TEST BANK 21ST CENTURY ASTRONOMY THE SOLAR SYSTEM 5TH EDITION BY KAY
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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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