Question 1

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

Accepted Answer

We can use Kepler's Third Law to calculate the period of revolution:
(T^2)/(a^3) = 1, where T is the period in years and a is the semi-major axis of the asteroid's orbit in astronomical units (AU).
The semi-major axis is the average of the perihelion and aphelion distances:
a = (0.5 AU + 7.5 AU)/2 = 4 AU
Plugging in the values, we get:
(T^2)/(4^3) = 1
T^2 = 64
T = 8 years
Therefore, the period of revolution is 8 years, which is choice B.

Question 2

Two satellites are placed in geosynchronous orbits, orbits with a period of 24 hours, where each satellite hovers over a spot on the Earth's equator. Satellite B has three times the mass of satellite A. What is the relationship between the magnitudes of the gravitational forces of the Earth on the two satellites?

Accepted Answer

The gravitational force on an object is given by the equation F = GmM/r^2, where G is the gravitational constant, m and M are the masses of the two objects, and r is the distance between the centers of the objects. Since the two satellites are in geosynchronous orbit, they are at the same distance from the center of the Earth. Therefore, the only difference in the gravitational force acting on each satellite is their mass. Since satellite B has three times the mass of satellite A, the gravitational force on satellite B will be three times greater than the force on satellite A. Therefore, FB = 3FA.

Question 3

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to

Accepted Answer

The answer of When two solid spheres of the same...

Question 4

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

The answer of The figure below shows a planet traveling...

Question 5

Three galaxies, each of mass m = 4.0 × 1041 kg, lie in a plane at the corners of an equilateral triangle with sides of 5.0 × 1022 m length. The magnitude of the force the other two galaxies exert on each galaxy is

Accepted Answer

The answer of Three galaxies, each of mass m =...

Question 6

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have

Accepted Answer

According to Kepler's Third Law, the period of a planet's orbit is proportional to the semi-major axis of its orbit raised to the 3/2 power. Since the planet farther from the star has a larger semi-major axis, it must have a greater period. The gravitational mass and universal gravitational constant are not relevant to determining the period of the orbits.

Question 7

Suppose the gravitational force of the Earth on a body was  . What escape velocity ve would a body need to escape the gravitational field of the Earth?

Accepted Answer

The answer of Suppose the gravitational force of the Earth...

Question 8

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

The answer of The figure below shows a planet traveling...

Question 9

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.

Accepted Answer

For a planet orbiting a star in a circular orbit, the only force acting on the planet is the gravitational force due to the star, which is a conservative force. As a result, the mechanical energy of the planet is conserved since there is no external work being done on the planet. Additionally, the angular momentum of the planet is conserved since there is no net torque acting on the planet about the center of the circular orbit. Therefore, the correct choice(s) is B, energy and angular momentum.

Question 10

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

According to Kepler's Second Law, the planet will move faster when it is closer to the star and slower when it is further away. At point A, the planet is moving away from the star and therefore its speed is decreasing.

Question 11

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (R⊕= 6.37 × 106 m; RMoon= 1.74 × 106 m; m⊕ = 5.98 × 1024 kg; mMoon = 7.36 × 1022 kg.)

Accepted Answer

The answer of The period of oscillation of a near-Earth...

Question 12

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

When the planet is at point A, it is at its closest point to the star (perihelion). According to Kepler's second law, the planet sweeps out equal areas in equal times, which means that it moves faster when it is closer to the star. As the planet approaches perihelion, its speed increases, and as it moves away from perihelion, its speed decreases. Therefore, since point A is the closest point to the star, the planet's speed is at its maximum, and it is decreasing.

Question 13

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

The answer of The figure below shows a planet traveling...

Question 14

Planet Zero has a mass of 4.0 × 1023 kg and a radius of 2.0 × 106 m. A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 × 107 J. What maximum distance from the center of Zero is achieved by the probe?

Accepted Answer

The answer of Planet Zero has a mass of 4.0...

Question 15

Knowing that  at sea level and that R⊕ = 6.37 × 106 m, we find that the value of g in  at a distance RE from the surface of the Earth is

Accepted Answer

The answer of Knowing that  at sea level and...

Question 16

A satellite revolves around the Earth in a circular orbit with a mechanical energy of  J. What is its kinetic energy?

Accepted Answer

The answer of A satellite revolves around the Earth in...

Question 17

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)

Accepted Answer

In an isolated system of two bodies that exert gravitational forces on one another, the total energy and total angular momentum of the system remain constant. The angular positions of the two bodies can change due to the gravitational forces they exert on each other. Therefore, the correct choice is only (a) and (b) above.

Question 18

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?

Accepted Answer

The satellite is in a state of free fall toward the Earth, but its forward motion is such that it falls around the Earth rather than into it, maintaining a constant altitude and position relative to the Earth's surface. This is characteristic of any orbit, including geosynchronous orbits.

Question 19

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

The answer of The figure below shows a planet traveling...

Question 20

A satellite of mass m₁ circles a planet of mass m₂ and radius r in an orbit at a height 2r above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3r above the surface of the planet?

Accepted Answer

The answer of A satellite of mass m₁ circles a...

Quiz 7: Gravity

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Three galaxies, each of mass m = 4.0 × 1041 kg, lie in a plane at the corners of an equilateral triangle with sides of 5.0 × 1022 m length. The magnitude of the force the other two galaxies exert on each galaxy is

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have

Suppose the gravitational force of the Earth on a body was . What escape velocity ve would a body need to escape the gravitational field of the Earth?

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (R⊕= 6.37 × 106 m; RMoon= 1.74 × 106 m; m⊕ = 5.98 × 1024 kg; mMoon = 7.36 × 1022 kg.)

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Planet Zero has a mass of 4.0 × 1023 kg and a radius of 2.0 × 106 m. A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 × 107 J. What maximum distance from the center of Zero is achieved by the probe?

Knowing that at sea level and that R⊕ = 6.37 × 106 m, we find that the value of g in at a distance RE from the surface of the Earth is

A satellite revolves around the Earth in a circular orbit with a mechanical energy of J. What is its kinetic energy?

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

A satellite of mass m1 circles a planet of mass m2 and radius r in an orbit at a height 2r above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3r above the surface of the planet?

A satellite of mass m₁ circles a planet of mass m₂ and radius r in an orbit at a height 2r above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3r above the surface of the planet?