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Chapter 12 Homework
Chapter 12 Homework
Due: 11:59pm on Tuesday, October 25, 2016
To understand how points are awarded, read the Grading Policy for this assignment.
Question 1
Choose the best answer.
Part A
What two pieces of information would you need in order to measure the masses of stars in an eclipsing binary system?
ANSWER:
the time between eclipses and the average distance between the stars
the period of the binary system and its distance from the Sun
the velocities of the stars and the Doppler shifts of their absorption lines
Correct
Question 2
Part A
The total amount of power (in watts, for example) that a star radiates into space is called its _________.
ANSWER:
absolute magnitude
luminosity
apparent brightness
flux
Correct
Question 3
Part A
According to the inverse square law of light, how will the apparent brightness of an object change if its distance to us triples?
ANSWER:
Its apparent brightness will decrease by a factor of 3.
Its apparent brightness will increase by a factor of 3.
Its apparent brightness will increase by a factor of 9.
Its apparent brightness will decrease by a factor of 9.
Correct
Question 4
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Part A
Assuming that we can measure the apparent brightness of a star, what does the inverse square law for light allow us to do?
ANSWER:
Determine the distance to the star from its apparent brightness.
Determine both the star's distance and luminosity from its apparent brightness.
Calculate the star's luminosity if we know its distance, or calculate its distance if we know its luminosity.
Calculate the star's surface temperature if we know either its luminosity or its distance.
Correct
Question 5
Part A
Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category.
Hint 1. What are giant and supergiant stars?
Giants and supergiants exceed most other stars in __________.
ANSWER:
surface temperature only
luminosity only
radius only
both radius and luminosity
both surface temperature and luminosity
Hint 2. What are main­sequence stars?
ANSWER:
Main­sequence stars are __________. a rare type of extremely massive star
stars that are in the longest­lasting phase of their lives, in which they fuse hydrogen into helium in their cores
stars that have exhausted their supplies of energy for fusion
Hint 3. What are white dwarfs?
ANSWER:
dim
White dwarfs are small and _____. very luminous
short lived
cool
ANSWER:
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Be sure that you understand why each of these characteristics goes with either giants/supergiants, main­sequence stars, or white dwarfs. If you are
unsure, review the H­R diagram in your textbook.
Question 6
First, launch the animation below. Explore the interactive figure before beginning to answer the questions. Click the “show stars” button to see the main
sequence and then move the “radius” slider (at bottom) to see the location along the main sequence of a main­sequence star with that particular radius. You
can do the same for temperature, luminosity, mass, or lifetime: Clicking one of these properties in the list along the right changes the slider to that property.
Note that this interactive figure allows you to vary properties of main­sequence stars only, not of any other type of star (such as giants or white dwarfs).
Part A
Compared to a main­sequence star with a short lifetime, a main­sequence star with a long lifetime is __________.
Hint 1. What is the surface temperature of a high­luminosity main­sequence star?
A typical surface temperature for a high­luminosity main­sequence star is __________.
ANSWER:
less than about 10,000 K
between about 10,000 K and 50,000 K
greater than about 50,000 K
Hint 2. What is the mass of a hot main­sequence star?
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A typical mass for a main­sequence star with high surface temperature is __________.
ANSWER:
less than about 5 solar masses
between about 5 and 100 solar masses
greater than about 100 solar masses
ANSWER:
more luminous, hotter, larger, and more massive
more luminous, hotter, smaller, and less massive
less luminous, cooler, larger, and more massive
less luminous, cooler, smaller, and less massive
Correct
Note that there are physical reasons why long­lived stars have these properties: They are less luminous because they burn their fuel at a much lower
rate than short­lived stars; they burn it at this lower rate because they are less massive (which means less compression and hence a lower fusion
rate in their cores); and their lower masses lead to their smaller sizes and lower surface temperatures.
Part B
Compared to a high­luminosity main­sequence star, stars in the upper right of the H­R diagram are __________.
Hint 1. Which star is hotter?
Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper
right) in the H­R diagram.
True or False? Spica has a higher surface temperature than Betelgeuse.
ANSWER:
True
False
Hint 2. Which star is larger?
Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper
right) in the H­R diagram.
True or False? Betelgeuse is larger in radius than Spica.
ANSWER:
True
False
ANSWER:
hotter and larger in radius
cooler and larger in radius
cooler and smaller in radius
hotter and smaller in radius
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Be sure to notice that luminosity increases upward on the diagram, surface temperature increases to the left, and radius increases diagonally from
the lower left to the upper right. Therefore, stars in the upper right must be high in luminosity and radius, but low in surface temperature. These stars
are called giants or supergiants because of their large radii.
Part C
Compared to a low­luminosity main­sequence star, stars in the lower left of the H­R diagram are __________.
Hint 1. Which star is hotter?
Be sure you have clicked on the "show stars" button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H­R
diagram.
True or False? Sirius B has a higher surface temperature than Ross 128.
ANSWER:
True
False
Hint 2. Which star is larger?
Be sure you have clicked on the "show stars" button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H­R
diagram.
True or False? Sirus B is larger in radius than Ross 128.
ANSWER:
True
False
ANSWER:
hotter and larger in radius
cooler and larger in radius
cooler and smaller in radius
hotter and smaller in radius
Correct
Notice that the stars in the lower left of the diagram are called white dwarfs: white because they are hot enough to appear “white hot” to our eyes, and
dwarfs because of their small sizes. A typical white dwarf is no larger in size (radius) than our Earth, but has as much mass as the Sun.
Question 7
Part A
Why is a star's birth mass its most fundamental property?
ANSWER:
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A star's birth mass is the most important predictor of a star's luminosity. A star born with low mass will have a high luminosity; a star born with
high mass will have a significantly lower luminosity.
A star's birth mass is the most important predictor of a star's surface temperature. A star born with low mass will have a high surface
temperature; a star born with high mass will have a significantly lower surface temperature.
A star's birth mass is the most important predictor of a star's lifetime. A star born with high mass will have a short lifespan; a star born with low
mass will have a significantly longer lifespan.
A star's birth mass is the most important predictor of a star's size. A star born with high mass will have a small radius; a star born with low
mass will have a significantly greater radius.
Correct
Question 8
Choose the best answer.
Part A
Which of these stars is the most massive?
ANSWER:
a main­sequence A star
a main­sequence G star
a main­sequence M star
Correct
Question 9
Choose the best answer.
Part A
Which of these stars has the longest lifetime?
ANSWER:
a main­sequence A star
a main­sequence G star
a main­sequence M star
Correct
Question 10
Choose the best answer.
Part A
Which of these stars has the largest radius?
ANSWER:
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a supergiant A star
a giant K star
a supergiant M star
Correct
Question 11
Choose the best answer.
Part A
Which of these stars has the greatest surface temperature?
ANSWER:
a 30 MSun main­sequence star
a supergiant A star
a Cepheid variable star
Correct
Question 12
Part A
From hottest to coolest, the order of the spectral types of stars is _________.
ANSWER:
ABFGKMO
OBAGFKM
OMKGFBA
OBAFGKM
ABCDEFG
Correct
Question 13
Part A
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?
ANSWER:
We know the star's luminosity and distance.
The star is of spectral type G.
The star is a member of a binary star system.
The star is of spectral type A.
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Question 14
Part A
What is the common trait of all main sequence stars?
ANSWER:
They are all spectral type G.
They all have approximately the same mass.
They are in the final stage of their lives.
They generate energy through hydrogen fusion in their core.
Correct
Question 15
Learning Goal:
To understand how we learn about stars through a combination of direct observations and quantities that we infer from data and calculations.
Part A
Consider a relatively nearby, single star, that is, a star that is not a member of a binary system and has no known orbiting planets. Listed below are a few
properties of this star. Classify each property as either something that we can observe or measure directly (with the aid of a telescope and instruments
such as cameras or spectrographs) or something that we must infer indirectly (and hence is correct only if all of our assumptions are correct).
Hint 1. What is the difference between luminosity and apparent brightness?
Consider three stars that are all identical to the Sun, each one located at a different distance from Earth. Which of the following must be true?
ANSWER:
The stars all have the same luminosity but different apparent brightness.
The stars all have the same apparent brightness but different luminosity.
The stars all have the same luminosity and the same apparent brightness.
Hint 2. Is the inverse square law for the apparent brightness of light always valid?
Consider two stars that are identical to the Sun, but one is 10 times as far away as the other. According to the inverse square law for light, the
more distant star should appear dimmer by a factor of 10 2 = 100. But is this necessarily true in all cases?
ANSWER:
Yes. The inverse square law for light is an absolute law that is always valid.
No. It is true only if no light from either star is absorbed or scattered away as the light travels from the star to Earth.
No. The inverse square law for light is valid only for stars that are relatively nearby, not for stars at great distances from Earth.
Hint 3. What is a parallax angle used for?
If you know a star’s parallax angle, then you can calculate its _____.
ANSWER:
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radius
distance
mass
Hint 4. How do we know the temperature of the Sun’s photosphere?
We learn the temperature of the Sun’s photosphere by __________.
ANSWER:
sending space probes that carry thermometers into the photosphere
applying the inverse square law for light
studying the Sun’s color and spectrum
Hint 5. How do we find the masses of distant objects?
We can calculate the mass of a distant star by __________.
ANSWER:
measuring its parallax angle
applying the inverse square law for light
applying Newton’s version of Kepler’s third law
Hint 6. How do we determine the radius of a distant star?
The most common way of determining a star’s radius is to ___________.
ANSWER:
calculate it from the star’s luminosity and surface temperature
determine it from the star’s parallax angle
measure the star’s angular diameter in the sky
ANSWER:
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Now continue to the follow­up questions to be sure you understand how we infer some of the properties of stars.
Part B
From Part A, you know that surface temperature is a stellar property that we infer indirectly. What must we measure directly so that we can infer a star’s
surface temperature?
Hint 1. Which gas is hotter?
Consider three gas clouds consisting mostly of hydrogen. One cloud has most of its hydrogen in molecular form (H2), one has mostly neutral
hydrogen atoms, and one has mostly hydrogen ions (and free electrons). Which cloud is the hottest?
ANSWER:
the neutral cloud
the molecular cloud
the ionized cloud
ANSWER:
mass
parallax angle
spectral type
apparent brightness
Correct
A star’s spectral type (OBAFGKM) tells us its surface temperature, because different sets of lines form more easily at different temperatures. Color
can also be used as a rough measure of surface temperature; for example, a blue star is hotter than a red star.
Part C
Which of the following must be true if we are to infer (calculate) a star's luminosity directly from the inverse square law for light?
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Check all that apply.
Hint 1. What is the inverse square law for light?
Consider two stars that are all identical to the Sun, but one is 10 times as far away as the other. According to the inverse square law for light, the
more distant star should appear __________.
ANSWER:
brighter by a factor of 10
dimmer by a factor of 10 2
= 100
dimmer by a factor of 10
Hint 2. Can you determine the luminosity of a street light on a foggy night?
Suppose you measure the apparent brightness of a street light that is located 100 meters away from you. If it is a foggy night and you apply the
inverse square law for light, then the luminosity you calculate for the street light will be __________.
ANSWER:
too high, because the fog makes the light appear brighter than it really is
accurate, because the inverse square law for light is always valid
too low, because the fog absorbs some of the light, making the light appear dimmer than it really is
ANSWER:
We have measured the star’s spectral type.
We have measured the star’s distance.
We have measured the star’s apparent brightness.
The star must be a member of a binary system.
No interstellar gas or dust absorbs or scatters light between us and the star.
Correct
We can use the inverse square law for light to calculate the star’s luminosity from its apparent brightness and distance. However, this calculated
value will be accurate only if there is no absorption or scattering of the light on its way from the star to us. (If there is interstellar dust between us and
the star, we can sometimes measure the amount and therefore determine the star's luminosity by accounting for the light this dust absorbs or
scatters.)
Part D
We found that mass must be inferred for the star described in Part A. However, we can measure a star’s mass directly if __________.
Hint 1. How do we know Earth’s mass?
Which two measured quantities can enable us to calculate Earth’s mass?
ANSWER:
Earth’s radius and Earth’s surface atmospheric pressure
the Moon’s average distance from Earth and the Moon’s orbital period around Earth
Earth’s radius and Earth’s distance from the Sun
ANSWER:
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it is a member of an eclipsing binary system
it is near enough for us to measure its distance with parallax
it is unusually high in mass
we know its spectral type
Correct
We can use Newton’s version of Kepler’s third law to calculate the masses of distant objects, but only if we know the period and distance of an
orbiting object. This is possible for an eclipsing binary system, because the two stars orbit each other (and the eclipses tell us that we are viewing
the orbit edge­on).
Part E
You should now see that the reason the mass of the star in Part A must be inferred is that the star has no known orbiting objects, which means we cannot
apply Newton’s version of Kepler’s third law. Which of the following must be true if the star’s inferred mass is to be accurate?
Check all that apply.
Hint 1. Do all G2 stars have the same mass as the Sun?
The Sun has spectral type G2, so we might expect another star of the same spectral type to be similar to the Sun in mass, luminosity, and radius.
However, this will be true only if the star is also __________.
ANSWER:
a main­sequence star
located within the Milky Way Galaxy
the same age as the Sun
ANSWER:
The star must be located within the Milky Way Galaxy and not in another galaxy.
We have determined that the star is a main­sequence star.
We have measured the star’s spectral type.
We have measured the star’s velocity.
Correct
All main­sequence stars of a particular spectral type have approximately the same mass. Therefore, if we know the star’s spectral type and know
that it is a main­sequence star, then we can infer its mass.
Question 16
Part A
Consider the four stars shown following. Rank the stars based on their surface temperature from highest to lowest.
Hint 1. How is the color of light related to its wavelength?
Which of the following lists the visible colors in correct order from shortest wavelength to longest wavelength?
ANSWER:
red, orange, green, blue
blue, green, orange, red
blue, orange, green, red
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Hint 2. How does the wavelength of light depend on an object’s temperature?
According to the laws of thermal radiation, hotter objects have spectra that peak at __________.
ANSWER:
shorter wavelength
longer wavelength
Hint 3. The Color of the Sun
The Sun appears yellow or white to the eye, but its spectrum actually peaks in the middle of the visible region, which corresponds to yellow or
green in color. Note that this means the Sun's spectrum peaks at a wavelength longer than that of a blue star, but shorter than that of an orange or
red star.
ANSWER:
Reset
Highest temperature
Help
Lowest temperature
Correct
Notice that temperature is related to color, and follows the order of the colors in the rainbow: Blue (or violet) stars are the hottest, while red stars are
the coolest. In the parts that follow, the H­R diagrams show the correlation between color and temperature on the horizontal axis.
Part B
Five stars are shown on the following H­R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have
the same surface temperature, drag one star on top of the other(s).
Hint 1. How does the H­R diagram show surface temperature?
On the H­R diagram, surface temperature increases __________.
ANSWER:
upward, so stars low on the luminosity axis have lower surface temperature than stars higher up
right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right
diagonally from the lower left to the upper right
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ANSWER:
Reset
Highest temperature
Help
Lowest temperature
Correct
All five stars appear at the same place along the horizontal axis showing spectral type. Because spectral type is related to surface temperature, all
five stars must have the same surface temperature. Now proceed to Part C to determine how these stars vary in luminosity.
Part C
Five stars are shown on the following H­R diagrams; notice that these are the same five stars shown in Part B. Rank the stars based on their luminosity
from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s).
ANSWER:
Reset
Highest luminosity
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Lowest luminosity
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Luminosity is shown along the vertical axis, with stars higher up more luminous than those lower down. Note that each tickmark along the luminosity
axis represents a change by a factor of 10 from the prior tickmark, so the range of luminosities is quite large. Continue to Parts D and E to
investigate surface temperature and luminosity for a different set of five stars.
Part D
Five stars are shown on the following H­R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have
the same surface temperature, drag one star on top of the other(s).
Hint 1. How does the H­R diagram show surface temperature?
On the HR diagram, surface temperature increases __________.
ANSWER:
upward, so stars low on the luminosity axis have lower surface temperature than stars higher up
right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right
diagonally from the lower left to the upper right
ANSWER:
Reset
Highest temperature
Help
Lowest temperature
Correct
Spectral type is related to surface temperature, with stars of spectral type O having the highest surface temperature and stars of spectral type M
having the lowest surface temperature. In other words, spectral type increases to the left on the H­R diagram. Now proceed to Part E to determine
how these stars compare in luminosity.
Part E
Five stars are shown on the following H­R diagrams. Rank the stars based on their luminosity from highest to lowest; notice that these are the same five
stars shown in Part D. If two (or more) stars have the same luminosity, drag one star on top of the other(s).
ANSWER:
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Chapter 12 Homework
Reset
Highest luminosity
Help
Lowest luminosity
Correct
All five stars have the same luminosity because they are all at the same height along the vertical (luminosity) axis. Continue to Parts F and G for
more practice in reading surface temperature and luminosity on the HR diagram.
Part F
Five stars are shown on the following H­R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have
the same surface temperature, drag one star on top of the other(s).
Hint 1. How does the H­R diagram show surface temperature?
On the H­R diagram, surface temperature increases __________.
ANSWER:
upward, so stars low on the luminosity axis have lower surface temperature than stars higher up
right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right
diagonally from the lower left to the upper right
ANSWER:
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Chapter 12 Homework
Reset
Highest temperature
Help
Lowest temperature
Correct
Spectral type is related to surface temperature, with stars of spectral type O having the highest surface temperature and stars of spectral type M
having the lowest surface temperature. In other words, spectral type increases to the left on the H­R diagram.
Part G
Five stars are shown on the following H­R diagrams; notice that these are the same five stars shown in Part F. Rank the stars based on their luminosity
from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s).
ANSWER:
Reset
Highest luminosity
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Lowest luminosity
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As always, the H­R diagram shows surface temperature along the horizontal axis and luminosity along the vertical axis.
Question 17
Choose the best answer.
Part A
Which of these star clusters is oldest?
ANSWER:
a cluster whose brightest main­sequence stars are white
a cluster whose brightest main­sequence stars are yellow
a cluster containing stars of all colors
Correct
Question 18
Part A
What do we mean by the main­sequence turnoff point of a star cluster, and what does it tell us?
ANSWER:
It is the spectral type of the hottest main sequence star in a star cluster, and it tells us the cluster's age.
It is the mass of the most massive star in the star cluster, and it tells us the cluster's size.
It is the point in a star cluster beyond which main sequence stars are not found, and it tells us the cluster's distance.
It is the faintest and coldest main sequence star in a cluster, and it tells us the cluster's age.
Correct
Score Summary:
Your score on this assignment is 50.8%.
You received 24.4 out of a possible total of 48 points.
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