Question 1

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

Accepted Answer

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

Question 2

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

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. In this case, Mercury's mass is 0.06 times that of the Earth, and its average distance from the Sun is 0.4 AU. Therefore, the gravitational force that the Sun exerts on Mercury is 0.06 * (1/0.4)^2 = 0.4 times the force of gravity that the Sun exerts on the Earth.

Question 3

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

Accepted Answer

Escape velocity is calculated using the formula v = sqrt(2GM/R). Plugging in the given mass and radius, the escape velocity is approximately 580 m/s.

Question 4

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

Accepted Answer

The gravitational force between two objects is inversely proportional to the square of the distance between them, according to Newton's law of universal gravitation. Therefore, if the distance between the Earth and Sun were halved (i.e. decreased by a factor of 2), the gravitational force between them would increase by a factor of 2² = 4. Therefore, the correct answer is D) increase by 4.

Question 5

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

Accepted Answer

The acceleration due to gravity is directly proportional to the mass of the object. Since rock S has 20 times the mass of rock T, it will experience 1/20th the acceleration due to gravity compared to rock T. Therefore, rock T will accelerate faster in response to gravity.

Question 6

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

Accepted Answer

The Moon's orbital speed can be calculated using the formula for orbital speed: v = 2πr/T, where r is the radius of the orbit and T is the period. Plugging in the values (r = 400,000 km, T = 27 days converted to seconds), the speed is approximately 1 km/s.

Question 7

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

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 has an orbital period of 12 years and a semimajor axis of 5.4 AU. Therefore, the mass of the star must be 0.25 times the mass of the Sun.

Question 8

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

Accepted Answer

The formula for escape velocity is $v_e=\sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $r$ is the radius of the planet. Plugging in the values for Mars, we get:

$v_e=\sqrt{\frac{2(6.67	imes10^{-11})(6	imes10^{23})}{3,400	imes10^3}}\approx4,900	ext{ m/s}$

Therefore, the best choice is B.

Question 9

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

Accepted Answer

Astronauts in the space shuttle are constantly falling towards the Earth due to the Earth's gravitational pull, but their forward momentum and velocity keeps them in a perpetual state of free fall. This creates the sensation of weightlessness or zero gravity.

Question 10

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.

Accepted Answer

An object moving in a circular orbit at a constant speed has a centripetal acceleration directed towards the center of the circle, so its acceleration is not zero.

Question 11

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.

Accepted Answer

The velocity of the Hubble Space Telescope in a circular orbit can be found using the formula v = sqrt(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the orbiting object (in this case, the sum of the Earth's radius and the altitude of the orbit). Plugging in the given values, we get v = sqrt((6.67 x 10^-11 Nm^2/kg^2) x (6 x 10^24 kg) / (6400 km + 600 km) x 1000 m/km) = 7,500 m/s. Therefore, the answer is B.

Question 12

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

Accepted Answer

The answer of If we wanted to increase the Hubble...

Question 13

_________ 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

Accepted Answer

Isaac Newton hypothesized the law of universal gravitation, which states that 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. This law was able to explain the motions of planets around the Sun.

Question 14

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.

Accepted Answer

The escape velocity from a celestial body depends only on the mass and radius of the body, not on the mass of the object trying to escape. For Mars, the escape velocity is approximately 5,000 m/s.

Question 15

The force of gravity that an object has is directly proportional to its:
A) inertia
B) size
C) mass
D) density
E) distance

Accepted Answer

The force of gravity that an object has is directly proportional to its mass. This means that the more massive an object is, the stronger the force of gravity it will have.

Question 16

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

Accepted Answer

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

Question 17

-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

Accepted Answer

The gravitational force between two objects is inversely proportional to the square of the distance between them. If the distance is increased to four times its original value, the gravitational force becomes 1/(4^2) = 1/16 of its original value.

Question 18

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

Accepted Answer

The gravitational force is proportional to the product of the masses and inversely proportional to the square of the distance. Saturn is 100 times more massive than Earth, but it is also 10 times farther from the Sun, so the force is approximately equal.

Question 19

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

Accepted Answer

Using Kepler's third law and the gravitational constant, the orbital period and distance can be used to calculate the sum of the masses of the Earth and the Moon.

Question 20

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.

Accepted Answer

Escape velocity is proportional to the square root of the mass. Since Moon A has 2 times the mass of Moon B, its escape velocity is √2 times that of Moon B, which is approximately 1.4 times larger.

Quiz 4: Gravity and Orbits

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.

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

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?

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 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.

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

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

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

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.

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.

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.

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

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.

-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.

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.

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

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?