Deck 4: Gravity and Orbits

Question 1

The escape velocity on the Moon is less than that on Earth.

Answer 1

True

Question 2

According to the scales in the figure, 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.

Answer 2

6

Question 3

If you weighed 150 lbs on Earth, what would you weigh on Mars? For reference, Mars has a mass that is 0.1 times the Earth's mass and Mars has a radius that is 0.5 times the Earth's radius.

A) 30 lbs
B) 110 lbs
C) 75 lbs
D) 60 lbs
E) 15 lbs

Answer 3

60 lbs

Question 4

Because of the Moon's tidal effect on the oceans, the Moon's orbital distance is shrinking and eventually the Moon will collide with the Earth.

Question 5

An unbound orbit results when a satellite has a velocity greater than the escape velocity.

Question 6

More massive objects fall faster in the Earth's gravitational field than less massive objects.

Question 7

Moons that wander inside of a planet's Roche limit can be torn apart due to tidal forces.

Question 8

Once two objects are far enough away from each other, they no longer exert any gravitational attraction on each other.

Question 9

All objects on Earth, regardless of the size of their mass, fall with the same acceleration.

Question 10

The tidal force on the Earth due to the Moon is about two times stronger than that due to the Sun.

Question 11

Ocean tides on Earth are caused primarily by the gravitational pull of the Sun.

Question 12

Suppose you are suddenly transported to a planet that had 1/4 the radius of Earth but the same mass as the Earth. Your weight would _________ by a factor of _________.

A) increase; 4
B) increase; 16
C) decrease; 4
D) decrease; 16
E) decrease; 8

Question 13

If you weighed 100 lbs on Earth, what would you weigh at the upper atmosphere of Jupiter? For reference, Jupiter has a mass that is about 300 times the Earth's mass and a radius that is 10 times the Earth's radius.

A) 10,000 lbs
B) 3,000 lbs
C) 1,000 lbs
D) 300 lbs
E) 30 lbs

Question 14

The only acceleration you experience on a merry-go-round is when it starts or stops.

Question 15

Mass and weight are different names for the same physical property of matter.

Question 16

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

Question 17

Suppose you are suddenly transported to a planet with 1/4 the mass of Earth but the same radius as the Earth. Your weight would _________ by a factor of _________.

A) increase; 4
B) increase; 16
C) decrease; 4
D) decrease; 16
E) increase; 2

Question 18

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.

Question 19

An astronaut orbiting the Earth in a circular orbit at a constant speed does not feel the force of gravity because his or her acceleration is zero.

Question 20

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) all of the above
E) Nothing changes.

Question 21

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, the Earth's mass is 6 * 10²⁴ kg.

A) 290 M_Earth
B) 130 M_Earth
C) 90 M_Earth
D) 40 M_Earth
E) 4 M_Earth

Question 22

Mercury orbits the Sun with an average distance of 0.4 AU, and its mass is 0.06 times that of the Earth. The gravitational force that the Sun exerts on Mercury is _______________ times the force of gravity that the Sun exerts on the Earth.

A) 20
B) 6
C) 4
D) 0.4
E) 0.1

Question 23

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

Question 24

If the distance between the Earth and 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

Question 25

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 available to answer

Question 26

How fast is the Moon moving as it orbits the 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

Question 27

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 M _$\odot$
B) 0.5 M _$\odot$
C) 2.0 M _$\odot$
D) 1.5 M _$\odot$
E) not enough information available to answer

Question 28

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

Question 29

Astronauts orbiting Earth in the space shuttle feel weightless in space because:

A) they are farther away from the Earth
B) they eat less food while in orbit
C) the gravitational pull of the Moon counteracts the Earth's gravitational pull
D) they are in constant free fall around the Earth
E) they are in space where there is no gravity

Question 30

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.

Question 31

The Hubble Space Telescope orbits at an altitude of 600 km above the Earth's surface. Assuming it is in a stable circular orbit, what is its velocity? For reference, the 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.

Question 32

If we wanted to increase the Hubble Space Telescope's altitude above the 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

Question 33

_________ hypothesized that planetary motions could be explained by a force arising from the attraction between the mass of the planet and 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

Question 34

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.

Question 35

The force of gravity that an object has is directly proportional to its:

A) inertia
B) size
C) mass
D) density
E) distance

Question 36

The force of gravity between the Earth and the Sun is _________ the force of gravity between the Earth and the Moon. For reference, the average distance between the Earth and the Moon is 0.003 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

Question 37

According to the progression shown in the figure above, 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

Question 38

The force of gravity between Saturn and the Sun is _________ the force of gravity between the 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

Question 39

If you measured the orbital period of the Moon and the distance between the Earth and the Moon then you could calculate:

A) the mass of the Moon
B) the sum of the masses of the Earth and the Moon
C) the average distance between the Earth and Sun
D) the radius of the Earth
E) the radius of the Moon

Question 40

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.

Question 41

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 M _$\odot$
B) 12 M _$\odot$
C) 8 M _$\odot$
D) 5 M _$\odot$
E) 17 M _$\odot$

Question 42

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 the Earth and Sun
E) all sides of the moon face Earth at one time or another

Question 43

Figure 2
According to Figure 2, 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

Question 44

If you discovered a planet orbiting another star, and the planet had an orbital period of 2 years and a semimajor axis of 1 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 M _$\odot$
B) 0.5 M _$\odot$
C) 1.0 M _$\odot$
D) 1.25 M _$\odot$
E) 2.0 M _$\odot$

Question 45

Figure 1
According to Figure 1, a high tide at a given location will occur ____ time(s) a day.

A) one
B) three
C) two
D) four
E) eight

Question 46

In the figure shown below, the person on the Moon is standing at the same location on the Moon as the Moon rotates around the Earth. Based on this, we see that the Moon's rotational period is equal to:

A) the Earth's rotational period
B) half the Earth's rotational period
C) the Moon's orbital period
D) half the Moon's orbital period
E) the Earth's orbital period around the Sun

Question 47

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; smaller
B) spring; larger
C) lunar; smaller
D) neap; smaller
E) neap; larger

Question 48

Figure 2
According to Figure 2, neap tides occur at which phases of the Moon?

A) new and full
B) third quarter
C) first quarter and third quarter
D) full
E) new

Question 49

Figure 1
According to Figure 1, the approximate amount of time between a high tide and a low tide at a given location is:

A) 3 hours
B) 8 hours
C) 6 hours
D) 12 hours
E) 24 hours

Question 50

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 M_Jupiter
B) 0.4 M_Jupiter
C) 1 M_Jupiter
D) 4 M_Jupiter
E) 10 M_Jupiter

Question 51

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 gravitiational 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

Question 52

The moon keeps the same hemisphere facing the Earth because the _________ is equal to the _________.

A) rotational period of the Earth;
Orbital period of the Moon around the Earth
B) orbital period of the Earth;
Orbital period of the Moon around the Earth
C) orbital period of the Moon around the Earth;
Rotational period of the Earth
D) rotational period of the Moon;
Orbital period of the Moon around the Earth
E) rotational period of the Earth;
Orbital period of the Earth

Question 53

Figure 2
According to Figure 2, when the Moon is in between Earth and the Sun, _________ tides occur.

A) spring
B) no
C) neap
D) high
E) low

Question 54

Figure 2
According to Figure 2, 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

Question 55

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 the Earth
E) will increase or decrease depending on future changes in the tides on the Earth due to the Moon

Question 56

Figure 2
According to Figure 2, when Earth is in between the Moon and the Sun, _________ tides occur.

A) spring
B) no
C) neap
D) high
E) low

Question 57

Figure 1
According to Figure 1, the approximate amount of time between two high tides at a given location is:

A) 3 hours
B) 8 hours
C) 6 hours
D) 12 hours
E) 24 hours

Question 58

Because of the tidal force between the Earth and Moon:

A) the 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.

Question 59

Figure 2
According to Figure 2, spring tides occur at which phases of the Moon?

A) third quarter
B) new and full
C) first and third quarter
D) full
E) new

Question 60

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

Question 61

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 the Earth at a distance of 1 AU from the Sun? Give your answer in units of m/s.

Question 62

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

Question 63

Tidal forces can affect:

A) moons
B) galaxies
C) planets
D) satellites
E) all of the above

Question 64

How does the force of gravity between the Sun and Mercury compare to the gravitational force between the Sun and the 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 the Earth.

Question 65

The International Space Station orbits at an altitude of 400 km above the Earth's surface. Assuming it is in a stable circular orbit, what is its velocity? For reference, the Earth's radius is 6,400 km, and Earth's mass is 6 * 10²⁴ kg and G = 6.7 * 10^-11 N m²/kg².

Question 66

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 the Earth?

Question 67

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

Question 68

Mars has about one tenth the mass of Earth and half the Earth's radius. How does the acceleration of gravity on Mars compare to that on Earth?

Question 69

Is there a difference in your weight between when you are on top of a mountain at 1,000 meters above sea level compared to when you are sitting in a classroom at 10 meters above sea level?

Question 70

Explain the difference between being weightless and being in free fall.

Question 71

The 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

Question 72

In a system with three gravitating bodies, there are _________ stable locations called _________ points for the third object to orbit in lockstep with the two more massive objects.

A) 3; tidal
B) 2; tidal
C) 4; Roche
D) 2; Lagrange
E) 5; Lagrange

Question 73

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.

Question 74

How much stronger is the gravitational force of the Sun on the 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 the Earth.

Question 75

How does the force of gravity between the Sun and Jupiter compare to the gravitational force between the Sun and the Earth? Note that the semimajor axis of Jupiter's orbit is 5.2 AU, and Jupiter's mass is 320 times the mass of the Earth.

Question 76

Explain what the terms circular velocity and escape velocity mean. Give the formula for each and explain what each mathematical symbol represents.

Question 77

_________ 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) Techtonic activity
E) A collision with a Mars-sized object

Question 78

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.

Question 79

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.

Question 80

Saturn has 95 times the mass of Earth, and its atmosphere extends outward 9.5 times the Earth's radius. How does the acceleration due to gravity at the edge of Saturn's atmosphere compare to that on the Earth?