Question 1

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.

Accepted Answer

The answer of What is the velocity one would need...

Question 2

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

Accepted Answer

Mercury experiences tidal forces from the Sun that have caused it to become tidally locked, meaning it rotates on its axis exactly three times for every two revolutions around the sun. So, for every three rotations on its axis, it completes two orbits around the Sun.

Question 3

Tidal forces can affect:
A) moons
B) galaxies
C) planets
D) satellites
E) all of the above

Accepted Answer

Tidal forces are the gravitational forces exerted on an object by another object, and they can affect any object that has a gravitational interaction with another object. Moons, planets, galaxies, and satellites all have gravitational interactions with other objects and can be affected by tidal forces. Therefore, all of the above choices are correct.

Question 4

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.

Accepted Answer

The answer of How does the force of gravity between...

Question 5

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.

Accepted Answer

The answer of The International Space Station orbits at an...

Question 6

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?

Accepted Answer

The answer of How would the acceleration due to gravity...

Question 7

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

Accepted Answer

The distance between Earth and the Moon is increasing due to tidal forces from the Moon, which cause the Earth's rotation to slow and the Moon to gradually move away.

Question 8

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?

Accepted Answer

The answer of Mars has about one tenth the mass...

Question 9

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?

Accepted Answer

The answer of Is there a difference in your weight...

Question 10

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

Accepted Answer

The answer of Explain the difference between being weightless and...

Question 11

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

Accepted Answer

The gravitational forces of the moon cause tides on Earth, which creates a tidal bulge that interacts with the Moon's gravity. As a result, the Earth's rotation slows down slightly. This effect is known as tidal braking. Over the course of several millennia, the slowing of Earth's rotation rate will lead to longer days.

Question 12

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

Accepted Answer

The correct answer is D, as there are two stable points in a system with three gravitating bodies known as Lagrange points. At these points, the gravitational forces from the two more massive objects and the centrifugal force acting on the third object are in balance, allowing it to maintain a stable orbit. Tidal points (A) refer to locations where the gravitational forces of the two larger bodies cancel out and the tidal forces of each body prevail. Roche points (C) refer to locations where the gravitational forces are so strong that a third object would be torn apart by tidal forces. There are five Lagrange points in a system with two gravitating bodies, but the addition of a third object changes the dynamics.

Question 13

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.

Accepted Answer

The answer of Show that the gravitational pull on Earth...

Question 14

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.

Accepted Answer

The answer of How much stronger is the gravitational force...

Question 15

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.

Accepted Answer

The answer of How does the force of gravity between...

Question 16

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

Accepted Answer

The answer of Explain what the terms circular velocity and...

Question 17

_________ 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

Accepted Answer

The answer of _________ may have been instrumental in shaping...

Question 18

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.

Accepted Answer

The answer of Which of the statements below are TRUE...

Question 19

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.

Accepted Answer

The ring systems around giant planets are typically located within the Roche limit, not beyond it.

Question 20

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?

Accepted Answer

The answer of Saturn has 95 times the mass of...

Quiz 4: Gravity and Orbits

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.

Because of tidal forces, for every _ time(s) it rotates on its axis, Mercury revolves around the Sun _ time(s) .

Tidal forces can affect:

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.

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.

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?

The distance between Earth and the Moon is increasing because of:

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?

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?

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

The Earth's rotation rate is slowing because of:

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.

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.

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.

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.

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

_________ may have been instrumental in shaping the interface between Earth's land and oceans where the chemistry needed to develop life may have occurred.

Which of the statements below are TRUE about the Roche limit of a giant planet?

Which one of the statements below about a planet's Roche limit is FALSE?

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?

Quiz 4: Gravity and Orbits

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.

Because of tidal forces, for every _________ time(s) it rotates on its axis, Mercury revolves around the Sun _________ time(s) .

Tidal forces can affect:

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.

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.

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?

The distance between Earth and the Moon is increasing because of:

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?

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?

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

The Earth's rotation rate is slowing because of:

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.

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.

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.

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.

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

_________ may have been instrumental in shaping the interface between Earth's land and oceans where the chemistry needed to develop life may have occurred.

Which of the statements below are TRUE about the Roche limit of a giant planet?

Which one of the statements below about a planet's Roche limit is FALSE?

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?

Because of tidal forces, for every _ time(s) it rotates on its axis, Mercury revolves around the Sun _ time(s) .

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.

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.

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.