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Chapter 12: Dwarf
Planets and Small Solar System Bodies
Learning
Objectives
12.1 Dwarf Planets May Outnumber Planets
Distinguish the characteristics of a dwarf
planet from a planet.
Multiple Choice: 1, 2, 3, 4, 6, 7, 8, 9
Short Answer: 1, 3, 4
Establish why Pluto was once considered a planet, but now is
classified as a dwarf planet.
Multiple Choice: 5, 11
Short Answer: 2
12.2 Asteroids Are Pieces of the Past
Identify the different locations of asteroids in the solar
system.
Multiple Choice: 12, 15, 17, 20
Differentiate an asteroid from a dwarf planet.
Multiple Choice: 10, 13, 14, 18, 19, 29
Summarize the differences between C-, S-, and M-type
asteroids.
Multiple Choice: 21, 23, 24, 25
Short Answer: 8
Describe how tidal effects from Jupiter keep main-belt
asteroids from forming a planet and cause the Kirkwood gaps.
Multiple Choice: 16
Short Answer: 6
Summarize what we have learned about asteroids from satellite
visits and landings.
Multiple Choice: 22, 26, 27, 28
Short Answer: 7, 10
12.3 Comets Are Clumps of Ice
Describe the two homes of comets.
Multiple Choice: 30, 35
Distinguish between the orbital characteristics of long- and
short-period comets.
Multiple Choice: 31, 34, 36, 37, 38, 39, 46, 47
Short Answer: 12
Describe the four parts of an active comet.
Multiple Choice: 33, 40, 41, 45
Short Answer: 18, 19, 21
Illustrate the changes in a comet’s appearance over the
course of its orbit.
Multiple Choice: 42, 43
Short Answer: 13, 14, 15, 16, 17, 20
Summarize what we have learned about comets from satellite
visits and landings
Multiple Choice: 32, 44
12.4 Meteorites Are Remnants of the Early
Solar System
Differentiate between meteors, meteorites, and meteoroids.
Multiple Choice: 56, 57
Short Answer: 22
Differentiate between the different compositions and origins
of meteorites.
Multiple Choice: 48, 49, 59, 61, 63, 64, 65, 66
Short Answer: 23
Summarize the origins of meteoroids that Earth encounters.
Multiple Choice: 58
Illustrate the origin of meteor showers.
Multiple Choice: 51, 52, 53, 54, 55
Short Answer: 26
Explain how asteroids and meteorites provide critical clues
to the origin and history of our Solar System
Multiple Choice: 50, 60, 62, 67
Short Answer: 24, 25
12.5 Collisions Still Happen Today
Summarize why it is important to search for and characterize
all near-Earth objects.
Multiple Choice: 68, 70
Short Answer: 27, 28, 29
Working It Out 12.1
Calculate perihelion and aphelion distances of an orbit based
on an object’s orbital eccentricity.
Short Answer: 9
Working It Out 12.2
Calculate the energy of an impact.
Multiple Choice: 69
Short Answer: 30
MULTIPLE CHOICE
1.
Which of the following
types of solar system debris were not discovered until the age of
telescopes?
a.
comets
b.
meteoroids
c.
zodiacal dust
d.
asteroids
e.
all of the above
2.
What group of solar
system objects does Pluto belong to?
a.
the Trojan asteroids
b.
the dwarf planets
c.
the giant objects
d.
the terrestrial planets
3.
Pluto is composed
primarily of
a.
rock.
b.
ice.
c.
a rocky core surrounded
by ice.
d.
metallic hydrogen.
4.
Pluto has an atmosphere
that comes and goes over an orbital period, because
a.
the atmosphere escapes
into space because of the low escape velocity from Pluto.
b.
the atmosphere is
pulled away from the planet by interaction with its moon Charon.
c.
the atmosphere “freezes
out” when Pluto is at its farthest from the Sun.
d.
chemical reactions
between Pluto’s atmosphere and gas expelled by its many volcanoes generates
carbon dioxide, which is too heavy to stay aloft in the atmosphere.
5.
Pluto is classified as
a dwarf planet because
a.
it has not cleared out
other bodies from its orbit.
b.
it is more than 1,000
times smaller than Earth’s moon.
c.
it has no moons of its
own.
d.
it has a unique
chemical composition that is very different from other planets.
e.
it orbits just outside
the Solar System.
6.
Which of following is false?
a.
Pluto has five moons.
b.
Pluto has a mass that
is 10 times less than Earth’s mass.
c.
Pluto’s orbit sometimes
brings it closer to the Sun than Neptune.
d.
Pluto was discovered by
Clyde Tombaugh in 1930.
e.
Pluto has a thin
atmosphere.
7.
Pluto has a density
that is roughly equal to two times that of
a.
a feather.
b.
water.
c.
lead.
d.
a rock.
e.
air.
8.
Currently the surface
of the dwarf planet Eris is covered with _________, which makes it have the
highest albedo of any object in the Solar System.
a.
methane ice
b.
water ice
c.
nitrogen ice
d.
sulfur dioxide ice
e.
carbon dioxide ice
9.
Eris, Ceres, and Haumea
are examples of
a.
asteroids.
b.
dwarf planets.
c.
meteoroids.
d.
comets.
e.
meteor showers.
10.
The dwarf planet Eris
has a moon called Dysnomia, which is much smaller in mass than Eris. If
Dysnomia has an orbital period of 16 days and orbits Eris at a distance of
40,000 km, then what is the mass of Eris?
a.
2 × 1013
kg
b.
2 × 1022
kg
c.
2 × 1028
kg
d.
2 × 1032
kg
e.
2 × 1035
kg
11.
How does the mass of
Pluto compare to that of Earth?
a.
It is around 100 times
smaller.
b.
It is around 1000 times
smaller.
c.
It is around 450 times
smaller.
d.
It is around 10 times
smaller.
12.
Where are asteroids
found?
a.
between Mars and
Jupiter
b.
inside Earth’s orbit,
halfway to the Sun
c.
in the farthest reaches
of the Solar System, beyond Pluto
d.
throughout the Solar
System
13.
When combined,
asteroids have a mass equivalent to
a.
about 1/10th the mass
of Earth’s Moon.
b.
about equal to the mass
of Earth’s Moon.
c.
about 1/2 the mass of
Earth’s Moon.
d.
about 1/25th the mass
of Earth’s Moon.
14.
Meteorites are
a.
remnants of a single
object near Pluto that never coalesced to form a planet.
b.
fragments of
planetesimals between Mars and Jupiter.
c.
comets that formed
close enough to the Sun to have lost all their volatiles.
d.
objects ejected from
Saturn’s rings.
15.
Why do some short
period comets have orbits within the orbit of Jupiter?
a.
They were created from
the asteroid belt between Mars and Jupiter.
b.
They actually orbit
Jupiter rather than the Sun.
c.
As they traveled to the
inner Solar System from the Kuiper Belt, they suffered a gravitational
encounter with Jupiter, which trapped them.
d.
As they traveled to the
inner Solar System from the Kuiper Belt, they collided with one another and no
longer had enough speed to reach the Kuiper Belt again.
16.
The Kirkwood gaps are
regularly spaced gaps in the asteroid distribution. What causes the gaps to
appear?
a.
The pressure of the
solar wind is especially strong at these locations, evacuating asteroids out of
them.
b.
They are regions where
gravitational pull from Mars is overcome by gravitational pull from Jupiter.
c.
They are regions where
an object and Jupiter would regularly line up during their orbits, causing the
object to repeatedly be tugged by Jupiter’s gravity until it leaves that orbit.
d.
They are regions
between Jupiter and Saturn where the combined effect of both planets’ gravity
prevents objects from orbiting there.
17.
Most asteroids are
located between the orbits of
a.
Earth and Mars.
b.
Mars and Jupiter.
c.
Jupiter and Saturn.
d.
Neptune and Pluto.
e.
the Kuiper Belt and the
Oort Cloud.
18.
Most asteroids are
a.
very large (>100 km).
b.
large (30−100 km).
c.
medium (10−30 km).
d.
small (1−10 km).
e.
very small (<1 km).
19.
The mass of all the
known asteroids combined is approximately equal to
a.
half the mass of Earth.
b.
three times the mass of
Earth.
c.
twice the mass of Mars.
d.
the mass of Mars.
e.
less than one-third the
mass of the Moon.
20.
Which group of
asteroids regularly crosses Earth’s orbit and thus might possibly collide with
our planet?
a.
the Amors
b.
the Atens
c.
the Kuiper Belt objects
d.
the Trojans
e.
all of the above
21.
Asteroids are primarily
composed of
a.
hydrogen and helium.
b.
ice and dust.
c.
rock.
d.
iron.
e.
methane.
22.
Most asteroids are
closest in shape to
a.
a potato.
b.
a banana.
c.
a hot dog.
d.
a stick.
e.
a baseball.
23.
The darkest asteroids
are
a.
M-type.
b.
S-type.
c.
C-type.
d.
A-type.
e.
Q-type.
24.
Iron meteorites are
fragments of which type of asteroid?
a.
A-type
b.
C-type
c.
M-type
d.
Q-type
e.
S-type
25.
Carbonaceous chondrite
meteorites are fragments of which type of asteroid?
a.
A-type
b.
C-type
c.
M-type
d.
Q-type
e.
S-type
26.
Until spacecraft flew
by asteroids, scientists did not have a good idea of what they looked like.
Which of the following missions was the first to fly by an asteroid?
a.
NEAR Shoemaker
b.
Rosetta
c.
Galileo
d.
Dawn
e.
Stardust
27.
The most
straightforward way to determine the mass of an asteroid is if it has
a.
a rocky composition.
b.
a moon.
c.
an orbit that lies
between Earth and Mars.
d.
carbonaceous
chondrites.
e.
a magnetic field.
28.
In November 2005, the
Japanese spacecraft Hayabusa brought back a sample from which type of
object for the first time?
a.
comet
b.
asteroid
c.
moon
d.
terrestrial planet
e.
gas giant planet
29.
Remnants of volcanic
activity on the asteroid Vesta indicate that members of the asteroid belt
a.
were once part of a
single protoplanet that was shattered by collisions.
b.
have all undergone
significant chemical evolution since formation.
c.
occasionally grow large
enough to become differentiated and geologically active.
d.
were once a part of a
young Mars.
e.
used to be volcanic
moons orbiting other planets.
30.
What is the relative
importance of collisions between comets compared to collisions between
meteoroids and asteroids?
a.
They are not very
important.
b.
They are very
important.
c.
They are somewhat
important, especially for short-period comets.
d.
They are only important
for long-period comets.
31.
Which type of comet is
the most common?
a.
short-period comets
b.
long-period comets
c.
There are approximately
equal numbers of both.
d.
Astronomers have no way
of knowing this.
32.
How do astronomers
identify the parent comet of a meteor observed in Earth’s atmosphere?
a.
They use the brightness
of the meteor.
b.
They accurately measure
the time of the night when the meteor is seen.
c.
They measure how long a
streak the meteor generates in the atmosphere.
d.
They use the speed and
direction of a cometary meteor’s flight to identify its parent comet.
33.
Identify the object
shown in the figure below.
a.
an active comet
b.
a meteor shower
c.
a meteorite
d.
an asteroid
e.
zodiacal dust
34.
A comet having an orbit
of 50 years would likely have come from the
a.
Atens family.
b.
Oort Cloud.
c.
Trojan family.
d.
zodiacal zone.
e.
Kuiper Belt.
35.
Most comets originate
a.
near Earth and Venus,
in the early Solar System.
b.
far from the planets,
many thousands of astronomical units (AU) from the Sun.
c.
from the region between
the orbits of Jupiter and Neptune.
d.
between the Sun and
Mercury.
e.
between the orbits of
Mars and Jupiter.
36.
The one orbital
characteristic that both short- and long-period comets share is
a.
mostly prograde orbits.
b.
orbits with completely
random tilts.
c.
mostly retrograde
orbits.
d.
orbital periods longer
than any planet.
e.
highly eccentric
orbits.
37.
Approximately how often
does a spectacularly active, visible comet appear?
a.
once a year
b.
once every 5 years
c.
once every 10 years
d.
once every 50 years
e.
once every 1,000 years
38.
Comet Halley is unique
because
a.
it was the first comet
whose return was predicted.
b.
it is a member of the
Jovian family but has a retrograde orbit.
c.
its period is less than
a human lifetime.
d.
it was successfully
visited by a spacecraft.
e.
it was the brightest
comet ever observed by humans.
39.
With a semimajor axis
of 18 AU, Comet Halley has a period of
a.
7 years.
b.
16 years.
c.
32 years.
d.
67 years.
e.
76 years.
40.
The nucleus of the
typical comet is approximately _________ in size.
a.
10 km
b.
1,000 km
c.
100 m
d.
10 m
e.
1 cm
41.
The nuclei of a comet
is mostly
a.
solid ice.
b.
solid rock.
c.
liquid water.
d.
a porous mix of ice and
dust.
e.
frozen carbon dioxide.
42.
When a comet comes
close to the Sun, its volatile ice sublimates and transforms directly from the
solid to _________ phase.
a.
liquid
b.
crystalline
c.
energized
d.
gas
e.
ionized
43.
Why does the dust tail
separate from the ion tail?
a.
The dust has no charge,
so it is not affected by the solar wind.
b.
Dust cannot sublimate
as ice can, so it cannot form a tail as easily.
c.
The dust tail forms on
the leading side of the nucleus, whereas the gas tail forms on the opposite
side.
d.
Dust particles are more
massive than ions, so their accelerations are less.
e.
The dust tail has the
opposite charge as the ion tail.
44.
Which of the following
comets has not been visited by spacecraft?
a.
Halley
b.
Wild 2
c.
Tempel 1
d.
Hartley 2
e.
Shoemaker-Levy 9
45.
Comet nuclei, absent
their tails, are very dark because
a.
they are made of water
ice.
b.
they have iron and
nickel mixed with ice.
c.
they have organic
molecules mixed with ice.
d.
they are covered in
rock.
e.
they are too cold to
emit any light.
46.
Suppose we discover a
comet whose orbit was very highly eccentric, retrograde, had a very large tilt
with respect to the ecliptic plane, and a period of 2,000 years. Where is the
most likely place of origin for this comet?
a.
the Kuiper Belt
b.
the Oort Cloud
c.
the asteroid belt
d.
the Jovian family
e.
outside the Solar
System
47.
Which of the following
does not describe comets in the Oort Cloud?
a.
long period
b.
pristine condition
c.
cold temperatures
d.
randomly directed
orbits
e.
flattened distribution
in space
48.
What is the main source
of meteors?
a.
short-period comets
b.
long-period comets
c.
asteroids
d.
terrestrial planets
49.
Which type of meteorite
is most commonly found on Earth?
a.
metallic
b.
stony
c.
glassy
d.
They are all equally
common.
50.
What implication does
the composition of cometary nuclei have for the creation of life?
a.
They hold water, which
is needed by all life.
b.
They hold organic
compounds, evidence that the ingredients necessary for the creation of life
were present in the early solar nebula.
c.
Bacteria have been
found in cometary nuclei, proving that life on Earth came from comets.
d.
They hold oxygen, which
is needed for all life.
51.
The minimum size of a
meteoroid that is capable of surviving its passage through Earth’s atmosphere
and hitting the ground is about as big as
a.
a car.
b.
a house.
c.
a basketball.
d.
a grain of sand.
e.
your fist.
52.
The Perseid meteor
shower will occur
a.
every month.
b.
every year.
c.
every 4 years.
d.
every 76 years.
e.
every 132 years.
53.
The meteoroids in the
Leonids meteor shower, which occurs every November, come from
a.
dust in the
star-forming Leo nebula.
b.
dust melted off Comet
Tempel-Tuttle.
c.
debris from the
collision of Comet Shoemaker-Levy 9.
d.
zodiacal dust.
e.
dust blown off of
Earth’s surface.
54.
The Lyrid meteor shower
occurs every year on approximately April 21 because
a.
the Lyrae constellation
is directly overhead at midnight.
b.
Earth passes through a
cloud of debris left behind by Comet Thatcher.
c.
Earth passes through a
cloud of debris left over from the Solar System’s formation.
d.
Earth undergoes a
periodic volcanic eruption every April.
e.
the Sun is located in
the Lyrae constellation at noon.
55.
A large meteor shower
will often occur once a year because
a.
Earth typically has one
large volcanic eruption every year.
b.
Earth’s orbit passes
through the Apollo asteroid belt.
c.
the Sun goes through a
yearly solar cycle.
d.
Jupiter routinely
disturbs the orbits of asteroids in the Jovian belt.
e.
Earth passes through
the debris left behind by a specific comet.
56.
Identify the phenomenon
shown in the figure below.
a.
an active comet
b.
a meteor shower
c.
a meteorite
d.
an asteroid
e.
zodiacal dust
57.
Meteor showers appear
as if they are coming from one particular place in the sky because
a.
that is the direction
in which the comet is coming toward us.
b.
that is the direction
in which the comet is moving away from us.
c.
that is the direction
toward which Earth is traveling.
d.
that is the direction
Earth just passed.
e.
that is the location in
the sky from which the meteors originate.
58.
Antarctica is the best
hunting ground for meteorites for all of the following reasons except
a.
the ground is covered
with ice.
b.
more meteorites fall
there than on other locations on Earth.
c.
few native rocks are
found on the glaciers.
d.
meteorites are
protected from weathering and contamination there.
e.
by searching at
different depths in the ice you can determine the history of impacts over time.
59.
Identify the object
shown in the figure below.
a.
a meteor
b.
a chondrite meteorite
c.
an achondrite meteorite
d.
an iron meteorite
e.
an asteroid
60.
Meteorites contain
clues to all of the following except
a.
the age of the Solar
System.
b.
the temperature in the
early solar nebula.
c.
changes in the rate of
cratering in the early Solar System.
d.
the composition of the
primitive Solar System.
e.
the physical processes
that controlled the formation of the Solar System.
61.
The most common type of
meteorites are
a.
stony meteorites.
b.
iron meteorites.
c.
achondrite meteorites.
d.
stony-iron meteorites.
e.
carbonaceous chondrite
meteorites.
62.
Which group of
meteorites represents the conditions in the earliest stages of the formation of
the Solar System?
a.
chondrites
b.
achondrites
c.
icy meteorites
d.
iron meteorites
e.
stony-iron meteorites
63.
Although most
meteorites have ages around 4.5 billion years, a small subset has ages around
1.3 billion years. What caused the substantial difference in age between these
two populations of meteorites?
a.
These meteorites just
happened to form later than most meteorites.
b.
Not all meteorites hit
Earth in the early Solar System. We should expect to find younger meteorites as
more meteors pass through the atmosphere.
c.
The younger meteorites
were created when a protoplanet collided with Earth, creating the Moon. The
leftover fragments became meteorites.
d.
These meteorites were
thrown into space after an impact with Mars and afterward some happened to
collide with Earth.
e.
The younger ones are
the result of comets repeatedly passing close to the Sun, melting their
surfaces and making them appear younger.
64.
Identify the object
shown in the image below.
a.
an active comet
b.
a meteor shower
c.
a meteorite
d.
an asteroid
e.
zodiacal dust
65.
most?
a.
comets
b.
asteroids
c.
the Moon
d.
volcanoes on Earth
e.
tornados on Earth
66.
All of the zodiacal
dust in the Solar System combined is roughly equal in mass to
a.
a meteoroid.
b.
a comet.
c.
Jupiter.
d.
the Moon.
e.
a terrestrial planet.
67.
In the early universe,
when the Solar System had yet to be cleared of the debris out of which it
formed, which type of object would have been most likely to deposit water onto
Earth’s surface?
a.
comets
b.
asteroids
c.
a Mars-sized
protoplanet
d.
Both comets and
asteroids appear to be sources.
e.
None, because water is
not a major component of any of the objects above.
68.
In 1994, dozens of
fragments of Comet Shoemaker-Levy 9 collided with
a.
Jupiter.
b.
Earth.
c.
Neptune.
d.
the Moon.
e.
Saturn.
69.
Consider a meteoroid
with a diameter of 10 cm and a mass of 2 kg that hits Earth head-on while traveling
at a speed of 25,000 m/s. How many times larger or smaller is the meteoroid’s
kinetic energy compared to that of a typical train whose mass is 2 × 106 kg
and speed is 25 m/s?
a.
The meteoroid’s kinetic
energy is equal to that of the train.
b.
The meteoroid’s kinetic
energy is 1,000 times less than that of the train.
c.
The meteoroid’s kinetic
energy is 1,000 times greater than that of the train.
d.
The meteoroid’s kinetic
energy is 106 times greater than that of the train.
e.
The meteoroid’s kinetic
energy is 109 times greater than that of the train.
70.
A recent estimate finds
that approximately 800 meteorites with mass greater than 0.1 kg strike the
surface of Earth each day. If a house covers an area of roughly 100 m2,
then what is the probability that your house will be struck by a meteorite in
your 100-year lifetime? Note that the radius of Earth is 6,400 km.
a.
1 in 1 × 104
b.
1 in 2 × 105
c.
1 in 4 × 106
d.
1 in 6 × 107
e.
1 in 8 × 108
SHORT ANSWER
1.
List the names of the
known dwarf planets and their approximate location in the Solar System.
2.
Give the two main
differences between the orbital properties of the dwarf planet Pluto and those
of planets in our Solar System.
3.
The dwarf planet Eris
is covered in methane ice, whereas the surface of Saturn’s moon Enceladus is
covered in water ice. Why does methane exist in ice form on Eris but not Enceladus?
4.
An astronomer observes
a dwarf planet that has a small diameter but is rather bright, so she concludes
that it must have a high albedo. Why?
5.
Name three properties
of the dwarf planets Pluto and Eris that are similar.
6.
Suppose a collision
between two large asteroids creates a handful of smaller asteroid fragments,
some of which orbit at 2.7 AU from the Sun and some which orbit at 2.5 AU from
the Sun. Based on the asteroid distribution plot shown in Figure 12.5, which of
the two smaller asteroid groups will have a stable orbit around the Sun, and
why?
7.
Give examples of a
C-type asteroid and an S-type asteroid that have been observed by spacecraft.
What did we learn about each type?
8.
What does the existence
of M-type asteroids tell us about their origin?
9.
Comets have highly
eccentric orbits, with eccentricities of 0.95 to 0.99 being common. Suppose a
certain comet has an eccentricity of 0.99. If the semimajor axis of its orbit
is 2,500 AU, what will be its distance at perihelion and at aphelion? Is this
most likely a Kuiper Belt object or an Oort Cloud comet? (Note: For an ellipse,
a(1 + e) is the distance from one focus to the farther edge
of the long axis and a(1 − e) is the
distance from the same focus to the closer edge of the long axis.)
10.
Why are asteroids
considered to be excellent sources for studying conditions in the early Solar
System, whereas planets themselves are not?
11.
Describe the
relationship between planets, dwarf planets, planetesimals, asteroids, and
meteorites.
12.
Consider three comets
that have orbital periods of 10, 100, and 1,000 years. Where would each of
these comets likely originate, in the Oort Cloud or the Kuiper Belt? If you
wanted to study material that was the best example of pristine Solar System
material, which would you study?
13.
Why do long-period
comets usually put on a much more visually spectacular display than
short-period comets?
14.
In its 1986 trip around
the Sun, it was estimated that Comet Halley lost approximately 100 billion kg
of material. The total mass of the nucleus was estimated to be 3 × 1014
kg. Assuming the mass loss rate is constant with each passage, and assuming the
nucleus remains intact until there is nothing left, how many more times will we
see Comet Halley? Explain why your answer is an upper limit.
15.
Do icy cometary nuclei
melt and move from solid to liquid phase as they are warmed by the radiation
from the Sun?
16.
Assume the larger
circle shown in the figure below is the Sun, and the smaller circle is the head
of a comet. If the comet is moving away from the Sun, draw and label the
two tails onto the comet.
17.
How is it possible for
the tail of a comet to actually move ahead of the comet itself?
18.
Looking at the image
below, identify the two tails.
19.
If you can model the
mass in Comet Halley as a sphere 5 km in radius, what is its density if it has
a mass of 1014 kg? How does that density compare to that of water
(1,000 kg/m3)?
20.
Let’s say that you
discovered a comet in the outer Solar System that had an average albedo of 0.6.
If its surface was composed of a mixture of organic substances, which had an
albedo of 0, and ice, which had an albedo of 1.0, then what percent of its
surface is covered by organic substances?
21.
Why does a comet usually
have two tails, one that is straight and one that is curved? What materials
compose each tail, and why do they have different shapes?
22.
Give the definitions of
meteoroid, meteor, and meteorite, and clearly explain how they differ.
23.
You find a blackened rock
lying on top of the snow. You find that it is fairly dense and suspect it might
be a meteorite. You take it to a lab, and they cut it open to reveal many small
spherical, glassy particles set into the surrounding rock. Is this a meteorite?
Why, or why not?
24.
How might impacts have
helped increase Earth’s water supply in the early history of the Solar System?
25.
What is the best way to
look for comet and asteroid dust in the solar system?
26.
What is the origin of
meteor showers, and why are they sometimes more intense than at other times?
27.
What kind of comet was
Shoemaker-Levy 9, and why?
28.
Describe two modern-day
(within the past 150 years) events when comets or asteroids collided with a
planet. Cite the planet, and describe the major consequences of the collision.
29.
Describe two challenges
faced by astronomers in identifying potential collisions between Earth and
Earth-crossing asteroids and meteorites.
30.
Consider a small comet
nucleus whose diameter is 1 km and mass is 5 × 1011
kg. It hits Earth head-on, traveling at a speed of 1,000 m/s. How many times
larger or smaller is the comet’s kinetic energy compared to that of a typical
train pulling 20 boxcars whose total mass is 2 × 106 kg
and speed is 25 m/s?
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Chapter 13: Taking the
Measure of Stars
Learning
Objectives
Define the bold-faced vocabulary terms within the chapter.
13.1 Astronomers Can Measure the Distance,
Brightness, and Luminosity of Stars
Illustrate how parallax is used to measure the distance to
nearby stars.
Multiple Choice: 1, 2, 3, 4, 6, 7, 8, 9, 10
Short Answer: 1, 2, 5
Relate luminosity, brightness, and distance.
Multiple Choice: 11, 12, 13, 14, 15
Short Answer: 3
13.2 Astronomers Can Determine the
Temperature, Size, and Composition of Stars
Explain how the spectrum or color of a star is used to
determine its temperature.
Multiple Choice: 18, 23, 24, 25
Short Answer: 8, 9, 10
List the spectral types of stars in order of decreasing
temperature.
Multiple Choice: 26
Explain why stars of different temperatures have different
spectral lines.
Multiple Choice: 20, 22, 31
Short Answer: 11
Relate the spectral type of a star to its temperature and
size.
Multiple Choice: 19, 27, 28, 29, 30, 35, 36, 40
Short Answer: 13
Illustrate how a stellar spectrum reveals the star’s chemical
composition.
Multiple Choice: 21, 32, 33, 34
Short Answer: 12
13.3 Measuring the Masses of Stars in
Binary Systems
Show how Kepler’s laws and orbital velocities are used to
determine the masses of binary stars.
Multiple Choice: 42, 45, 46, 48, 51
Short Answer: 20
Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
Multiple Choice: 44, 49, 50
Short Answer: 18, 19, 21
13.4 The Hertzsprung-Russell Diagram Is
the Key to Understanding Stars
Define the axes of the H-R diagram, and the direction in
which each axis increases.
Multiple Choice: 52, 53, 60
Short Answer: 28
Compare the temperature, luminosity, spectral type, color,
and size of stars at different positions on the H-R diagram.
Multiple Choice: 54, 55, 56, 57, 62
Short Answer: 15, 27
Illustrate how the H-R diagram is used to determine the
distance to a star.
Explain how the luminosity class of a star effects the use of
spectroscopic parallax.
Short Answer: 24, 25, 26
Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
Multiple Choice: 61, 64, 65, 66, 67, 68, 69
Short Answer: 22, 23, 29, 30
Relate how common main-sequence stars are relative to other
stars in the galaxy.
Multiple Choice: 58, 59
Short Answer: 31
Compare and contrast the habitable zones around different
types of stars.
Multiple Choice: 63, 70
Short Answer: 32
Working It Out 13.1
Compute the distance of a star given its parallax.
Multiple Choice: 5
Short Answer: 4
Working It Out 13.2
Relate magnitude to the brightness of a star.
Short Answer: 6, 7
Compare and contrast apparent and absolute magnitude.
Working It Out 13.3
Use the Stefan-Boltzmann law to find the size of a star from
its temperature and luminosity.
Multiple Choice: 37, 38, 39
Short Answer: 14
Working It Out 13.4
Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
Multiple Choice: 41, 43, 47
Short Answer: 16, 17
MULTIPLE CHOICE
1.
What advantage do you
gain by having two eyes that are separated on your face, rather than being very
close together?
a.
better collecting area,
which allows you to see dimmer objects
b.
double vision, which
allows you to see multiple objects at once
c.
color vision, which
allows you to determine temperatures
d.
stereoscopic vision,
which allows you to determine distances
e.
better magnification,
which allows you to see smaller objects
ANS: D DIF:
Medium REF: Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
2.
To measure the parallax
of the most distant stars measurable, we would make two measurements of the
star’s position on the sky separated by
a.
6 hours.
b.
12 hours.
c.
24 hours.
d.
6 months.
e.
12 months.
ANS: D DIF: Easy REF: Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
3.
Parallax is used to
measure a star’s
a.
distance,
b.
velocity,
c.
luminosity,
d.
mass,
e.
radius,
ANS: A DIF: Easy REF: Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
4.
How is the distance to
a star related to its parallax?
a.
Distance is directly
proportional to parallax.
b.
Distance is inversely
proportional to parallax.
c.
Distance is directly
proportional to parallax squared.
d.
Distance is inversely
proportional to parallax squared.
e.
Distance and parallax
are not related to each other at all.
ANS: B DIF:
Medium REF: Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
5.
If a star’s measured
parallax is 0.2 arcsec, what is its distance?
a.
2 pc
b.
5 pc
c.
20 pc
d.
40 pc
e.
50 pc
ANS: B DIF:
Medium REF: Working It Out 13.1
MSC: Applying
OBJ: Compute the distance of a star given its parallax.
6.
If a star’s distance is
10 pc, what is its parallax?
a.
0.01 arcsec
b.
0.05 arcsec
c.
0.1 arcsec
d.
0.5 arcsec
e.
1 arcsec
ANS: C DIF:
Medium REF: Section 13.1
MSC: Applying
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
7.
How many arcseconds are
there in 1 degree?
a.
60
b.
360
c.
3,600
d.
6,000
e.
36,000
ANS: C DIF: Easy REF: Section 13.1
MSC: Remembering
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
8.
With today’s advanced
technology, what is the maximum distance to which we can measure a star’s
distance using its parallax?
a.
about 100,000 parsecs
b.
about 10,000 parsecs
c.
about 1000 parsecs
d.
about 100 parsecs
ANS: C DIF: Easy REF: Section 13.1
MSC: Applying
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
9.
A parsec is a measure
of
a.
time.
b.
size.
c.
distance.
d.
both b. and c.
ANS: D DIF:
Medium REF: Section 13.1
MSC: Remembering
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
10.
Stars with a larger
brightness must be
a.
closer to us than
fainter stars.
b.
larger in size than
fainter stars.
c.
intrinsically brighter
than fainter stars.
d.
any combination of the
above.
ANS: D DIF: Easy REF: Section 13.1
MSC: Remembering
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
11.
The absolute magnitude
of a star is a measure of its
a.
luminosity.
b.
composition.
c.
distance.
d.
color.
ANS: A DIF:
Medium REF: Section 13.1
MSC: Remembering
OBJ: Relate luminosity, brightness, and distance.
12.
Star A and star B
appear equally bright, but star A is twice as far away from us as star B. Which
of the following is true?
a.
Star A is twice as luminous
as star B.
b.
Star A is four times as
luminous as star B.
c.
Star B is twice as
luminous as star A.
d.
Star B is four times as
luminous as star B.
e.
Star A and star B have
the same luminosity because they have the same brightness.
ANS: B DIF:
Medium REF: Section 13.1
MSC: Applying
OBJ: Relate luminosity, brightness, and distance.
13.
Two main-sequence stars
have the same temperature. If star A is four times brighter than star B, then
a.
star B is two times
farther away than star A.
b.
star B is four times
farther away than star A.
c.
star B is eight times
farther away than star A.
d.
star B and star A lie
at the same distance from us.
e.
it is impossible to
determine their relative distances from the information given.
ANS: A DIF:
Medium REF: Section 13.1
MSC: Applying
OBJ: Relate luminosity, brightness, and distance.
14.
What is the difference
between brightness and luminosity?
a.
These are different
names for the same property.
b.
Luminosity is how much
light we see from a star; brightness is how much light it emits.
c.
Brightness is how much
light we see from a star; luminosity is how much light it emits.
d.
Luminosity measures
size; brightness measures temperature.
e.
Brightness measure
size; luminosity measures temperature.
ANS: C DIF: Easy REF: Section 13.1
MSC: Understanding
OBJ: Relate luminosity, brightness, and distance.
15.
Star A is a red star.
Star B is a blue star. You are able to determine that both stars are the same
size. Which star is brighter?
a.
Star A is brighter.
b.
Star B is brighter.
c.
They have the same
brightness.
d.
We also need to know
the distance of the stars to determine their brightness.
e.
Color is not related to
brightness at all.
ANS: D DIF:
Medium REF: Section 13.1
MSC: Applying
OBJ: Relate luminosity, brightness, and distance.
16.
The star named Capella
has an apparent magnitude of 0, while the star named Polaris has an apparent
magnitude of 2. This means that Capella is _________ than Polaris.
a.
18 times fainter
b.
6 times fainter
c.
2 times fainter
d.
2 times brighter
e.
6 times brighter
ANS: E DIF:
Medium REF: Working It Out 13.2
MSC: Applying
OBJ: Relate magnitude to the brightness of a star.
17.
Star A and star B both
have the same temperature but different sizes and distances. As a result, star
A is more luminous than star B, but star B is brighter than star A. Which of
these statements about the absolute and apparent magnitudes of the two stars is
correct?
a.
Star A has a larger
apparent magnitude and a larger absolute magnitude.
b.
Star A has a larger
apparent magnitude, while star B has a larger absolute magnitude.
c.
Star B has a larger
apparent magnitude and a larger absolute magnitude.
d.
Star B has a larger
apparent magnitude, while star A has a larger absolute magnitude.
e.
Both stars have the
same apparent and absolute magnitudes.
ANS: B DIF:
Medium REF: Working It Out 13.2
MSC: Applying
OBJ: Relate magnitude to the brightness of a star.
18.
You observe two stars
in a visual binary system using a blue filter that is centered at a wavelength
of 550 nm and a red filter that is centered at a wavelength of 650 nm. Star A
has a temperature of 10,000 K, while star B has a temperature of 4000 K, and
you know that both stars are the same size. Which star will be the brightest in
each filter?
a.
Star A is the brightest
in the blue filter, and star B is the brightest in the red filter.
b.
Star B is the brightest
in the blue filter, and star A is the brightest in the red filter.
c.
Star A is the brightest
in both filters.
d.
Star B is the brightest
in both filters.
e.
Both stars have the
same brightness in each filter.
ANS: C DIF:
Difficult REF: Section 13.2
MSC: Applying
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
19.
Stars that have
spectral type B ___________ in temperature compared with stars that have
spectral type M.
a.
are cooler
b.
are hotter
c.
are the same
d.
are sometimes hotter
and sometimes cooler
ANS: B DIF:
Medium REF: Section 13.2
MSC: Remembering
OBJ: Relate the spectral type of a star to its temperature.
20.
Which spectral type has
the strongest hydrogen absorption lines?
a.
O
b.
B
c.
A
d.
M
ANS: C DIF:
Medium REF: Section 13.2
MSC: Remembering
OBJ: Explain why stars of different temperatures have
different spectral lines.
21.
Which of the following
is not directly measurable from the absorption lines of a star?
a.
the surface temperature
of the star
b.
the identity of an atom
producing a given absorption line
c.
the ionization stage of
the atom producing a given absorption line
d.
the distance to the
star
ANS: D DIF:
Medium REF: Section 13.2
MSC: Understanding
OBJ: Illustrate how a stellar spectrum reveals the star’s
chemical composition.
22.
Which stars show the
largest amount of absorption from molecules such as TiO and CN?
a.
the least massive
main-sequence stars
b.
the most massive
main-sequence stars
c.
only main-sequence
stars with masses close to 1 solar mass
d.
only red giant stars
ANS: A DIF:
Difficult REF: Section 13.2
MSC: Remembering
OBJ: Explain why stars of different temperatures have
different spectral lines.
23.
Star A is a red star.
Star B is a blue star. Which star is hotter?
a.
Star A is hotter.
b.
Star B is hotter.
c.
They are the same
temperature.
d.
We also need to know
the luminosities of the stars to determine their temperatures.
e.
Color is not related to
temperature at all.
ANS: B DIF: Easy REF: Section 13.2
MSC: Applying
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
24.
Star A is a red star.
Star B is a blue star. You are able to determine that both stars are the same
size. Which star is more luminous?
a.
Star A is more
luminous.
b.
Star B is more
luminous.
c.
They have the same
luminosities.
d.
We also need to know
the distance of the stars to determine their luminosity.
e.
We cannot tell because
color is not related to luminosity.
ANS: B DIF: Easy REF: Section 13.2
MSC: Applying
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
25.
What type of spectrum
do most stars produce?
a.
an absorption spectrum
on top of a blackbody spectrum
b.
an emission spectrum on
top of a blackbody spectrum
c.
an absorption spectrum
on top of an emission spectrum
d.
a pure emission
spectrum
e.
a pure blackbody
spectrum
ANS: A DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
26.
Which sequence
correctly lists the spectral classes of stars in order from hottest to coolest?
a.
A B F G K M O
b.
O A B G F M K
c.
A F O B M G K
d.
O B A F G K M
e.
M K G F A B O
ANS: D DIF: Medium REF: Section 13.2
MSC: Remembering
OBJ: List the spectral types of stars in order of decreasing
temperature.
27.
The spectral class of a
star is related to its
a.
luminosity.
b.
brightness.
c.
radius.
d.
mass.
e.
temperature.
ANS: E DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Relate the spectral type of a star to its temperature
and size.
28.
What spectral class is
the Sun?
a.
A0
b.
B7
c.
F5
d.
M3
e.
G2
ANS: E DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Relate the spectral type of a star to its temperature
and size.
29.
Two stars with similar
temperatures but different sizes will have
a.
similar spectral types
but different luminosities.
b.
similar luminosities
but different brightnesses.
c.
similar brightnesses
but different distances.
d.
similar distances but
different masses.
e.
similar masses but
different spectral types.
ANS: A DIF:
Medium REF: Section 13.2
MSC: Applying
OBJ: Relate the spectral type of a star to its temperature
and size.
30.
A star classified as a
K0III star is
a.
a giant that is cooler
than the Sun.
b.
a supergiant that is
hotter than the Sun.
c.
a main-sequence star
that is hotter than the Sun.
d.
a subgiant that is
cooler than the Sun.
e.
a dwarf that is hotter
than the Sun.
ANS: A DIF:
Difficult REF: Section 13.4
MSC: Remembering
OBJ: Relate the spectral type of a star to its temperature and
size.
31.
Why do O- and B-type
stars have weaker hydrogen absorption lines than A-type stars?
a.
O- and B-type stars are
cooler than A-type stars.
b.
O- and B-type stars are
smaller than A-type stars.
c.
A larger fraction of
hydrogen atoms in O- and B-type stars is ionized.
d.
O- and B-type stars
have converted much more of their hydrogen into heavier elements.
e.
A-type stars have a
higher mass than O- and B-type stars, so they have more hydrogen.
ANS: C DIF:
Difficult REF: Section 13.2
MSC: Understanding
OBJ: Explain why stars of different temperatures have
different spectral lines.
32.
When astronomers refer
to “heavy elements,” which elements are they talking about?
a.
all elements
b.
all elements more
massive than hydrogen
c.
all elements more
massive than helium
d.
all elements more massive
than carbon
e.
all elements more
massive than iron
ANS: C DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Illustrate how a stellar spectrum reveals the star’s
chemical composition.
33.
Stars are made mostly
of
a.
helium.
b.
oxygen.
c.
hydrogen.
d.
nitrogen.
e.
carbon.
ANS: C DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Illustrate how a stellar spectrum reveals the star’s
chemical composition.
34.
The fraction of the
Sun’s mass that is made of heavy elements is
a.
0.5 percent.
b.
2 percent.
c.
10 percent.
d.
20 percent.
e.
50 percent.
ANS: B DIF:
Medium REF: Section 13.2
MSC: Remembering
OBJ: Illustrate how a stellar spectrum reveals the star’s
chemical composition.
35.
If we know the
temperature and luminosity of a star, we can also calculate its
a.
radius.
b.
mass.
c.
chemical composition.
d.
brightness.
e.
all of the above
ANS: A DIF: Easy REF: Section 13.2
MSC: Applying
OBJ: Relate the spectral type of a star to its temperature
and size.
36.
Star C is a red star.
Star D is a blue star. Which has a larger radius?
a.
Star C has a larger
radius.
b.
Star D has a larger
radius.
c.
Stars C and D have the
same radius.
d.
We also need to know
the luminosities of the stars to determine their radii.
e.
We cannot determine the
radii because color is not related to the radius.
ANS: D DIF:
Medium REF: Section 13.2
MSC: Applying
OBJ: Relate the spectral type of a star to its temperature
and size.
37.
Star E is the same
temperature as star F, but star E is four times as luminous as star F. How do
the radii of the stars compare?
a.
The radius of star E is
twice that of star F.
b.
The radius of star E is
four times that of star F.
c.
The radius of star F is
twice that of star E.
d.
The radius of star F is
four times that of star E.
e.
The radii are the same
length.
ANS: A DIF:
Difficult REF: Working It Out 13.3
MSC: Applying
OBJ: Use the Stefan-Boltzmann law to find the size of a star
from its temperature and luminosity.
38.
If star A has a
temperature that is twice as hot as the Sun, but it has the same luminosity as
the Sun, the diameter of star A must be _________ times the diameter of the
Sun.
a.
16
b.
4
c.
2
d.
e.
ANS: E DIF:
Difficult REF: Working It Out 13.3
MSC: Applying
OBJ: Use the Stefan-Boltzmann law to find the size of a star
from its temperature and luminosity.
39.
The bright star named
Rigel has a luminosity of 66,000 L⊙and a temperature of 11,000 K. What is its radius? Note that
the temperature of the Sun is 5,800 K.
a.
5 R⊙
b.
30 R⊙
c.
70 R⊙
d.
135 R⊙
e.
190 R⊙
ANS: C DIF:
Difficult REF: Working It Out 13.3
MSC: Applying
OBJ: Use the Stefan-Boltzmann law to find the size of a star
from its temperature and luminosity.
40.
Which stars are the
most common?
a.
Stars with a mass and a
radius larger than the Sun’s are the most common.
b.
Stars with a smaller
mass and radius than the Sun’s are most common.
c.
Stars with a mass
larger than the Sun’s and a radius smaller than the Sun’s are the most common.
d.
Stars with a mass
smaller than the Sun’s and a radius larger than the Sun’s are the most common.
e.
All of the above are
equally common.
ANS: B DIF: Easy REF: Section 13.2
MSC: Remembering
OBJ: Relate the spectral type of a star to its temperature
and size.
41.
Star X and star Y are 5
AU apart from each other. Star X is four times as massive as star Y. The center
of mass of this system is _________ AU away from star X and _________ AU away
from star Y.
a.
3; 2
b.
2; 3
c.
2.5; 2.5
d.
1; 4
e.
4; 1
ANS: D DIF:
Difficult REF: Working It Out 13.4
MSC: Applying
OBJ: Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
42.
The faster-moving star
in a binary is the
a.
less massive star.
b.
more massive star.
c.
smaller radius star.
d.
larger radius star.
e.
lower temperature star.
ANS: A DIF:
Medium REF: Section 13.3
MSC: Applying
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
43.
In a binary star system
that contains stars with 2M⊙ and 1M⊙, the velocity of the 2M⊙ star will be _________
times the velocity of the 1M⊙ star.
a.
0.2
b.
0.5
c.
1
d.
2
e.
3
ANS: B DIF:
Medium REF: Working It Out 13.4
MSC: Applying
OBJ: Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
44.
Which of the following
properties are NOT useful in determining the masses of stars in a typical
binary system?
a.
The period of the
orbits of the two stars is not useful.
b.
The average separation
between the two stars is not useful.
c.
The radii of the two
stars are not useful.
d.
The velocities of the
two stars are not useful.
e.
All of the above are
useful for determining the masses of stars in a binary.
ANS: C DIF:
Medium REF: Section 13.3
MSC: Applying
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
45.
Binary star systems are
extremely useful in studying stars because they allow us to determine
a.
the stars’
temperatures.
b.
the stars’ sizes.
c.
the stars’ masses.
d.
the stars’ distances.
ANS: C DIF: Easy REF: Section 13.3
MSC: Understanding
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
46.
Which of the following
methods is not useful for determining masses of a binary star system having an
orbital plane entirely in the plane of the sky as seen from Earth?
a.
eclipses
b.
the Doppler effect
c.
measuring the wobble of
a visual binary’s path
d.
both a. and b.
ANS: D DIF:
Medium REF: Section 13.3
MSC: Understanding
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
47.
You discover a binary
star system in which star A has a velocity of 10 km/s and star B has a velocity
of 30 km/s. If you study the system further and find out that the orbital
period is 30 days and the orbital separation is a constant 0.3 AU, then what
are the masses of stars A and B?
a.
Star A is 3M⊙, and star B is 1M⊙.
b.
Star A is 1M⊙, and star B is 0.3M⊙.
c.
Star A is 6M⊙, and star B is 2M⊙.
d.
Star A is 2M⊙, and star B is 0.5M⊙.
e.
Star A is 0.3M⊙, and star B is 1M⊙.
ANS: A DIF: Difficult REF: Working It Out 13.4
MSC: Applying
OBJ: Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
48.
Astronomers can measure
the speed of the stars in a binary system by measuring the _________ of the
stars.
a.
temperatures
b.
luminosities
c.
distance
d.
colors
e.
spectra
ANS: E DIF: Easy REF: Section 13.3
MSC: Remembering
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
49.
For which type of
binary system are astronomers able to resolve each of the two stars
individually?
a.
eclipsing binary
b.
spectroscopic binary
c.
visual binary
d.
binaries in which the
two stars have the same mass
e.
binaries in which the
two stars have the same luminosity
ANS: C DIF: Easy REF: Section 13.3
MSC: Remembering
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
50.
Eclipsing binary
systems
a.
orbit in the plane of
the sky.
b.
exhibit large radial
velocity shifts.
c.
contain equal mass
stars.
d.
contain stars that pass
in front of one another during their orbit.
e.
contain stars that can
be resolved as two separate stars.
ANS: D DIF:
Medium REF: Section 13.3
MSC: Remembering
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
51.
Main-sequence stars
range in mass from approximately
a.
0.5 to 10 M⊙.
b.
0.08 to 150 M⊙.
c.
1 to 100 M⊙.
d.
to 75 M⊙.
e.
5 to 50 M⊙.
ANS: B DIF: Easy REF: Section 13.3
MSC: Remembering
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
52.
The Hertzsprung-Russell
diagram is a graph of _________ for stars.
a.
mass versus brightness
b.
size versus mass
c.
luminosity versus
temperature
d.
mass versus spectral
type
e.
luminosity versus
brightness
ANS: C DIF: Easy REF: Section 13.4
MSC: Remembering
OBJ: Define the axes of the H-R diagram, and the direction in
which each axis increases.
53.
Any of the following
properties could be plotted on the horizontal axis of an H-R diagram except
for:
a.
Color
b.
Luminosity
c.
Temperature
d.
Spectral class
e.
All of the above are
plotted on the horizontal axis of an H-R diagram.
ANS: B DIF: Easy REF: Section 13.4
MSC: Remembering
OBJ: Define the axes of the H-R diagram, and the direction in
which each axis increases.
54.
The figure below shows
an H-R diagram, with five stars labeled A through E. Which star has the highest
temperature?
a.
A
b.
B
c.
C
d.
D
e.
E
ANS: A DIF: Easy REF: Section 13.4
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
55.
The figure below shows
an H-R diagram, with five stars labeled A through E. Which star has the highest
luminosity?
a.
A
b.
B
c.
C
d.
D
e.
E
ANS: B DIF: Easy REF: Section 13.4
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
56.
The figure below shows
an H-R diagram, with five stars labeled A through E. Which star has the
smallest radius?
a.
A
b.
B
c.
C
d.
D
e.
E
ANS: D DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
57.
On a typical H-R
diagram, where are the stars with the largest radii located?
a.
in the upper left
corner
b.
in the upper right
corner
c.
in the center
d.
in the lower left
corner
e.
in the lower right
corner
ANS: B DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
58.
What type of star is
most common in the solar neighborhood?
a.
subgiants
b.
supergiant
c.
white dwarf
d.
giant
e.
main-sequence
ANS: E DIF: Easy REF: Section 13.4
MSC: Remembering
OBJ: Relate how common main-sequence stars are relative to
other stars in the galaxy.
59.
Roughly what percentage
of stars in our galaxy are main-sequence stars?
a.
10 percent
b.
25 percent
c.
50 percent
d.
75 percent
e.
90 percent
ANS: E DIF:
Medium REF: Section 13.4
MSC: Remembering
OBJ: Relate how common main-sequence stars are relative to
other stars in the galaxy.
60.
A star’s position in
the H-R diagram is determined by its
a.
temperature and size.
b.
temperature and
distance.
c.
brightness and size.
d.
mass and distance.
ANS: A DIF:
Difficult REF: Section 13.4
MSC: Understanding
OBJ: Define the axes of the H-R diagram, and the direction in
which each axis increases.
61.
A star’s location on
the main sequence is determined entirely by its
a.
mass.
b.
composition.
c.
distance.
d.
size.
ANS: A DIF:
Medium REF: Section 13.4
MSC: Understanding
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
62.
The stars that have the
largest radii are classified as
a.
main sequence stars.
b.
blue supergiants.
c.
red supergiants.
d.
white dwarfs.
ANS: C DIF: Easy REF: Section 13.4
MSC: Understanding
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
63.
In which region of an
H-R diagram would you find the main-sequence stars with the widest habitable
zones?
a.
upper left
b.
upper right
c.
center
d.
lower left
e.
lower right
ANS: A DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Compare and contrast the habitable zones around
different types of stars.
64.
The figure below shows
an H-R diagram, with five stars labeled A through E. Which of the main-sequence
stars has the smallest mass?
a.
A
b.
B
c.
C
d.
D
e.
E
ANS: E DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
65.
What is the approximate
luminosity of a 5 M⊙ main-sequence star?
a.
50 L⊙
b.
80 L⊙
c.
150 L⊙
d.
280 L⊙
e.
510 L⊙
ANS: D DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
66.
What is the approximate
luminosity of a 0.5 M⊙main-sequence star?
a.
0.09 L⊙
b.
0.01 L⊙
c.
0.2 L⊙
d.
0.5 L⊙
e.
0.7 L⊙
ANS: A DIF:
Medium REF: Section 13.4
MSC: Applying
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
67.
The one property of a
main-sequence star that determines all its other properties is its
a.
luminosity.
b.
mass.
c.
temperature.
d.
spectral type.
e.
brightness.
ANS: B DIF: Easy REF: Section 13.4
MSC: Understanding
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
68.
The stars that have the
largest radii are classified as
a.
giants.
b.
ultragiants.
c.
supergiants.
d.
megagiants.
e.
supernovae.
ANS: C DIF: Easy REF: Section 13.4
MSC: Remembering
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
69.
The brightest stars in
the sky also tend to be
a.
the highest-mass stars.
b.
the hottest stars in
the sky.
c.
very near to us (within
5 parsecs).
d.
very luminous.
e.
all of the above
ANS: D DIF:
Difficult REF: Section 13.4
MSC: Applying
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
70.
The habitable zone for
the Sun covers the area that is between _________ from the Sun.
a.
0 to 0.8 AU
b.
0.5 to 10 AU
c.
1.2 to 4.2 AU
d.
0.9 to 1.4 AU
e.
0.2 to 10.2 AU
ANS: D DIF:
Medium REF: Section 13.4
MSC: Remembering
OBJ: Compare and contrast the habitable zones around
different types of stars .
SHORT ANSWER
1.
If a star’s parallax is
measured using identical telescopes, one on Earth and the other on Mars, which
planet’s telescope would measure the biggest parallax? Explain your answer.
ANS: The telescope on Mars would measure a larger parallax.
Because Mars has a larger orbit than the Earth, it will have a greater distance
between the two parallax observations. This greater distance between
observations for the telescope on Mars will lead to a greater apparent motion
of a star.
DIF: Difficult REF:
Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
2.
If you want to measure
the distance to a star via measuring its parallax, how far apart should your
observations of the star ideally be, and why?
ANS: Ideally one would want to observe the star at two
positions as far apart as possible for ease in measuring its parallax. For
Earth, this means your observations should be when the Earth is on opposite
sides of the Sun, such that the two measurement points are separated by 2 AU,
the diameter of Earth’s orbit. This occurs for the two points that are six
months apart from one another.
DIF: Medium REF: Section 13.1
MSC: Understanding
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
3.
Star A is exactly the
same color as star B and appears equally bright. Through stellar parallax
measurements, we find that star B is twice as far away from us as star A.
Determine which star has the largest radius and how much larger it is.
ANS: For stars of equal brightness, luminosity is directly
proportional to their distance squared. If star B is twice as far away, then it
must be four times as luminous as star A. Second, if the two stars are exactly
the same color, then they are also the same temperature. For stars of the same
temperature, luminosity is directly proportional to the square of the radius.
If star B is four times as luminous, it must be twice as big as star A.
DIF: Difficult REF: Section 13.1 MSC:
Applying
OBJ: Relate luminosity, brightness, and distance.
4.
A star with a stellar
parallax of 0.025 arcsecond has a distance of how many parsecs?
ANS: The inverse of stellar parallax given in arcsec-onds is
its distance in parsecs: 
arcseconds = 40 parsecs.
arcseconds = 40 parsecs.
DIF: Medium REF: Working It Out 13.1
MSC: Applying
OBJ: Compute the distance of a star given its parallax.
5.
How is the unit of
length known as a parsec defined?
ANS: The parsec is defined such that an object at a distance
of 1 parsec has a parallax exactly equal to 1 arcsecond.
DIF: Easy REF: Section 13.1
MSC: Remembering
OBJ: Illustrate how parallax is used to measure the distance
to nearby stars.
6.
Rigel is a star with an
apparent magnitude of +0.1, and Betelgeuse is a star with an apparent magnitude of +0.4. Which star
appears brighter, and what is the ratio of their brightnesses?
ANS: Rigel is brighter than Betelgeuse by a factor of 2.512(0.4–0.1)
= 1.32. Thus, Rigel is 32 percent brighter than Betelgeuse.
DIF: Difficult REF: Working It Out
13.2
MSC: Applying
OBJ: Relate magnitude to the brightness of a star.
7.
If the Hubble space
telescope can see stars as faint as magnitude 27, how much fainter are these
stars than the faintest ones you can see in a very dark night sky, which have
magnitude 6?
ANS: The Hubble space telescope can see objects that are
2.512(27–6) = 2.5 × 108 = 250 million times
fainter than the stars you can see in a dark night sky.
DIF: Medium REF: Working It Out 13.2
MSC: Applying
OBJ: Relate magnitude to the brightness of a star.
8.
Explain how astronomers
can use the blue and visible filters to determine the temperatures of stars.
ANS: Astronomers compare the relative intensities of light
measured through each filter. Stars with more blue than visual light are
hotter, whereas stars with more visual than blue light are cooler.
DIF: Easy REF: Section 13.2
MSC: Understanding
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
9.
The sequence of stellar
spectral types is shown in the figure below. Explain why the hottest star (O5)
has so little emission in the visible portion of the spectrum (450-700 nm),
spectral types F-K show the most emission in the visible band, and still cooler
stars (M type) once again show very little in the visible band.
ANS: O stars are very hot blackbodies (40,000 K), so, based
on Wien’s law, their emission peaks in the UV band, at wavelengths shorter than
350 nm. As a result, most of the light from O stars is not emitted in the
visible band. On the other hand, the blackbody peak from stars of spectral type
F-K (4000-7000 K) peaks in the visible band between 350 and 700 nm, so they are
bright throughout the visible band. M stars (3,000 K), in contrast produce blackbody
radiation peaking in the infrared band, at wavelengths longer than 700 nm. As a
result, most of their emission is not visible to us. In addition, molecular
absorption lines from species such as TiO in M stars absorb much of the
emission in the optical.
DIF: Difficult REF:
Section 13.2 MS: Applying
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
10.
The blackbody spectra
of a star with a temperature of 6000 K and a star with a temperature of 4000 K
are shown in the figure below.
An astronomer uses a telescope to observe each of these two
stars in both the blue and red filters. The blue filter is centered at 450 nm,
while the red filter is centered at 660 nm. For each of the two stars, indicate
through which filter that star will be the brightest. Explain your answer.
ANS: Looking at the blackbody curves, the 6000 K star emits
more light at 450 nm than it does at 660 nm, so it will be brighter when using
the blue filter than it will be when using the red filter. For the 4000 K star,
the opposite is true, so it will appear brighter through the red filter than it
will through the blue filter.
DIF: Medium REF:
Section 13.2
MSC: Applying
OBJ: Explain how the spectrum or color of a star is used to
determine its temperature.
11.
What is the spectral
type of star that has the strongest hydrogen absorption lines? Why do stars
that are hotter than these have weaker hydrogen lines?
ANS: The A-type star has the strongest hydrogen absorption
lines in its spectra. O- and B-type stars are hotter than A stars, so the
hydrogen in O and B stars becomes ionized. Electrons not in atoms do little
absorbing, so the hydrogen absorption lines in O and B stars are weaker than
those in A stars.
DIF: Difficult REF:
Section 13.2
MSC: Applying
OBJ: Explain why stars of different temperatures have
different spectral lines.
12.
What are the two main
chemical elements that make up the Sun? How much of the mass of the Sun is
composed of elements other than these two?
ANS: By mass, the Sun is made up of 74.5 percent hydrogen and
23.7 percent helium. All the other elements in the periodic table make up only
about 2 percent of the mass of the Sun.
DIF: Medium REF:
Section 13.2
MSC: Remembering
OBJ: Illustrate how a stellar spectrum reveals the star’s
chemical composition.
13.
If we measure a star’s
luminosity and temperature, what other property of the star can we calculate?
Explain how.
ANS: If we measure the luminosity L and temperature T
of a star, then we can use the Stefan-Boltzmann law that says L/4 πR2 = σT4 to calculate the
star’s radius R.
DIF: Medium REF:
Section 13.2
MSC: Applying
OBJ: Relate the spectral type of a star to its temperature
and size.
14.
The bright star
Arcturus has a luminosity of 210 L⊙ and a temperature of 4300 K. What is its radius? Note that
the Sun has a temperature of 5800 K.
ANS: Using the Stefan-Boltzmann law and solving for the
radius we get 
. Comparing Arcturus to the Sun, we find 
Thus
the radius of Arcturus is 26 R⊙
. Comparing Arcturus to the Sun, we find Thus
the radius of Arcturus is 26 R⊙
DIF: Difficult REF:
Working It Out 13.3
MSC: Applying
OBJ: Use the Stefan-Boltzmann law to find the size of a star
from its temperature and luminosity.
15.
Star A emits its peak
energy at a wavelength of 500 nm, and star B emits its peak energy at a
wavelength of 750 nm. If both stars have the same radii, which star is hotter
and by how much?
ANS: By Wien’s law, the temperature of a star is inversely
proportional to the wavelength of its peak emission: λpeakA/λpeakB = 
. This means that star A is 
= 1.5 times hotter
than star B.
. This means that star A is = 1.5 times hotter
than star B.
DIF: Difficult REF:
Section 13.2
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
16.
You observe a binary
star system and find that star 1 has a velocity of 10 m/s while star 2 has a
velocity of 35 m/s. What is the ratio of masses of the two stars (M1/M2)?
ANS: The ratio of masses of stars in a binary system is
inversely proportional to the ratio of velocities: M1/M2
= v2/v1 = (35 m/s)/(10 m/s)
= 3.5. Therefore, star 1 is 3.5 times as massive as star 2.
DIF: Medium REF:
Working It Out 13.4
MSC: Applying
OBJ: Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
17.
You observe a binary
star system and find that star 1 has a velocity of 20 m/s while star 2 has a
velocity of 40 m/s. What is the ratio of masses of the two stars (M1/M2)?
If you find that the separation of the two stars is 0.5 AU and the orbital
period is 70 days, then what are the individual masses of the two stars?
ANS: The ratio of masses of stars in a binary system is
simply inversely proportional to the ratio of velocities: M1/M2
= v2/v1 = 40 m/s / 20 m/s = 2. Therefore, M1
= 2M2. Using Kepler’s third law, we can
calculate the sum of the masses:
P = 70 days × 24 hr/day × 3,600 s/hr = 6.0 × 106 s
(M1 + M2) = 4 π2A3/GP2 = 4π2 (0.5 × 1.5 × 1011 m)3 / (6.7 × 10−11 Nm2/kg
× (6.0 × 106 s)2) (M1 + M2)
= 6.9 × 1030 kg × 1 M⊙/2
× 1030 kg = 3.5 M⊙.
Solving for the individual masses gives (2M2 + M2)
= 3M2 = 3.5M⊙or
M2 = 1.1 M⊙, and M1
= 2.2 M⊙.
DIF: Difficult REF:
Working It Out 13.4
MSC: Applying
OBJ: Use Kepler’s Laws and orbital velocities to measure the
masses of binary stars.
18.
What is the physical
difference between an eclipsing binary system and a spectroscopic binary
system?
ANS: The only real difference is the tilt of the stars’
orbits relative to the Earth’s position (also known as the inclination angle).
For an eclipsing binary system, the stars are aligned in a way so that one star
passes directly between the Earth and the other star. For a spectroscopic
binary, the stars’ orbits do not line up exactly with the Earth’s position.
DIF: Easy REF:
Section 13.3
MSC: Understanding
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing binaries,
and spectroscopic binaries.
19.
The figure below shows
the light curve of an eclipsing binary system consisting of two main sequence
stars. The dip in observed light is stronger when the cooler star passes in
front of the hotter star than when the cooler star is behind the hotter star.
Why?
ANS: Cooler main sequence stars are by definition also
smaller than hotter main sequence stars, so they have a lower luminosity and
contribute less to the combined light of the stars. Since we observe the
combined light of the two stars (they can’t be resolved in the telescope), the
cooler star passing in front of the hotter star causes a larger fraction of the
total light to be blocked than when the cooler star passes behind the hotter
star, so the corresponding dip is larger for the former than for the latter.
DIF: Difficult REF:
Section 13.3
MSC: Understanding
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
20.
A main sequence star
follows a circular orbit around its companion with a speed of 22 km/s. Its
orbital period is 1.3 years. What is the radius of its orbit?
ANS: We know that the circumference of a circle is 2πR, where R is its radius, while the velocity v
of the star in a circular orbit is just distance / time, or v = 2πR / P, where P is its period. So solving this
for R, we have R = Pv / 2π = (1.3 yr) × (3.15
× 107 s/yr) × (22 km/s) / 2π = 1.44×108
km.
DIF: Difficult REF:
Section 13.3
MSC: Applying
OBJ: Show how Kepler’s laws and orbital velocities are used
to determine the masses of binary stars.
21.
Suppose you observe the
visual binary pair Alpha Cen A and Alpha Cen B, as seen in the figure shown
below. Assuming that it can be observed repeatedly over a period of time, what
two orbital parameters can be measured from the image?
ANS: The semi-major axis can be measured from the angular
separation of the two stars, while the orbital period can be estimated by
observing how long the binary takes to return to its original separation and
orientation on the sky.
DIF: Medium REF:
Section 13.3
MSC: Applying
OBJ: Differentiate between the observational information and
methods used to determine stellar masses in visual binaries, eclipsing
binaries, and spectroscopic binaries.
22.
What is the main
property of a main-sequence star that determines all its other properties?
ANS: The star’s mass has the most effect on all its other
properties.
DIF: Easy REF:
Section 13.4
MSC: Remembering
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
23.
When main-sequence
stars are plotted on an HR diagram (luminosity vs. temperature), they fall
along a swath running diagonally from the upper left to the lower right. Why
don’t they fall in arbitrary locations on the HR diagram?
ANS: The mass of a star determines both its temperature and
radius, so arbitrary combinations of radius and temperature can’t occur.
DIF: Difficult REF:
Section 13.4
MSC: Understanding
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
24.
Explain how we can use
spectroscopic parallax to determine the distance to a star farther away than a
few hundred light-years.
ANS: First, we can determine the temperature of the star
based on its absorption line spectrum, as well as determine whether the star is
a main-sequence star. If the star is a main-sequence star, and if we know the
temperature of the star, we can simply read off its luminosity from the
diagram. We then measure how bright the star appears and use the inverse square
law of radiation to determine its distance.
DIF: Medium REF:
Section 13.4
MSC: Understanding
OBJ: Explain how the luminosity class of a star affects the
use of spectroscopic parallax.
25.
Suppose you take images
of star SBD 1256 in different filters and find that, by comparing the
brightness of the star through the different filters, it’s an F5 star. You
assume the star is on the main sequence (F5V), and then use the HR diagram to
figure out that it’s at a distance of 120 parsecs. A few months later you take
a spectrum of SBD 1256 and notice that its absorption lines are very narrow,
indicating that it’s not an F5V main-sequence star but rather a giant F5III
star. Explain how this now affects the distance estimate and why.
ANS: Because the star is now found to be a giant, this means
it’s intrinsically more luminous that it would be if it were on the main
sequence. So to get the observed brightness of the star, it must now be farther
away than 120 parsecs.
DIF: Difficult REF:
Section 13.4
MSC: Applying
OBJ: Explain how the luminosity class of a star affects the
use of spectroscopic parallax.
26.
Suppose you take a
spectrum of a yellow star and, based on the shape of its blackbody curve as
well as its absorption lines, that it is of spectral type K3. However, you do
not know its distance. How can you then determine whether it is a main-sequence
star or a giant star?
ANS: If it is a main-sequence star, it will have a radius
smaller than that a giant star of the same temperature. The greater compactness
of the star means it will have a higher surface gravity, so its absorption
lines will be broader due to increased Doppler motion of the atoms in the
stronger gravitational field. If it were a giant star, on the other hand, its
absorption lines would be narrower due to its larger size and lower surface
gravity.
DIF: Difficult REF:
Section 13.4
MSC: Understanding
OBJ: Explain how the luminosity class of a star affects the
use of spectroscopic parallax.
27.
Imagine you are
observing a nearby star. You know that it is a main-sequence star but don’t
know anything else about it. If you had access to any telescope equipment you
wanted, explain how you would determine this star’s temperature, luminosity,
distance, and radius.
ANS: You could measure the temperature either by determining
its color using different filters, or by taking a spectrum to determine its
spectral type. Once you know the color of a main-sequence star, you can use an
H-R diagram to read off the luminosity of that temperature star. Then, since
you know the luminosity, measuring the brightness of this star tells you the
distance, using the equation B = L/(4πd 2). Alternatively, if
the star was relatively nearby, you could measure the distance to it using
parallax and then use the brightness equation to determine the luminosity.
Finally, since you already know the temperature and luminosity of the star, you
can use the Stefan-Boltzmann equation L = 4πR2σT4 to calculate its radius.
DIF: Difficult REF:
Section 13.4
MSC: Applying
OBJ: Compare the temperature, luminosity, spectral type,
color, and size of stars at different positions on the H-R diagram.
28.
Along the main
sequence, how do the luminosity, temperature, radius, and mass of stars change
as you go from the upper-left to the lower-right corners of the H-R diagram?
ANS: Stars near the upper-left end of the main sequence are
very luminous, hot, large, and massive stars. Stars near the lower-right end of
the main sequence are low-luminosity, cool, small, and low-mass stars.
DIF: Medium REF:
Section 13.4
MSC: Understanding
OBJ: Define the axes of the H-R diagram, and the direction in
which each axis increases.
29.
Based on the
mass-luminosity diagram for main sequence stars shown in the figure below,
approximately how many more time luminous is a 25 M⊙ star compared with a
0.3 M⊙ star?
ANS: From the graph, the luminosity of a 25 M⊙ star is approximately
104 L⊙, while that of a 0.3 M⊙ star is approximately
10-2 L⊙. Therefore the more massive star is 104 / 10-2
= 106 times more luminous that the less massive
star.
DIF: Medium REF:
Section 13.4
MSC: Understanding
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
30.
Based on the figure
shown below, approximately how many more time luminous is a main-sequence star
having a radius of 10 R⊙ compared with a star
having a radius of 1 R⊙?
ANS: From the mass-radius graph, the mass of a star having a
radius 10 R⊙ is approximately 25 M⊙. Turning now to the
mass-luminosity graph, a 25 M⊙ star has a luminosity
of approximately 104 L⊙. Doing this same procedure for the 1 R⊙ star, its mass must 1 M⊙, so that translates to
a luminosity of 1 L⊙. The ratio of the two is 104L⊙/ 10 L⊙ = 104,
so a main-sequence star of radius 10 R⊙is 10,000 times more
luminous than the Sun.
DIF: Difficult REF:
Section 13.4
MSC: Understanding
OBJ: Use the mass-luminosity relationship to determine the
luminosity of main-sequence stars.
31.
Based on the figure
shown below, which shows the relative number of stars as a function of stellar
luminosity, how common are stars having 0.01 L⊙ compared with those having a luminosity of 100 L⊙?
ANS: Drawing a line vertically from the horizontal axis at 10-2
L⊙, the relative number of stars at that luminosity is 4 stars
for every solar mass star. Similarly, drawing a line vertically from the
horizontal axis at 100 L⊙, the relative number of stars at that luminosity is around
0.05 star for every solar mass star. The ratio of these is 4 / 0.05 = 80, so stars
having a luminosity 1/100th that of the Sun are 80 times more common than those
having a luminosity 100 times that of the Sun.
DIF: Medium REF:
Section 13.4
MSC: Understanding
OBJ: Relate how common main-sequence stars are relative to
other stars in the galaxy.
32.
How does the size and
distance of a habitable zone depend on the spectral type of the star?
ANS: Habitable zones (distances from the star where water can
exist as liquid) are both wider and farther from the star when it is hotter and
narrower and closer to the star when the star is cooler. So the habitable zone
narrows and moves closer to the star as one goes from spectral type O to
spectral type M.
DIF: Medium REF:
Section 13.4
MSC: Applying
OBJ: Compare and contrast the habitable zones around
different types of stars.
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