Question 1

How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare?

Accepted Answer

Escape velocity depends only on the mass and radius of the celestial body being escaped from, not on the mass of the object attempting to escape.

Question 2

Most asteroids are oblong in shape. Approximate an asteroid as being made up of two identical spheres of mass M and radius R that are just touching each other, in a figure eight. In terms of G, M, and R, what is the escape velocity for a spaceship taking off from the top of the figure eight?

Accepted Answer

The escape velocity is derived from the gravitational potential energy and kinetic energy. For two spheres touching, the potential energy is the sum of the potential energies due to each sphere. The escape velocity is calculated as v = sqrt(2 * (G * M / R + G * M / (2R))) = sqrt(8GM/3R).

Question 3

The gravitational force between two objects is proportional to

Accepted Answer

The answer of The gravitational force between two objects is...

Question 4

Kepler's second law tells us that planets sweep out equal areas in equal times. If you compare the amount of area per time swept by Earth with the one of Jupiter, you would conclude:

Accepted Answer

Kepler's second law states that planets sweep out equal areas in equal times. However, the size of the area swept out depends on the speed of the planet and its distance from the sun. Jupiter, being farther from the sun than Earth, moves at a slower velocity, and therefore, it sweeps out a larger area. Thus, Jupiter and Earth sweep different areas per time.

Question 5

A satellite is orbiting Earth in a circular orbit of radius r when it fires its rockets and acquires speed rapidly. Following this, the satellite's orbit

Accepted Answer

The answer of A satellite is orbiting Earth in a...

Question 6

The acceleration due to gravity on the surface of Earth is g. Calling R the radius of Earth, at what distance from Earth's center would the acceleration due to gravity drop to g/16?

Accepted Answer

The acceleration due to gravity decreases with the square of the distance from the center of the Earth. To reduce gravity to g/16, the distance must be 4 times the Earth's radius, since (1/4)^2 = 1/16.

Question 7

Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force

Accepted Answer

The gravitational force between two objects is inversely proportional to the square of the distance between their centers. If the distance is cut in half, the force increases by a factor of four (quadruples).

Question 8

Two bodies, one of mass M and the other of mass m, are subject only to their mutual gravitational attraction. One possible motion is for both of them to revolve in concentric circles about their center of mass. What is the connection between the period of the revolutions and the separation R between the two bodies in this case?

Accepted Answer

The period of revolution is given by:T = 2πR^(3/2)/[G(M+m)]^(1/2)

Question 9

You have discovered a star system consisting of three equally spaced stars of equal mass arranged in a straight line. The two outermost stars, Zenith and Nadir, revolve synchronously around the central star, Janus. What is the period of revolution for this system in terms of M, the mass of each of the stars, and R, the radius of the circular orbit of Zenith and Nadir?

Accepted Answer

The answer of You have discovered a star system consisting...

Question 10

What is the ratio of potential energy to kinetic energy for a comet that has just enough energy to escape from the Sun's gravitational field?

Accepted Answer

For an object to escape a gravitational field, its total mechanical energy (kinetic + potential) must be zero. The potential energy is negative, and the kinetic energy is positive. At the escape velocity, the magnitude of potential energy equals the kinetic energy, but with opposite signs, making the ratio -1.

Question 11

A satellite completes one full orbit around Earth. The work performed by Earth's gravitational force on the satellite is

Accepted Answer

The work performed by the gravitational force is given by the formula W = Fd cosθ, where F is the force, d is the distance, and θ is the angle between the force and the displacement. In the case of a satellite completing one full orbit around Earth, the force and displacement are always perpendicular to each other, so θ = 90°. Therefore, cosθ = 0, and the work done by the gravitational force is zero joules.

Question 12

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity at the satellite, as compared to the acceleration of gravity on the surface of Mars, is

Accepted Answer

The answer of A satellite encircles Mars at a distance...

Question 13

Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

Accepted Answer

The answer of Planet Z-34 has a mass equal to...

Question 14

During the period of one day, the number of high tides on the East or West coast is usually

Accepted Answer

Most coastal areas experience two high tides and two low tides during a 24-hour period due to the gravitational pull between the Earth, moon, and sun.

Question 15

What is the ratio of potential energy to total energy for a planet in a circular orbit around the Sun?

Accepted Answer

The answer of What is the ratio of potential energy...

Question 16

How does the escape speed from Mars compare with that of the Earth? [ M_Earth=9.31∗ M_Mars; R_Earth=1.88 ∗ R_Mars]

Accepted Answer

The escape speed from a planet depends on its mass and radius. Using the given equations, we can calculate that the escape speed from Mars is approximately 44.9% of the escape speed from Earth. Therefore, the best choice is C.

Question 17

Because Earth's orbit is slightly elliptical, Earth actually gets closer to the Sun during part of the year. When Earth is closer to the Sun its orbital speed is

Accepted Answer

According to Kepler's laws, when a planet is closer to the Sun, it moves faster. Therefore, when Earth is closer to the Sun, its orbital speed is faster than when it is farthest away from the Sun. Therefore, choice C is the correct option.

Question 18

If Earth were twice as massive but it revolved at the same distance from the Sun, its orbital period would be

Accepted Answer

The orbital period of a planet depends on its distance from the Sun, not its mass, according to Kepler's Third Law. Therefore, if Earth were twice as massive but at the same distance, its orbital period would remain 1 year.

Question 19

The gravitational force between two objects is inversely proportional to

Accepted Answer

According to Newton's law of gravitation, 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. Therefore, the correct answer is B, which states that the force is inversely proportional to the square of the distance between the two objects.

Question 20

An astronaut is in a capsule in a stable orbit, about two Earth radii from the center of Earth. Her weight is

Accepted Answer

The gravitational force decreases with the square of the distance from the center of the Earth. At two Earth radii, the force is (1/2)^2 = 1/4 of the force at the surface.

Quiz 12: Gravity