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Chapter 4: Gravity and
Orbits
Learning Objectives
Define the bold-faced vocabulary terms within the chapter.
Multiple Choice: 3, 4, 7, 9, 14, 15, 16, 17, 18, 47
Short Answer:
4.1 Gravity Is a Force Between Any Two
Objects due to Their Masses
Differentiate gravity, mass, and weight.
Multiple Choice: 1, 2, 10, 12
Describe the behavior of the gravitational force using
Newton’s universal law of gravitation.
Multiple Choice: 5, 6
Short Answer:
Use Newton’s universal law of gravitation to quantify the
force of gravity between two objects in different physical situations.
Multiple Choice: 11, 13
Explain how gravitational force from a real object can be
considered to come from that object’s center.
Multiple Choice: 8
Short Answer: 4.2 An Orbit Is One Body
“Falling around” Another
Illustrate that orbits are a perpetual state of free fall.
Multiple Choice: 23
Short Answer:
Relate an object’s speed to its orbital path.
Multiple Choice: 19, 20, 21, 22
Show how Kepler’s laws are consistent with Newton’s universal
law of gravitation.
Multiple Choice: 24
4.3 Tidal Forces Are Caused by Gravity
Use Newton’s universal law of gravitation to explain why
objects of real physical size experience tidal forces.
Short Answer: Characterize how tidal forces from the Moon and
Sun cause the rise and fall of Earth’s ocean tides.
Multiple Choice: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37
Short Answer:
4.4 Tides Affect Solid Bodies
Explain how tidal forces cause orbital locks.
Multiple Choice: 39, 40, 46, 50, 52
Short Answer: Describe how tidal forces change the orbital
and rotational periods of objects.
Multiple Choice: 38, 41, 42, 43, 51
Short Answer: Compare and contrast how tidal forces affect
approaching objects of different sizes.
Multiple Choice: 44, 45, 48, 49
Short Answer: Working It Out 4.1
Use proportional reasoning with Newton’s universal law of
gravitation to explore how changing input parameters effects the resulting
force.
Multiple Choice: 53, 54, 55, 56, 57, 58, 59
Short Answer: Calculate the gravitational acceleration on
another planet or body.
Short Answer: Working It Out 4.2
Calculate the circular and escape velocities from an object.
Multiple Choice: 60, 61, 62, 63, 64, 65
Short Answer: Working It Out 4.3
Calculate the mass of a central object using the orbital
properties of a satellite.
Multiple Choice: 66, 67, 68, 69, 70
Short Answer: Working It Out 4.4
Compute the relative strength of tidal forces from different
objects.
Multiple Choice: MULTIPLE
CHOICE
1.
Two rocks (call them S
and T) are released at the same time from the same height and start from rest.
Rock S has 20 times the mass of rock T. Which rock will fall faster if the only
forces involved are each rock’s mutual gravitational attraction with Earth?
a.
Rock S
b.
Rock T
c.
Both rocks will fall at
the same rate.
d.
Not enough information
is available to answer.
2.
Which of the following
properties of an astronaut changes when he or she is standing on the Moon,
relative to when the astronaut is standing on Earth?
a.
weight
b.
mass
c.
inertia
d.
Nothing changes.
3.
_________ hypothesized
that planetary motions could be explained by a force arising from the
attraction between the mass of the planet and the Sun that decreased with the
square of the distance between them.
a.
Johannes Kepler
b.
Isaac Newton
c.
Tycho Brahe
d.
Nicolaus Copernicus
e.
Galileo Galilei
4.
The force of gravity
that an object has is directly proportional to its
a.
inertia.
b.
size.
c.
mass.
d.
density.
e.
distance.
5.
If the distance between
Earth and the Sun were cut in half, the gravitational force between these two
objects would
a.
decrease by 4.
b.
decrease by 2.
c.
increase by 2.
d.
increase by 4.
e.
decrease by 8.
6.
According to the
progression shown in the figure below, if the distance between two objects is
increased to four times its original value, the gravitational force between the
two objects would be _________ times its original value.
a.
1/2
b.
1/32
c.
1/4
d.
1/16
e.
4
7.
Newton’s gravitational
constant is
a.
a force.
b.
a weight.
c.
a number.
d.
an acceleration.
e.
a mass.
8.
The distance used in
Newton’s law of gravitation is
a.
the distance between
the closest faces of the two objects.
b.
the distance between
the centers of the objects.
c.
the radius of the
largest object.
d.
the radius of the
smallest object.
e.
always the same.
9.
Gravity is
a.
the strongest force.
b.
a fundamental force.
c.
a mutually attractive
force.
d.
a mutually repulsive
force.
e.
both B and C
10.
An astronaut who weighs
700 N on Earth is located in empty space, very far from any other objects.
Approximately what is the mass of the astronaut?
a.
0
b.
7 kg
c.
70 kg
d.
700 kg
e.
7000 kg
11.
Two rocks (call them S
and T) are a distance of 50 km from one another. Rock S has 20 times the mass
of rock T. Considering only their mutual gravitational force, which rock will
accelerate faster in response to gravity?
a.
rock S
b.
rock T
c.
Both rocks will have
the same acceleration.
d.
Not enough information
is available to answer.
12.
In the absence of air
friction, a 0.001-kg piece of paper and a 0.1-kg notebook are dropped from the
same height and allowed to fall to the ground. How do their accelerations
compare?
a.
The accelerations are
the same.
b.
The notebook’s
acceleration is 100 times faster than the paper’s acceleration.
c.
The notebook’s acceleration
is 1,000 times faster than the paper’s acceleration.
d.
The paper’s
acceleration is 100 times faster than the notebook’s acceleration.
e.
The paper’s
acceleration is 1,000 times faster than the notebook’s acceleration.
13.
According to the scales
shown in the figure below, about how many times stronger is gravity on Earth
than on the Moon?
a.
20
b.
3
c.
2
d.
6
e.
They are the same.
14.
Which of the following
is not true about orbits?
a.
Orbits are ellipses.
b.
Orbits can be circular.
c.
An orbit is the path of
an object in free fall around another object.
d.
Orbits are always
circular.
e.
Objects in orbits
experience acceleration.
15.
A centripetal force is
a.
a fundamental force.
b.
gravity.
c.
any force that points
toward center of a circular path.
d.
tension force.
e.
magnetic force.
16.
Uniform circular motion
applies to which of the following orbits?
a.
elliptical
b.
hyperbolic
c.
circular
d.
parabolic
17.
The term satellite in
astronomy means
a.
a means of
communication.
b.
a man-made object in
orbit of Earth.
c.
the Moon.
d.
any low-mass object
that is orbiting a more massive object.
e.
none of the above
18.
Which of the following
is a bound orbit?
a.
elliptical
b.
hyperbolic
c.
circular
d.
both A and C
19.
For which of the
following orbital velocities, V, is the orbit unbound?
a.
V = Escape velocity
b.
V = Circular velocity
c.
V > Escape velocity
d.
V < Escape velocity
e.
both A and C
20.
If an object is in
orbit with an orbital speed less than the escape speed but greater than the
circular orbit speed, what type of orbit is it?
a.
elliptical
b.
hyperbolic
c.
circular
d.
both A and C
21.
If an object is moving
in a circular orbit at a constant speed, which of the following is false?
a.
Its acceleration is not
zero.
b.
Its acceleration is
zero.
c.
Its velocity is not
zero.
d.
There is an unbalanced
force acting on it.
e.
All the above
statements are true.
22.
If we wanted to
increase the Hubble Space Telescope’s altitude above Earth and keep it in a
stable orbit, we also would need to
a.
increase its orbital
speed.
b.
increase its weight.
c.
decrease its weight.
d.
decrease its orbital
speed.
e.
increase its mass.
23.
Astronauts orbiting
Earth in the space shuttle experience so-called weightlessness in space because
a.
they are farther away
from Earth.
b.
they eat less food
while in orbit.
c.
the gravitational pull
of the Moon counteracts Earth’s gravitational pull.
d.
they are in constant
free fall around Earth.
e.
they are in space where
there is no gravity.
24.
If you measured the
orbital period of the Moon and the distance between Earth and the Moon, then
you could calculate
a.
the mass of the Moon.
b.
the sum of the masses
of Earth and the Moon.
c.
the average distance
between Earth and the Sun.
d.
the radius of Earth.
e.
the radius of the Moon.
25.
Why is Earth’s tidal
bulge not perfectly aligned with the line connecting the centers of Earth and
the Moon?
a.
friction
b.
Earth’s rotation
c.
gravity
d.
both A and B
26.
Tidal forces are caused
by
a.
the weight of the water
in the oceans on the ocean floor.
b.
the strength of the
gravitation pull of the Moon on Earth.
c.
the difference between
the weight of the water on the ocean floor at high and low tide.
d.
the difference between
the strength of the gravitational pull of the Moon and Sun on either side of
Earth.
e.
the strength of the
gravitation pull of the Moon and the Sun on Earth.
27.
Lunar tides are
approximately _________ solar tides.
a.
2 times weaker than
b.
2 times stronger than
c.
200 times weaker than
d.
200 times stronger than
e.
the same strength as
28.
According to the figure
below, spring tides occur when the lunar and solar tides ________, resulting in
_________ tides.
a.
add; above average
b.
partially cancel out;
above average
c.
add; below average
d.
partially cancel out;
below average
e.
completely cancel out;
no
29.
According to the figure
below, spring tides occur at which phases of the Moon?
a.
third quarter
b.
new and full
c.
first and third
quarters
d.
full
e.
new
30.
According to the figure
below, when the Moon is in between Earth and the Sun, _________ tides occur.
a.
spring
b.
no
c.
neap
d.
high
e.
low
31.
According to the figure
below, when Earth is in between the Moon and the Sun, _________ tides occur.
a.
spring
b.
no
c.
neap
d.
high
e.
low
32.
According to the figure
below, neap tides occur when the lunar and solar tides _________, resulting in
_________ tides.
a.
add; above average
b.
partially cancel out;
above average
c.
add; below average
d.
partially cancel out;
below average
e.
completely cancel out;
no
33.
According to the figure
below, neap tides occur at which phases of the Moon?
a.
new and full
b.
third quarter
c.
first and third quarters
d.
full
e.
new
34.
When the Sun and Moon
are separated by 90 degrees in the sky, _________ tides occur on Earth when the
strength of the tides are _________ than normal.
a.
spring; lower
b.
spring; higher
c.
lunar; lower
d.
neap; lower
e.
neap; higher
35.
According to the figure
below, a high tide at a given location will occur about ____ time(s) a day.
a.
one
b.
three
c.
two
d.
four
e.
eight
36.
According to the figure
below, the approximate amount of time between two high tides at a given
location is about
a.
3 hours.
b.
8 hours.
c.
6 hours.
d.
12 hours.
e.
24 hours.
37.
According to the figure
below, the approximate amount of time between a high tide and a low tide at a
given location is about
a.
3 hours.
b.
8 hours.
c.
6 hours.
d.
12 hours.
e.
24 hours.
38.
Because of tidal
forces, which type of eclipse will become impossible first?
a.
partial lunar
b.
total lunar
c.
partial solar
d.
total solar
e.
annular solar
39.
In the figure below,
the person on the Moon is standing at the same location on the Moon as the Moon
rotates around its own axis. Based on this, we see that the Moon’s rotational
period about its own axis is equal to
a.
Earth’s rotational
period.
b.
half Earth’s rotational
period.
c.
the Moon’s orbital
period.
d.
half the Moon’s orbital
period.
e.
Earth’s orbital period
around the Sun.
40.
The Moon always keeps
the same face toward Earth because of
a.
tidal locking.
b.
tidal forces from the
Sun.
c.
tidal forces from
Earth.
d.
tidal forces from Earth
and the Sun.
e.
all sides of the moon
face Earth at one time or another.
41.
The distance between
Earth and the Moon
a.
will never change.
b.
is slowly decreasing.
c.
is slowly increasing.
d.
will increase or
decrease depending on future changes in the tides on the Moon due to Earth.
e.
will increase or
decrease depending on future changes in the tides on Earth due to the Moon.
42.
Earth’s rotation rate
is slowing because of
a.
radioactive decays in
its core.
b.
relativistic effects of
gravity.
c.
tidal forces from the
Moon.
d.
the gravitational force
of the Sun.
e.
gravitational drag from
dark matter.
43.
The distance between
Earth and the Moon is increasing because of
a.
the expansion of the
universe.
b.
the expansion of the
Solar System.
c.
tidal forces from the
Moon.
d.
tidal forces from the
Moon and Sun.
e.
dark energy.
44.
Which one of the
statements below about a planet’s Roche limit is false?
a.
The Roche limit is
about 2.5 times the radius of gaseous planets.
b.
Objects orbiting closer
to a planet than the Roche limit are likely to be ripped apart by tidal forces.
c.
The Roche limit is
where tidal forces from an orbiting object are equal to its internal
self-gravity.
d.
Orbiting objects beyond
the Roche limit from the planet do not get ripped apart by tidal forces.
e.
The ring systems around
giant planets are located beyond the Roche limit.
45.
Tidal forces can affect
a.
moons.
b.
galaxies.
c.
planets.
d.
satellites.
e.
all of the above
46.
_________ may have been
instrumental in shaping the interface between Earth’s land and oceans where the
chemistry needed to develop life may have occurred.
a.
Meteor showers
b.
Collisions with comets
c.
Earth’s Moon
d.
Tectonic activity
e.
A collision with a
Mars-sized object
47.
The Roche limit
a.
is the distance at
which a planet’s tidal forces become equal to self-gravity of an object.
b.
is The limit on the
amount of mass an object can have in orbit.
c.
is the smallest orbit
possible around a planet.
d.
only applies to the
giant planets.
e.
only applies to stars.
48.
When two galaxies
collide long streams of stars can be observed. These “tails” are caused by
a.
pressure.
b.
magnetic forces.
c.
tidal forces.
d.
Roche forces.
e.
dark energy.
49.
Which of the statements
below are true about the Roche limit of a giant planet?
a.
It is about equal to
the radius of the planet.
b.
It is the closest to
the planet that moons normally are found.
c.
It is the closest to
the planet that rings will be found.
d.
It is the farthest from
the planet that moons normally are found.
e.
Because they have no
solid surfaces, giant planets do not have a Roche limit.
50.
The moon keeps the same
hemisphere facing Earth because the _________ is equal to the _________.
a.
rotational period of
Earth; orbital period of the Moon around Earth
b.
orbital period of
Earth; orbital period of the Moon around Earth
c.
orbital period of the
Moon around Earth; rotational period of Earth
d.
rotational period of
the Moon; orbital period of the Moon around Earth
e.
rotational period of
Earth; orbital period of Earth
51.
Because of the tidal
force between Earth and the Moon,
a.
Earth’s rotation rate
is decreasing.
b.
the Moon’s distance
from Earth is increasing.
c.
the Moon’s orbital
period is increasing.
d.
the Moon’s rotational
period is increasing.
e.
all of the above are
true.
52.
Because of tidal
forces, for every _________ time(s) it rotates on its axis, Mercury revolves
around the Sun _________ time(s).
a.
1; 1
b.
2; 3
c.
3; 2
d.
10; 1
e.
20; 1
53.
Suppose you are
suddenly transported to a planet with 1/4 the mass of Earth but the same radius
as Earth. Your weight would _________ by a factor of _________.
a.
increase; 4
b.
increase; 16
c.
decrease; 4
d.
decrease; 16
e.
increase; 2
54.
Suppose you are
suddenly transported to a planet that had 1/4 the radius of Earth but the same
mass as Earth. Your weight would _________ by a factor of _________.
a.
increase; 4
b.
increase; 16
c.
decrease; 4
d.
decrease; 16
e.
decrease; 8
55.
If you weighed 150 lb
on Earth, what would you weigh on Mars? For reference, Mars has a mass that is
0.1 times Earth’s mass and Mars has a radius that is 0.5 times Earth’s radius.
a.
30 lb
b.
110 lb
c.
75 lb
d.
60 lb
e.
15 lb
56.
If you weighed 100 lb
on Earth, what would you weigh at the upper atmosphere of Jupiter? For
reference, Jupiter has a mass that is about 300 times Earth’s mass and a radius
that is 10 times Earth’s radius.
a.
10,000 lb
b.
3,000 lb
c.
1,000 lb
d.
300 lb
e.
30 lb
57.
The force of gravity
between Earth and the Sun is _________ the force of gravity between Earth and
the Moon. For reference, the average distance between Earth and the Moon is
0.003 astronomical unit (AU), the mass of the Moon is 7 × 1022
kg, and the mass of the Sun is 2 × 1030
kg.
a.
86,000 times larger
than
b.
260 times larger than
c.
140 times smaller than
d.
6,400 times smaller
than
e.
the same as
58.
The force of gravity
between Saturn and the Sun is _________ the force of gravity between Earth and
the Sun. For reference, Saturn is approximately 100 times more massive than
Earth, and the semimajor axis of Saturn’s orbit is 10 AU.
a.
10 times smaller than
b.
1,000 times larger than
c.
1,000 times smaller
than
d.
100 times larger than
e.
approximately equal to
59.
Mercury orbits the Sun
with an average distance of 0.4 AU, and its mass is 0.06 times that of Earth.
The gravitational force that the Sun exerts on Mercury is _______________ times
the force of gravity that the Sun exerts on Earth.
a.
20
b.
6
c.
4
d.
0.4
e.
0.1
60.
If you have two moons
that have the same radius, but Moon A is denser and has 2 times the mass of
Moon B, how do their escape velocities compare?
a.
Moon A has an escape
velocity that is 1.4 times larger than Moon B.
b.
Moon A has an escape
velocity that is 1.4 times smaller than Moon B.
c.
Moon A has an escape
velocity that is 2 times smaller than Moon B.
d.
Moon A has an escape
velocity that is 2 times larger than Moon B.
e.
Because gravity affects
all masses the same, the escape velocities are the same.
61.
The Hubble Space
Telescope orbits at an altitude of 600 km above Earth’s surface. Assuming it is
in a stable circular orbit, what is its velocity? For reference, Earth’s radius
is 6,400 km and Earth’s mass is 6 × 1024
kg.
a.
240,000 m/s
b.
7,500 m/s
c.
51,000 m/s
d.
64,000 m/s
e.
You also must know the
mass of the Hubble Space Telescope to determine its speed.
62.
How fast is the Moon
moving as it orbits Earth? For reference, the Moon’s orbit is approximately
circular with a radius equal to 400,000 km, and the Moon’s orbital period is 27
days.
a.
1 km/s
b.
10 km/s
c.
50 km/
d.
100 km/s
e.
500 km/s
63.
What is the escape
velocity from Mars if its mass is 6 × 1023
kg and its radius is 3,400 km?
a.
2,400 m/s
b.
4,900 m/s
c.
8,600 km/s
d.
12,000 m/s
e.
25,000 km/s
64.
What is the escape
velocity from a large asteroid if its mass is 6 × 1021
kg and its radius is 2,400 km?
a.
98 km/s
b.
210 km/s
c.
340 m/s
d.
580 m/s
e.
12,400 m/s
65.
If a satellite sent to
Mars is designed to return a rock sample to Earth, how fast must the satellite
be launched from its surface in order to escape Mars’s gravity? For reference,
Mars has a mass of 6 × 1023 kg and a radius of 3,400 km.
a.
100 m/s
b.
5,000 m/s
c.
20 m/s
d.
20,000 m/s
e.
You must know the mass
of the satellite to determine the answer.
66.
If you found an
exoplanet whose mass was the same as Jupiter’s, but the planet orbited its star
with a period of 2 years and a semimajor axis of 1 AU, what would be the mass
of its star? For reference, Jupiter has a semimajor axis of 5.4 AU and an
orbital period of 12 years.
a.
0.25 MSun
b.
0.5 MSun
c.
2.0 MSun
d.
1.5 MSun
e.
Not enough information
is available to answer.
67.
Titan, the largest moon
of Saturn, has an orbital period of 16 days and a semimajor axis of 1.2 × 109 m.
Based on this information, what is Saturn’s mass? For reference, Earth’s mass
is 6 × 1024 kg.
a.
290 MEarth
b.
130 MEarth
c.
90 MEarth
d.
40 MEarth
e.
4 MEarth
.
68.
You find a moon
orbiting a planet. The moon has a period of 10 days, and the average distance
between the moon and planet is 106 km. What is the planet’s mass?
Note that the mass of Jupiter is 1.9 × 1027
kg.
a.
0.1 MJupiter
b.
0.4 MJupiter
c.
1 MJupiter
d.
4 MJupiter
e.
10 MJupiter
69.
If you discovered a
planet orbiting another star, and the planet had an orbital period of 2 years
and a semimajor axis of 2 AU, what would be the mass of its parent star? You
can assume the planet’s mass is much less than the star’s mass.
a.
0.25 MSun
b.
0.5 MSun
c.
1.0 MSun
d.
1.25 MSun
e.
2.0 MSun
70.
Assume that a planet
just like Earth orbits the bright star named Sirius. If this Earth-like planet
orbits with a semimajor axis of 1 AU and an orbital period of 7 months, what is
the mass of Sirius?
a.
3 MSun
b.
12 MSun
c.
8 MSun
d.
5 MSun
e.
17 MSun
71.
If you doubled the
distance the Moon is from Earth, by what fraction does the strength of the
tidal force change?
a.
2
b.
1/2
c.
1/4
d.
1/8
e.
1/16
SHORT ANSWER
1.
Is there a difference
in your weight when measured on top of a mountain 1,000 meters above sea level
and when measured in a classroom 10 meters above sea level?
2.
Newton’s law of gravity
says that gravity is a mutually attractive force. Explain the following
observation. A small object is dropped on Earth and we see it fall toward
Earth. However, we do not observe Earth moving toward the object.
3.
Explain why the
gravitational force an object experiences from Earth can be considered to come
from the center of Earth.
4.
Explain what the terms circular
velocity and escape velocity mean. Give the formula for each and
explain what each mathematical symbol represents.
5.
Explain the difference
between a bound orbit and an unbound orbit.
6.
Explain the difference
between being weightless and being in free fall.
7.
Explain the origin of
tidal forces on Earth due to the Moon.
8.
Do tidal forces only
affect the water on Earth?
9.
Why are there high and
low tides each day instead of having the same tide all day during a given phase
of the Moon?
10.
If Earth did not have a
moon, would we still have tides because of the Sun.? If so, explain how they
might be different, or why they might remain unchanged.
11.
Consider the figure
below, which illustrates the tidal bulge on Earth’s oceans due to the Moon and
four people at different longitudes on Earth from the point of view of an
observer looking down on the North Pole of Earth. If you were to arrive at the
beach and find that the Moon was visible in the western half of the sky, then
is the tide most likely to be coming in and the water level rising; or is the
tide going out and the water level going down? Explain the rationale for your
answer.
12.
Which is larger, the
tidal force on Earth due to the Moon or the tidal force on Earth due to the
Sun, and by approximately how much? Explain conceptually why this is possible
given that the gravitational force of the Sun on Earth is 200 times larger than
the gravitational force of the Moon on Earth.
13.
Consider the figure
below, which illustrates the tidal bulge on Earth’s oceans due to the Moon and
Sun from an observer looking down on the North Pole of Earth. At what phase of
the Moon will the lowest tides of the year occur? Explain the rationale for
your answer either in words or with a sketch.
14.
Show that the tidal
force on Earth from the Moon is approximately two times the tidal force on
Earth from the Sun. For reference, the Moon’s mass is 7.3 ×1022
kg, the Sun’s mass is 2 × 1030 kg, the Earth−Moon distance is
3.8 × 105 km, and the Earth−Sun distance is
1.5 × 108 km.
15.
Explain why the Moon
rotates in the same amount of time as it takes to orbit once around Earth.
16.
Explain what the Roche
limit is and how it is related to rings around giant planets.
17.
Explain why Saturn’s
rings do not clump together to form a moon.
18.
Earth’s tidal bulge
“leads” the Moon in its orbit. Does this have any effect on the Moon?
19.
Imagine a planet in a
very eccentric elliptical orbit around a Star. This planet has no moons, but it
has oceans. This planet’s orbit is not tidally locked. Are there tides? If so,
explain how they would behave.
20.
Show that the
gravitational pull on Earth from the Sun is about 200 times the gravitational
pull on Earth from the Moon. For reference, Moon’s mass is 7.3 × 10 22
kg, the Sun’s mass is 2 × 1030 kg, the Earth−Moon distance is
3.8 × 105 km, and the Earth−Sun distance is
1.5 × 108 km.
21.
How much stronger is
the gravitational force of the Sun on Earth compared to the gravitational force
of the Sun on Pluto? Note that Pluto’s semimajor axis is 40, AU, and Pluto’s
mass is 0.002 times the mass of Earth.
22.
How does the force of
gravity between the Sun and Mercury compare to the gravitational force between
the Sun and Earth? Note that the semimajor axis of Mercury’s orbit is 0.4 AU,
and Mercury’s mass is 0.06 times the mass of Earth.
23.
How does the force of
gravity between the Sun and Jupiter compare to the gravitational force between
the Sun and Earth? Note that the semimajor axis of Jupiter’s orbit is 5.2 AU,
and Jupiter’s mass is 320 times the mass of Earth.
24.
How would the
acceleration due to gravity on a planet that is 16 times as massive as Earth
and 4 times its radius compared to the acceleration of gravity on Earth?
25.
Saturn has 95 times the
mass of Earth, and its atmosphere extends outward 9.5 times Earth’s radius. How
does the acceleration due to gravity at the edge of Saturn’s atmosphere compare
to that on Earth?
26.
Mars has about
one-tenth the mass of Earth and half Earth’s radius. How does the acceleration
of gravity on Mars compare to that on Earth?
27.
What is the velocity
one would need to give a satellite in order for it to escape from the Solar
System (meaning escape the Sun’s gravity) if it was launched from Earth at a
distance of 1 AU from the Sun? Give your answer in units of m/s.
28.
The International Space
Station orbits at an altitude of 400 km above Earth’s surface. Assuming it is
in a stable circular orbit, what is its velocity? For reference, Earth’s radius
is 6,400 km, and Earth’s mass is 6 × 1024
kg and G = 6.7 × 10−11 N m2/kg2.
29.
What two pieces of
information would you need to obtain about one of the moons of the planet
Jupiter in order to measure the mass of Jupiter? What formulae would you use to
determine the mass?
30.
You discover a moon
orbiting a planet. The moon has an orbital period of three weeks, and the
average distance between the moon and planet is 1.2 × 106
km. What is the planet’s mass? Compare its mass to that of Jupiter, which is
1.9 × 1027 kg.
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Chapter 5: Light
Learning
Objectives
Define the bold-faced vocabulary terms within the chapter.
Multiple Choice: 10, 11, 12, 13, 35
Short Answer: 5.1 Light Brings Us the News
of the Universe
Summarize the electromagnetic properties of light.
Multiple Choice: 1, 2, 3, 4, 5, 23, 25
Short Answer: Explain how and when light acts like a wave,
and when it acts like a particle.
Multiple Choice: 15, 16, 17
Relate color, wavelength, and energy of photons.
Multiple Choice: 6, 7, 8, 14, 18, 19, 24
Short Answer: List the names and wavelength ranges of the
electromagnetic spectrum.
Multiple Choice: 9, 20, 21, 22
5.2 The Quantum View of Matter Explains
Spectral Lines
Illustrate the processes of atomic absorption and emission of
light.
Multiple Choice: 27, 28, 29, 38
Short AnswerRelate spectral features to changes in energy
state of an atom.
Multiple Choice: 26, 30, 31, 32, 33, 34, 36, 37, 39
Short Answer: 5.3 The Doppler Shift
Indicates Motion Toward or Away from Us
Explain why radial motion produces a Doppler shift.
Multiple Choice: 40, 41, 42, 43, 46
Short Answer:
5.4 Temperature Determines the Spectrum of
Light That an Object Emits
Summarize what it means for a system to be in equilibrium.
Multiple Choice: 44
Relate temperature to the rate of thermal motions.
Multiple Choice: 45, 52
Short Answer: Illustrate the relationship between flux and
luminosity.
Multiple Choice: 53
Characterize how blackbody spectra describe the luminosity,
temperature, and color of an object.
Multiple Choice: 47, 48, 49, 50, 51, 54, 55, 56
Short Answer: 5.5 The Brightness of Light
Depends on Its Luminosity and Distance
Use the inverse square law to relate luminosity, brightness,
and distance.
Multiple Choice: 57, 58, 59
Short Answer: Working It Out 5.2
Use the Doppler equation to relate radial velocity with
shifts in the wavelengths of spectral lines.
Multiple Choice: 60, 61, 62
Working It Out 5.3
Short Answer: Use Wien’s law to relate the temperature and
peak wavelength of blackbody emission.
Multiple Choice: 63, 64, 65
Short Answer: Working It Out 5.4
Calculate a planet’s temperature based on its parent star and
albedo.
Multiple Choice: 66, 67, 68, 69, 70
Short Answer: MULTIPLE CHOICE
1.
The speed of light was
first determined by which scientist?
a.
Galileo
b.
Newton
c.
Kepler
d.
Rømer
e.
Einstein
2.
The speed of light in a
vacuum is
a.
300,000 m/s.
b.
300,000 mph.
c.
300,000 km/s.
d.
300,000,000 mph.
e.
infinite.
3.
What is the difference
between visible light and X-rays?
a.
Speed; X-rays go faster
than visible light.
b.
Speed; X-rays go slower
than visible light.
c.
Wavelength; X-rays have
a shorter wavelength than visible light.
d.
Wavelength; X-rays have
a longer wavelength than visible light.
e.
X-rays are made up of
particles, whereas visible light is made up of waves.
4.
How does the speed of
light traveling through a medium (such as air or glass) compare to the speed of
light in a vacuum?
a.
It is the same as the
speed of light in a vacuum.
b.
It is always less than
the speed of light in a vacuum.
c.
It is always greater
than the speed of light in a vacuum.
d.
Sometimes it is greater
than the speed of light in a vacuum and sometimes it is less, depending on the
medium.
e.
Light can’t travel
through a medium; it only can go through a vacuum.
5.
A light-year is a unit
that is used to measure
a.
time.
b.
wavelength.
c.
speed.
d.
energy.
e.
distance.
6.
Which formula denotes
how the speed of light is related to its wavelength and frequency?
a.
c = λf
b.
c = λ/f
c.
c = f/λ
d.
c = 1/λf
e.
There is no
relationship between wavelength and frequency.
7.
The color of visible
light is determined by its
a.
speed.
b.
wavelength.
c.
mass.
d.
distance from you.
e.
size.
8.
How do the wavelength
and frequency of red light compare to the wavelength and frequency of blue
light?
a.
Red light has a longer
wavelength and higher frequency than blue light.
b.
Red light has a longer
wavelength and lower frequency than blue light.
c.
Red light has a shorter
wavelength and higher frequency than blue light.
d.
Red light has a shorter
wavelength and lower frequency than blue light.
9.
What wavelengths of
light can the human eye see?
a.
3.8 µm to 7.5 µm
b.
3.8 nm to 7.5 nm
c.
380 cm to 750 cm
d.
380 nm to 750 nm
e.
3.8 m to 7.5 m
10.
What does amplitude
reveal about light?
a.
wavelength
b.
frequency
c.
speed
d.
brightness
11.
The unit Hertz is a
measure of what quantity?
a.
wavelength
b.
frequency
c.
speed
d.
brightness
12.
When talking about a
wave, what does the term “medium” refer to?
a.
the size of an object
b.
the substance through
which the wave travels
c.
the brightness level
d.
the vacuum
13.
A nanometer is a
measure of which quantity?
a.
wavelength
b.
frequency
c.
speed
d.
brightness
14.
Which of the following
photons carries the smallest amount of energy?
a.
a blue photon of the
visible spectrum, whose wavelength is 450 nm
b.
an infrared photon,
whose wavelength is 10−5 m
c.
a red photon in the
visible spectrum, whose wavelength is 700 nm
d.
a microwave photon,
whose wavelength is 10−2 m
e.
an ultraviolet photon,
whose wavelength is 300 nm
15.
Einstein showed that
the _________ could be explained if photons carried quantized amounts of
energy.
a.
warping of space and
time
b.
Heisenberg uncertainty
principle
c.
photoelectric effect
d.
theory of special
relativity
e.
Bohr model of the atom
16.
Light has aspects of
a.
only a wave.
b.
only a particle.
c.
both a particle and a
wave.
d.
neither a particle nor
a wave.
17.
Saying that something
is quantized means that it
a.
is a wave.
b.
is a particle.
c.
travels at the speed of
light.
d.
can only have discrete
quantities.
e.
is smaller than an
atom.
18.
A red photon has a
wavelength of 650 nm. An ultraviolet photon has a wavelength of 250 nm. The
energy of an ultraviolet photon is _________ the energy of a red photon.
a.
2.6 times larger than
b.
6.8 times larger than
c.
2.6 times smaller than
d.
6.8 times smaller than
e.
the same as
19.
Light with a wavelength
of 600 nm has a frequency of
a.
2 × 105 Hz
b.
5 × 107 Hz
c.
2 × 1010
Hz
d.
5 × 1012
Hz
e.
5 × 1014
Hz
20.
Which of the following
lists different types of electromagnetic radiation in order from the shortest
wavelength to the longest wavelength?
a.
radio waves, infrared,
visible, ultraviolet, X-rays
b.
gamma rays,
ultraviolet, visible, infrared, radio waves
c.
gamma rays, X-rays,
infrared, visible, ultraviolet
d.
X-rays, infrared,
visible, ultraviolet, radio waves
e.
radio waves, ultraviolet,
visible, infrared, gamma rays
21.
As wavelength
increases, the energy of a photon _________ and its frequency _________.
a.
increases; decreases
b.
increases; increases
c.
decreases; decreases
d.
decreases; increases
22.
If the frequency of a
beam of light were to increase, its period would _________ and its wavelength
would _________.
a.
decrease; increase
b.
increase; decrease
c.
increase; increase
d.
decrease; decrease
e.
stay the same; stay the
same
23.
The fact that the speed
of light is constant as it travels through a vacuum means that
a.
photons with longer
wavelengths have lower frequencies.
b.
radio wave photons have
shorter wavelengths than gamma ray photons.
c.
X-rays can be
transmitted through the atmosphere around the world.
d.
ultraviolet photons
have less energy than visible photons.
24.
If the wavelength of a
beam of light were to double, how would that affect its frequency?
a.
The frequency would be
four times higher.
b.
The frequency would be
two times higher.
c.
The frequency would be
two times lower.
d.
The frequency would be
four times lower.
e.
There is no
relationship between wavelength and frequency.
25.
If the Sun
instantaneously stopped giving off light, what would happen on the day-side of
Earth?
a.
It would immediately
get dark.
b.
It would get dark 8.3
minutes later.
c.
It would get dark 27
minutes later.
d.
It would get dark 1
hour later.
e.
It would get dark 24
hours later.
26.
When an electron moves
from a higher energy level in an atom to a lower energy level,
a.
the atom is ionized.
b.
a continuous spectrum
is emitted.
c.
a photon is emitted.
d.
a photon is absorbed.
e.
the electron loses
mass.
27.
If you observe an
isolated hot cloud of gas, you will see
a.
an absorption spectrum.
b.
a continuous spectrum.
c.
an emission spectrum.
d.
a rainbow spectrum.
e.
a dark spectrum.
28.
Which of these objects
would emit an absorption spectrum?
a.
an incandescent
lightbulb
b.
a fluorescent lightbulb
c.
an isolated hot gas
cloud
d.
a hot, solid object
e.
a thin, cool gas cloud
that lies in front of a hotter blackbody
29.
If you observe a star,
you will see
a.
an absorption spectrum.
b.
a continuous spectrum.
c.
an emission spectrum.
d.
a rainbow spectrum.
e.
a dark spectrum.
30.
In the energy level
diagram shown in the figure below, the electron is excited to the E4
energy level. If the electron transitions to an energy level giving off a
photon, which level would produce a photon with the largest energy?
a.
E1
b.
E2
c.
E3
d.
E4
e.
E5
31.
In the energy level
diagram shown in the figure below, the electron is excited to the E4
energy level. If the electron transitions to an energy level giving off a
photon, which level would produce a photon with the largest frequency?
a.
E1
b.
E2
c.
E3
d.
E4
e.
E5
32.
In the energy level
diagram shown in the figure below, the electron is excited to the E4
energy level. If the electron transitions to an energy level giving off a
photon, which level would produce a photon with the largest wavelength?
a.
E1
b.
E2
c.
E3
d.
E4
e.
E5
33.
In the energy level
diagram shown in the figure below, the electron is excited to the E2
energy level. If the atom absorbs a photon with the exact frequency to move the
electron to another energy level, which energy level would correspond to the
largest frequency difference?
a.
E1
b.
E2
c.
E3
d.
E4
e.
E5
34.
In the energy level
diagram shown in the figure below, the electron is excited to the E2
energy level. If the atom absorbs a photon with the exact wavelength to move
the electron to another energy level, which energy level would correspond to
the largest wavelength difference?
a.
E1
b.
E2
c.
E3
d.
E4
e.
E5
35.
Astronomers measure the
amount of various elements in other stars and most commonly compare them to
which of the following when studying the composition of a star?
a.
solar abundance
b.
big bang abundance
c.
terrestrial abundance
d.
water
36.
In the figure below,
you see a stellar spectrum. The dip in the data near 650 nm corresponds most
closely with which of the following?
a.
sodium emission
b.
sodium absorption
c.
hydrogen emission
d.
hydrogen absorption
e.
iron absorption
37.
Why is a neutral iron
atom a different element than a neutral carbon atom?
a.
A carbon atom has fewer
neutrons in its nucleus than an iron atom.
b.
An iron atom has more
protons in its nucleus than a carbon atom.
c.
An iron atom has more
electrons than a carbon atom.
d.
A carbon atom is bigger
than an iron atom.
38.
In the quantum
mechanical view of the atom, electrons are often depicted as
a.
a cloud that is
centered on the nucleus.
b.
a particle orbiting the
nucleus.
c.
free to orbit at any
distance from the nucleus.
d.
a particle inside the
nucleus.
39.
The n = 5 electronic
energy level in a hydrogen atom is 1.5 × 10−19 J higher than the
n = 3 level. If an electron moves from the n = 5 level to the n = 3 level, then a
photon of wavelength
a.
1.3 nm, which is in the
ultraviolet region, is emitted.
b.
1.3 nm, which is in the
ultraviolet region, is absorbed.
c.
1,300 nm, which is in
the infrared region, is absorbed.
d.
1,300 nm, which is in
the infrared region, is emitted.
e.
No light will be
absorbed or emitted.
40.
The Doppler shift can
be used to determine the _________ of an object.
a.
energy
b.
temperature
c.
radial velocity
d.
color
e.
three-dimensional
velocity
41.
A spaceship is
traveling toward Earth while giving off a constant radio signal with a
wavelength of 1 meter (m). What will the signal look like to people on Earth?
a.
a signal with a
wavelength less than 1 m
b.
a signal with a
wavelength more than 1 m
c.
a signal moving faster
than the speed of light
d.
a signal moving slower
than the speed of light
e.
a signal with a
wavelength of 1 m, moving the normal speed of light
42.
Which of these stars
would have the biggest redshift?
a.
a star moving at low
speed toward you
b.
a star moving at high
speed toward you
c.
a star moving at low
speed away from you
d.
a star moving at high
speed away from you
e.
a star that is not moving
away from you or toward you
43.
A spaceship is
traveling from planet B on the left, toward planet A on the right. The
spaceship is traveling at a speed of 15,000 km/s to the left while it sends out
a signal with a wavelength of 4 m. If astronomers living on planets A and B
measure the radio waves coming from the spaceship, what wavelengths will they
measure?
a.
Planet A measures 6 m,
and planet B measures 2 m.
b.
Planet A measures 2 m,
and planet B measures 6 m.
c.
Planet A measures 4.2
m, and planet B measures 3.8 m.
d.
Planet A measures 3.8
m, and planet B measures 4.2 m.
e.
Both Planet A and
planet B measure 4 m.
44.
What does it mean to
say that an object is in thermal equilibrium?
a.
It isn’t absorbing any
energy.
b.
It isn’t radiating any
energy.
c.
It is radiating more
energy than it is absorbing.
d.
It is absorbing more
energy than it is radiating.
e.
It is absorbing the
same amount of energy that it is radiating.
45.
The Kelvin temperature
scale is used in astronomy because
a.
at 0 K an object has
absolutely zero energy.
b.
water freezes at 0 K.
c.
water boils at 100 K.
d.
hydrogen freezes at 0
K.
e.
the highest temperature
possible is 1000 K.
46.
You observe the
spectrum of two stars. Star A has an emission line from a known element at 600
nm. Star B has emission lines from the same atom, but the emission line is
occurring at 650 nm. One possible explanation for this observation is: that
star A is
a.
cooler than star B.
b.
farther away from us
than star B.
c.
moving toward us faster
than star B.
d.
made of different
elements than star B.
e.
larger than star B.
47.
In the figure below,
which blackbody spectrum corresponds to the object with the highest
temperature?
a.
A
b.
B
c.
C
d.
D
e.
E
48.
In the figure below,
which blackbody spectrum corresponds to the object that would appear the most
red to the human eye?
a.
A
b.
B
c.
C
d.
D
e.
E
49.
In the figure below, which
blackbody spectrum corresponds to the object that would appear white to the
human eye?
a.
A
b.
B
c.
C
d.
D
e.
E
50.
As a blackbody’s
temperature increases, it also becomes _________ and _________.
a.
more luminous; redder
b.
more luminous; bluer
c.
less luminous; redder
d.
less luminous; bluer
e.
more luminous; stays
the same color
51.
Compare two blackbody
objects, one at 200 K and one at 400 K. How much larger is the flux from the
400 K object compared to the flux from the 200 K object?
a.
2 times larger
b.
4 times larger
c.
8 times larger
d.
16 times larger
e.
They have the same
flux.
52.
At what temperature
does water freeze?
a.
0 K
b.
32 K
c.
100 K
d.
273 K
e.
373 K
53.
You observe a red star
and a blue star and are able to determine that they are the same size. Which
star has a higher surface temperature, and which star is more luminous?
a.
The red star has a
higher surface temperature and more luminous.
b.
The red star has a
higher surface temperature, and the blue star is more luminous.
c.
The blue star has a
higher surface temperature and more luminous.
d.
The blue star has a
higher surface temperature, and the red star is more luminous.
e.
They have the same
luminosities and temperatures.
54.
At what peak wavelength
does your body radiate the most given that your temperature is approximately
that of Earth, which is 300 K?
a.
10−5 m
b.
10−3 m
c.
10−2 m
d.
10 m
e.
1,000 m
55.
Why do some stars in
the sky appear blue, whereas other stars appear red?
a.
The red stars have
higher surface temperatures than the blue stars.
b.
The blue stars have
higher surface temperatures than the red stars.
c.
The blue stars are
closer to us than the red stars.
d.
The red stars are
closer to us than the blue stars.
e.
The blue stars are
moving toward us, while red stars are moving away from us.
56.
Consider an
incandescent lightbulb. If you wanted to turn a 10-W lightbulb into a 100-W lightbulb,
how would you change the temperature of the filament inside the bulb?
a.
Raise its temperature
by a factor of 3.2.
b.
Raise its temperature
by a factor of 1.8.
c.
Raise its temperature
by a factor of 10.
d.
Lower its temperature
by a factor of 2.6.
e.
Lower its temperature
by a factor of 5.4.
57.
Star A and star B
appear equally bright in the sky. Star A is twice as far away from Earth as
star B. How do the luminosities of stars A and B compare?
a.
Star A is twice as
luminous as star B.
b.
Star B is twice as
luminous as star A.
c.
Star A is four times as
luminous as star B.
d.
Star B is four times as
luminous as star A.
e.
Stars A and B have the
same luminosity.
58.
Star C and star D have
the same luminosity. Star C is twice as far away from Earth as star D. How do
the brightnesses of stars C and D compare?
a.
Star C appears four
times as bright as star D.
b.
Star C appears twice as
bright as star D.
c.
Star D appears twice as
bright as star C.
d.
Star D appears four
times as bright as star C.
e.
Stars C and D appear
equally bright.
59.
The average red giant
in the night sky is about 1,000 times more luminous than the average
main-sequence star. If both kinds of stars have about the same brightness, how
much farther away are the red giants compared to the main-sequence stars?
a.
32 times farther
b.
1,000 times farther
c.
65 times farther
d.
5.6 times farther
e.
The red giants and
main-sequence stars have approximately the same distances.
60.
You are driving on the
freeway when a police officer records a shift of −7 nm when he or
she your speed with a radar gun that operates at a wavelength of 0.1 m. How
fast were you going?
a.
43 mph
b.
83 mph
c.
21 mph
d.
65 mph
e.
47 mph
61.
You record the spectrum
of a star and find that a calcium absorption line has an observed wavelength of
394.0 nm. This calcium absorption line has a rest wavelength is 393.3 nm. What
is the radial velocity of this star?
a.
5,000 km/s
b.
500 km/s
c.
50 km/s
d.
5 km/s
e.
0.5 km/s
62.
If you find that the
hydrogen alpha line in a star’s spectrum occurs at a wavelength of 656.45 nm,
what is the star’s radial velocity? Note that the rest wavelength of this line
is 656.30 nm.
a.
150 km/s away from you
b.
150 km/s toward you
c.
350 km/s toward you
d.
70 km/s away from you
e.
70 km/s toward you
.
63.
If Jupiter has a
temperature of 165 K, at what wavelength does its spectrum peak? Use the
electromagnetic spectrum in the figure below to answer this question.
a.
18 nm—orange visible
wavelengths
b.
1,800 mm—microwave
wavelengths
c.
1,800 nm—infrared
wavelengths
d.
18,000 nm—ultraviolet
wavelengths
e.
18,000 nm—infrared
wavelengths
64.
If the typical
temperature of a red giant is 3000 K, at what wavelength is its radiation the
brightest? Use the electromagnetic spectrum in the figure below to help you
answer this question.
a.
1 µm—infrared
wavelengths
b.
1 µm—red visible
wavelengths
c.
20 µm—infrared
wavelengths
d.
20 µm—red visible
wavelengths
e.
700 µm—red visible
wavelengths
65.
If a star has a peak
wavelength of 290 nm, what is its surface temperature?
a.
1000 K
b.
2000 K
c.
5000 K
d.
10,000 K
e.
100,000 K
66.
A black car left in the
sunlight becomes hotter than a white car left in the sunlight under the same
conditions because
a.
the white car absorbs
more sunlight than the black car.
b.
the white car reflects
more sunlight than the black car.
c.
the black car absorbs
only blue photons and reflects red photons, whereas the white car absorbs only
red photons and reflects blue photons.
d.
the atoms in the black
car are smaller than the atoms in the white car.]
67.
Which of the following
factors does not directly influence the temperature of a planet?
a.
the luminosity of the
Sun
b.
the distance of the
planet from the Sun
c.
the albedo of the
planet
d.
the size of the planet
e.
the atmosphere of the
planet
68.
An asteroid with an
albedo of 0.1 and a comet with an albedo of 0.6 are orbiting at roughly the
same distance from the Sun. How do their temperatures compare?
a.
They both have the same
temperature.
b.
The comet is hotter
than the asteroid.
c.
The asteroid is hotter
than the comet.
d.
You must know their
sizes to compare their temperatures.
e.
You must know their
compositions to compare their temperatures.
69.
Which of these planets
would be expected to have the highest average temperature?
a.
a light-colored planet
close to the Sun
b.
a dark-colored planet
close to the Sun
c.
a light-colored planet
far from the Sun
d.
a dark-colored planet
far from the Sun
e.
There is not enough
information to know which would be hotter.
70.
If Saturn has a semimajor
axis of 10 astronomical units (AU) and an albedo of 0.7. If Saturn were to emit
the same amount of energy as it absorbs from the Sun, what is Saturn’s expected
temperature?
a.
130 K
b.
15 K
c.
35 K
d.
170 K
e.
65 K
SHORT ANSWER
1.
Compare and contrast
the wavelengths, frequencies, speeds, and energies of red and blue photons.
2.
How is the energy of a
photon related to its, frequency, wavelength, and speed?
3.
What is the intensity
of light, and how does it depend on wavelength?
4.
What is an
electromagnetic wave?
5.
The first five energy
levels of hydrogen are E1 = 0 eV, E2
= 10.2 eV, E3 = 12.1 eV, E4
= 12.7 eV, and E5 = 13.1 eV. If the
electron is in the n = 4 level, what energies can a single emitted photon have?
6.
Explain what the term
“ground state” means.
7.
Explain how continuous,
emission, and absorption spectra are produced.
8.
How are atoms excited,
and why do they become de-excited?
9.
Explain how an emission
line is formed, and why it is unique to a given element.
10.
The difference in
energy between the n = 2 and n = 1 electronic energy levels in the hydrogen atom is 1.6 × 10−18 J. If an electron
moves from the n = 1 level to the n = 2 level, will a
photon be emitted or absorbed? What will its energy be, and what type of
electromagnetic radiation is it? Use the electromagnetic spectrum shown in the
figure below to answer this question.
Describe, in your own words, why electrons cannot orbit the
nucleus like the planets orbit Why do we see black lines in an absorption
spectrum if the absorbed photons are (almost) instantaneously reemitted by the
atoms in the cloud?
11.
For a star that lies in
the plane of Earth’s orbit around the Sun, how does the observed wavelength of
the hydrogen absorption line at 656.28 nm in its spectrum change in wavelength
(if at all) with the time of year?
12.
A spaceship approaches
Earth at 0.9 times the speed of light and shines a powerful searchlight onto
Earth. How fast will the photons from this searchlight be moving when they hit
Earth?
13.
If you are standing in
a fixed location, you may notice that the pitch of a passing train’s whistle
changes. What produces this effect?
14.
Suppose you observe a
star emitting a certain emission line of helium at 584.8 nm. The rest
wavelength of this line is 587.6 nm. How fast is the star moving? Is it moving
toward you or away from you?
15.
Imagine a satellite is
orbiting a planet. This satellite gives off radio waves with a constant
wavelength of 1 m. An observer on Earth then measures the signal from the
satellite when it is directly between Earth and the planet. How does the
wavelength received compare to the wavelength that the satellite gave off?
16.
Explain what is meant
when someone says “thermal motions.”
17.
Sketch two blackbody
curves, one for a hot blue object and the second for a cooler red object. Be
sure to label your axes.
18.
How does temperature
relate to the speed of gas particles?
19.
Name four physical
properties of an object that we can determine by analyzing the radiation that
it emits, and briefly describe how these properties are determined. Cite the
names of any laws that apply.
20.
Imagine you observed
three different stars: a red star, a blue star, and a yellow star. You are able
to determine that each of these stars has the same radius. Answer each question
below and explain how you know.
A: Which star has the highest surface temperature?
B: Which star is the most luminous?
C: Which star is the brightest?
21.
If you were driving
down a deserted country road and you saw a light in the distance, what would
you need to measure or know about it in order to calculate how far away it was?
22.
Imagine you see a
street lamp that is 100 m away from you and is 10,000 times more luminous than
a firefly. How close would you have to be to the firefly to make it look as
bright as the street lamp?
23.
How much would you have
to change the temperature of an object if you wanted to increase its flux by a
factor of 100?
24.
If you want a
blackbody’s peak wavelength to be cut in half, by how much do you need to
increase its temperature?
25.
What two factors
control a planet’s surface temperature if it has no atmosphere, and no internal
source of heat?
26.
How can the average
temperature of Earth stay approximately constant even though Earth is always
getting energy from the Sun?
27.
Astronomers have now
found a large number of exoplanets, which are planets that orbit around stars
other than the Sun. Imagine astronomers found a planet identical to Earth
orbiting a star that had the same radius as the Sun, but with a temperature
that is twice the temperature of the Sun. How far would this new planet need to
be away from its star to have the same average temperature as Earth?
28.
What would you expect
the temperature of a comet to be if its distance was 100 AU from the Sun?
Assume that it is very icy and reflective so that its albedo is equal to 0.6.
Does it matter what the radius of the comet is?
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