Question 1

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.

Accepted Answer

The answer of The force of gravity between Saturn and...

Question 2

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.

Accepted Answer

Using Kepler's third law, the mass of the planet can be calculated. The formula is M = (4π²a³)/(G T²), where a is the semi-major axis (distance), T is the period, and G is the gravitational constant. Plugging in the values, the mass is approximately 0.4 times the mass of Jupiter.

Question 3

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:

Accepted Answer

According to Kepler's laws of planetary motion, increasing the altitude of a satellite requires a decrease in its orbital speed to maintain a stable orbit. Therefore, we would need to decrease the Hubble Space Telescope's orbital speed to keep it in a stable orbit at a higher altitude.

Question 4

_________ 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.

Accepted Answer

This hypothesis was made by Isaac Newton in his law of universal gravitation.

Question 5

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

Accepted Answer

The force of gravity on an object is determined by its mass. The more massive an object is, the greater the force of gravity acting on it. This is described by the equation F = ma, where F is the force of gravity, m is the mass of the object, and a is the acceleration due to gravity.

Question 6

If the distance between the Earth and Sun were cut in half,the gravitational force between these two objects would:

Accepted Answer

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If the distance between the Earth and Sun were cut in half, the square of the distance would become (1/2)^2 = 1/4 of what it was before. Therefore, the gravitational force would increase by a factor of (1/(1/4)) = 4.

Question 7

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?

Accepted Answer

The answer of If you have two moons that have...

Question 8

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.

Accepted Answer

The answer of Titan,the largest moon of Saturn,has an orbital...

Question 9

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.

Accepted Answer

The answer of The force of gravity between the Earth...

Question 10

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.

Accepted Answer

The escape velocity from a planet's surface depends only on the planet's mass and radius, not on the mass of the satellite. The escape velocity from Mars is approximately 5,000 m/s.

Question 11

If an object is moving in a circular orbit at a constant speed,which of the following is FALSE?

Accepted Answer

The answer of If an object is moving in a...

Question 12

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.

Accepted Answer

The answer of Mercury orbits the Sun with an average...

Question 13

What is the escape velocity from a large asteroid if its mass is 6 × 10²¹ kg and its radius is 2,400 km?

Accepted Answer

Escape velocity is calculated using the formula v = sqrt(2GM/R). Plugging in the values for G, M, and R gives approximately 580 m/s.

Question 14

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.

Accepted Answer

Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semimajor axis of its orbit. In this case, the planet has the same mass as Jupiter, but its orbital period is 2 years and its semimajor axis is 1 AU. Jupiter's orbital period is 12 years and its semimajor axis is 5.4 AU. So, the ratio of the square of the orbital periods is (2/12)^2 = 1/36, and the ratio of the cubes of the semimajor axes is (1/5.4)^3 = 1/185. Therefore, the mass of the star must be 36/185 = 0.25 times the mass of the Sun.

Question 15

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?

Accepted Answer

The gravitational force between two objects is directly proportional to the mass of both objects and inversely proportional to the square of the distance between them. In this scenario, Rock S has 20 times the mass of Rock T, which means that the gravitational force between Rock S and Rock T will be 20 times greater on Rock T than on Rock S (since force is always reciprocally proportional to mass). However, since the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, Rock T will accelerate faster than Rock S since it experiences a larger force (as a result of its smaller mass) over the same distance. Therefore, the correct answer is B) Rock T will accelerate faster.

Question 16

What is the escape velocity from Mars if its mass is 6 × 10²³ kg and its radius is 3,400 km?

Accepted Answer

Escape velocity can be calculated using the formula:

v = √(2GM / r)

where:
G is the gravitational constant (6.67 × 10^-11 Nm^2/kg^2)
M is the mass of the planet
r is the radius of the planet

Plugging in the values for Mars, we get:

v = √(2(6.67 × 10^-11 Nm^2/kg^2)(6 × 10^23 kg) / 3,400,000 m)
v ≈ 4,900 m/s

Therefore, the escape velocity from Mars is about 4,900 m/s, which corresponds to choice B.

Question 17

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.

Accepted Answer

The answer of How fast is the Moon moving as...

Question 18

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

Accepted Answer

The answer of If you measured the orbital period of...

Question 19

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

Accepted Answer

Astronauts on the space shuttle feel weightless because they are in a state of constant free fall around the Earth. In other words, they are falling towards the Earth at the same rate as the shuttle, causing them to experience a sensation of weightlessness.

Question 20

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.

Accepted Answer

The velocity of an object in a circular orbit can be calculated with the formula:
v = √(GM/r)
Where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the orbit. 
Plugging in the given values:
v = √((6.67 × 10^-11)(6 × 10^24)/(6400 + 600) × 1000)
v ≈ 7,500 m/s

Quiz 4: Gravity and Orbits

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.

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.

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:

_________ 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.

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

If the distance between the Earth and Sun were cut in half,the gravitational force between these two objects would:

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?

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.

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.

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.

If an object is moving in a circular orbit at a constant speed,which of the following is FALSE?

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.

What is the escape velocity from a large asteroid if its mass is 6 × 10²¹ kg and its radius is 2,400 km?

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.

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?

What is the escape velocity from Mars if its mass is 6 × 10²³ kg and its radius is 3,400 km?

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.

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

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

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.

Quiz 4: Gravity and Orbits

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.

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.

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:

_________ 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.

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

If the distance between the Earth and Sun were cut in half,the gravitational force between these two objects would:

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?

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.

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.

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.

If an object is moving in a circular orbit at a constant speed,which of the following is FALSE?

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.

What is the escape velocity from a large asteroid if its mass is 6 × 1021 kg and its radius is 2,400 km?

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.

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?

What is the escape velocity from Mars if its mass is 6 × 1023 kg and its radius is 3,400 km?

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.

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

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

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.

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.

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.

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.

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.

What is the escape velocity from a large asteroid if its mass is 6 × 10²¹ kg and its radius is 2,400 km?

What is the escape velocity from Mars if its mass is 6 × 10²³ kg and its radius is 3,400 km?

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.