcome this limitation. Be sure to discuss the important role that observations of
star clusters play in revealing the evolution of stars.
4) Inferring stellar lifetimes: Scientists must often draw on a variety of concepts to develop new
understanding. Take, for example, the inferred lifetimes of stars. What two properties must be
precisely measured in order to estimate the lifetime? Outline the set of observations that must be
made in order to determine those properties. Then discuss the fundamental physics that must be
understood to relate these to the rate at which hydrogen is converted to helium in the stellar core,
and to determine the amount of hydrogen available in the core.
12.4 Short Answer Questions
1) The Earth is about 150 million km from the Sun, and the apparent brightness of the Sun in our
sky is about 1,300 watts per square meter. Determine the apparent brightness we would measure
for the Sun if we were located half the earth’s distance from the Sun.
2) Explain how an astronomer could determine the individual masses of the stars in an eclipsing
binary system.
3) Why can we only get a minimum mass estimate for the stars in a spectroscopic binary that is
not an eclipsing system?
4) Which is brighter in our sky, a star with apparent magnitude 2 or a star with apparent
magnitude 7? How many times brighter does it appear?
5) Explain why stars displaying spectral lines of molecules must be relatively cool.
6) Two stars, Tom and Jerry, have the same spectral type. Tom is luminosity class V and Jerry is
luminosity class I. Which star is bigger? Which star is more luminous? Which star has a hotter
surface temperature? Explain your answers.
7) Two stars, Fred and Barney, are of the same size. Fred has spectral type F, while Barney has
spectral type B. Which one is more luminous? What are their relative locations on the HR
diagram?
8) Two stars, Betty and Wilma, are both on the main sequence. Betty is more luminous than
Wilma. Which one has a hotter surface temperature? Which one is more massive? Which one is
bigger? If they both formed at the same time, which one will evolve off the main sequence first?
9) Explain why stars more massive than the Sun live shorter main-sequence lives than stars less
massive than the Sun, despite having more fuel available for nuclear reactions.
The following questions refer to the sketch of the H-R diagram below. Choose the best answer in
each case. Note that choice (a) refers to the entire main sequence, while (c) and (d) refer to only
small parts of the main sequence. If choice (c) or (d) offers a better answer to a particular
question than (a), use the best choice. You may use the same choice more than once.
10) Which group represents stars that are hot but dim?
11) Which group represents stars of the smallest radii?
12) Which group includes stars that are fusing hydrogen into helium in their cores?
13) Which group represents stars that are hot and very bright?
14) Which group represents main-sequence stars with the shortest lifetimes?
15) Which group includes stars that are fusing elements besides hydrogen in their cores?
16) Which group includes stars that are fusing helium in their cores?
The following questions refer to the representations below of H-R diagrams for different clusters
of stars. In each diagram, the dotted lines locate the position of the Sun.
17) Which cluster is the youngest?
18) Which cluster is the oldest?
19) Which cluster is approximately 10 billion years old?
12.5 Mastering Astronomy Reading Quiz
1) What is the approximate chemical composition (by mass) with which all stars are born?
A) Three quarters hydrogen, one quarter helium, no more than 2% heavier elements
B) Half hydrogen and half helium
C) 98% hydrogen, 2% helium
D) 95% hydrogen, 4% helium, no more than 1% heavier elements
2) The total amount of power (in watts, for example) that a star radiates into space is called its
________.
A) apparent brightness
B) absolute magnitude
C) luminosity
D) flux
3) According to the inverse square law of light, how will the apparent brightness of an object
change if its distance to us triples?
A) Its apparent brightness will decrease by a factor of 9.
B) Its apparent brightness will increase by a factor of 9.
C) Its apparent brightness will decrease by a factor of 3.
D) Its apparent brightness will increase by a factor of 3.
4) Assuming that we can measure the apparent brightness of a star, what does the inverse square
law of light allow us to do?
A) calculate the star’s luminosity if we know its distance, or calculate its distance if we know its
luminosity
B) determine both the star’s distance and luminosity from its apparent brightness
C) determine the distance to the star from its apparent brightness
D) calculate the star’s surface temperature if we know either its luminosity or its distance
5) If Star A is closer to us than Star B, then Star A’s parallax angle is ________.
A) larger than that of Star B
B) smaller than that of Star B
C) equal to that of Star B since parallax is the same for all stars, regardless of their distance
D) fewer parsecs than that of Star B
6) How do we know how massive stars are?
A) We measure their apparent brightness and distance (from parallax).
B) We don’t really know: stellar masses are based on an informed guess.
C) We measure the orbital periods and velocities of stars in binary systems.
D) We measure their density and radius.
7) Star A has an apparent magnitude of 3, and Star B has an apparent magnitude of 5. Which star
is brighter in our sky?
A) Star A
B) Star B
C) The two stars have the same brightness in our sky, but Star A is closer to us than Star B.
D) There is not enough information to answer the question.
8) Which of the following facts about stars in a cluster make it possible to determine the
approximate age of the cluster?
A) All the stars in a cluster are at about the same distance from us.
B) Stars in a cluster all formed at approximately the same time.
C) The mass of a star determines how long it will be on the main sequence.
D) all of the above
9) Our Sun is
A) fusing hydrogen to helium in its core.
B) still in the cluster of stars from which it formed.
C) considered to be a sub-giant star.
D) all of the above
10) Astronomers can measure a star’s mass in only certain cases. Which one of the following
cases might allow astronomers to measure a star’s mass?
A) The star is a member of a binary star system.
B) The star is of spectral type G.
C) The star is of spectral type A.
D) We know the star’s luminosity and distance.
11) Which of the following terms is given to a pair of stars that we can determine are orbiting
each other only by measuring their periodic Doppler shifts?
A) spectroscopic binary
B) eclipsing binary
C) visual binary
D) double star
12) The Hertzsprung-Russell (H-R) diagram shows the relationship between a star’s
A) luminosity and surface temperature.
B) mass and luminosity.
C) luminosity and apparent brightness.
D) mass and radius.
13) What is a star’s luminosity class related to?
A) its size (radius)
B) its mass
C) its age in years
D) its surface temperature
14) On an H-R diagram, stellar radii ________.
A) increase diagonally from the lower left to the upper right
B) are greatest in the lower left and least in the upper right
C) decrease from left to right
D) are impossible to determine
15) On an H-R diagram, stellar masses ________.
A) can be determined for main-sequence stars but not for other types of stars
B) are greatest in the lower left and least in the upper right
C) decrease from upper left to lower right
D) are impossible to determine
16) How is the lifetime of a star related to its mass?
A) More massive stars live much shorter lives than less massive stars.
B) More massive stars live slightly shorter lives than less massive stars.
C) More massive stars live much longer lives than less massive stars.
D) More massive stars live slightly longer lives than less massive stars.
17) Each choice below lists a spectral type and luminosity class for a star. Which one is a red
supergiant?
A) spectral type M2, luminosity class I
B) spectral type M1, luminosity class V
C) spectral type O9, luminosity class I
D) spectral type G2, luminosity class V
18) What is the common trait of all main-sequence stars?
A) They generate energy through hydrogen fusion in their core.
B) They are in the final stage of their lives.
C) They are all spectral type G.
D) They all have approximately the same mass.
19) Suppose our Sun were suddenly replaced by a red supergiant star. Which of the following
would be true?
A) Earth would be inside the supergiant.
B) The supergiant’s surface temperature would be much hotter than the surface temperature of
our Sun.
C) Earth would fly off into interstellar space.
D) The supergiant would appear as large as the full Moon in our sky.
20) What is a white dwarf?
A) the remains of a star that ran out of fuel for nuclear fusion
B) a main-sequence star of spectral type F, which tends to look white in color
C) a type of star that produces energy by gravitational contraction
D) a star that follows a period-luminosity relation
21) Which of the following statements comparing open and globular star clusters is not true?
A) Open and globular clusters each typically contain a few hundred stars.
B) Open clusters are found only in the disk of the galaxy while globular clusters may be found
both in the disk and the halo of the galaxy.
C) Stars in open clusters are relatively young while stars in globular clusters are very old.
D) For both open and globular clusters, we can assume that all the stars in a particular cluster are
about the same age.
22) What do we mean by the main-sequence turnoff point of a star cluster, and what does it tell
us?
A) It is the spectral type of the hottest main-sequence star in a star cluster, and it tells us the
cluster’s age.
B) It is the point in a star cluster beyond which main-sequence stars are not found, and it tells us
the cluster’s distance.
C) It is the luminosity class of the largest star in a star cluster, and it tells us the cluster’s age.
D) It is the mass of the most massive star in the star cluster, and it tells us the cluster’s size.
12.6 Mastering Astronomy Concept Quiz
1) All stars are born with the same basic composition, yet stars can look quite different from one
another. Which two factors primarily determine the characteristics of a star?
A) its mass and its stage of life
B) its apparent brightness and its distance
C) its age and its location in the galaxy
D) its mass and its surface temperature
E) its apparent brightness and its luminosity
2) What does the apparent magnitude of a star tell us about that star?
A) how bright it appears from Earth
B) how much energy it is emitting
C) its radius
D) its mass
3) Star A is identical to Star B, except that Star A is twice as far from us as Star B. Therefore,
________.
A) both stars have the same luminosity, but the apparent brightness of Star B is four times that of
Star A
B) both stars have the same luminosity, but the apparent brightness of Star B is twice that of
Star A
C) both stars have the same apparent brightness, but the luminosity of Star B is four times that of
Star A
D) both stars have the same luminosity, but the apparent brightness of Star A is four times that of
Star B
4) A star with a parallax angle of 1/20 arcsecond is ________.
A) 20 parsecs away
B) 20 light-years away
C) 1/20 parsec away
D) 10 parsecs away
5) The star Vega has an absolute magnitude of about 4 and an apparent magnitude of about 0.
Based on the definitions of absolute and apparent magnitude, we can conclude that ________.
A) Vega is nearer than 10 parsecs from Earth
B) Vega is farther than 10 parsecs from Earth
C) Vega’s luminosity is less than that of our Sun
D) Vega’s surface temperature is cooler than the Sun
6) Which of the following statements about spectral types of stars is not necessarily true?
A) The spectral type of a star can be used to determine its distance.
B) The spectral type of a star can be used to determine its surface temperature.
C) The spectral type of a star can be used to determine its color.
D) The spectral type of a star can be determined by identifying lines in its spectrum.
7) Sirius is a star with spectral type A and Rigel is a star with spectral type B. What can we
conclude?
A) Rigel has a higher surface temperature than Sirius.
B) Rigel has a higher core temperature than Sirius.
C) Sirius has a higher core temperature than Rigel.
D) Sirius has a higher surface temperature than Rigel.
8) To calculate the masses of stars in a binary system, we must measure their ________.
A) orbital period and average orbital distance
B) spectral types and distance from Earth
C) absolute magnitudes and luminosities
D) luminosities and distance from Earth
9) Careful measurements reveal that a star maintains a steady apparent brightness at most times,
except that at precise intervals of 73 hours the star becomes dimmer for about 2 hours. The
change in brightness alternates between a small change and a large change. The most likely
explanation is that ________.
A) the star is a member of an eclipsing binary star system
B) the star is a Cepheid variable
C) the star is periodically ejecting gas into space every 73 hours
D) the star is a white dwarf
10) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars that are cool and dim?
A) a
B) b
C) c
D) d
E) e
11) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars of the largest radii?
A) a
B) b
C) c
D) d
E) e
12) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents the most common type of stars?
A) e
B) b
C) c
D) d
13) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars that are extremely bright and emit most of their
radiation as ultraviolet light?
A) a
B) b
C) c
D) d
E) e
14) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars with the longest main-sequence lifetimes?
A) a
B) b
C) c
D) d
E) e
15) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars fusing hydrogen in their cores?
A) a
B) b
C) c
D) d
E) e
16) The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note
that (a) represents the entire main sequence while (c) and (d) represent only small parts of the
main sequence. Which group represents stars that have no ongoing nuclear fusion?
A) a
B) b
C) c
D) d
E) e
17) You observe a star and you want to plot it on an H-R diagram. You will need to measure all
of the following, except the star’s ________.
A) mass
B) distance
C) apparent brightness
D) spectral type
18) The main-sequence lifetime of a spectral type O star is _______ the main-sequence lifetime
of a spectral type A star.
A) shorter than
B) longer than
C) the same as
D) It is impossible to know since a spectral type A star is composed of only hydrogen.
19) How did astronomers discover that the position of a star on the main sequence depends on its
mass?
A) by measuring the masses of main-sequence stars in binary systems
B) by using computer models to predict the masses of stars with known luminosities and spectral
types
C) by measuring stellar radii to determine stellar masses
D) by measuring the distances and apparent brightness of stars to determine their masses
20) The choices below each describe the appearance of an H-R diagram for a different star
cluster. Which cluster is the youngest?
A) The diagram shows main-sequence stars of every spectral type except O, along with a few
giants and supergiants.
B) The diagram shows main-sequence stars of spectral types G, K, and M, along with numerous
giants and white dwarfs.
C) The diagram shows main-sequence stars of all the spectral types except O and B, along with a
few giants and supergiants.
D) The diagram shows no main-sequence stars at all, but it has numerous supergiants and white
dwarfs.
21) The choices below each describe the appearance of an H-R diagram for a different star
cluster. Which cluster is most likely to be located in the halo of our galaxy?
A) The diagram shows main-sequence stars of every spectral type except O, along with a few
giants and supergiants.
B) The diagram shows main-sequence stars of spectral types G, K, and M, along with numerous
giants and white dwarfs.
C) The diagram shows main-sequence stars of all the spectral types except O and B, along with a
few giants and supergiants.
D) The diagram shows no main-sequence stars at all, but it has numerous supergiants and white
dwarfs.
22) Why do O stars exhibit weak hydrogen absorption lines?
A) O stars contain very little hydrogen.
B) O stars are too cool to excite most hydrogen atoms to the first energy level, from which they
can then absorb visible wavelengths of light.
C) At these high temperatures, nearly all the hydrogen is ionized, and is therefore unable to
interact with light.
23) Stars exhibit strong hydrogen absorption lines because the surface temperature of 10,000 K
is high enough to place most hydrogen in an excited, but not yet ionized, state. The transitions
from this excited state then correspond to visible light wavelengths. Which of the following
statements is a plausible explanation for why G stars exhibit weaker hydrogen absorption lines?
A) G stars are too cool to excite most hydrogen atoms to the first energy level, from which they
can then absorb visible wavelengths of light.
B) G stars contain very little hydrogen.
C) At these high temperatures, nearly all the hydrogen is ionized, and unable to interact with
light.