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Gravitation HW - AP Physics C
Gravitation HW
1. A person weighing 800 N on Earth travels to another planet with twice the mass and twice the radius of Earth. Calculate the
person's weight on this other planet.
2. Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. Calculate the acceleration of a falling body near the
surface of Mars.
3. An object has a weight W when it is on the surface of a planet of radius R. In terms of W, what will be the gravitational force
on the object after it has been moved to a distance of 4R from the center of the planet?
4. A newly discovered planet has twice the mass of the Earth, but the acceleration due to gravity on the new planet's surface
is exactly the same as the acceleration due to gravity on the Earth's surface. Determine the radius of the new planet in
terms of the radius R of Earth.
5. A spacecraft orbits Earth in a circular orbit of radius R, as shown above. When the spacecraft is at position P shown, a short
burst of the ship's engines results in a small increase in its speed. What does the new orbit look like?
6. The escape speed for a rocket at Earth's surface is ve. In terms of ve, what would be the rocket's escape speed from the
surface of a planet with twice Earth's mass and the same radius as Earth?
7. Two artificial satellites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2
is twice the mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2? Answer in terms of T.
8. Two stars orbit their common center of mass as shown in the diagram below. The masses of the two stars are 3M and M.
The distance between the stars is d. What is the value of the gravitational potential energy of the two-star system? Answer
in terms of M, d, and universal constants.
9. When two stars are very far apart, their gravitational potential energy is zero; when they are separated by a distance d, the
gravitational potential energy of the system is U. In terms of U, what is the gravitational potential energy of the system if
the stars are separated by a distance 2d?
10. Two artificial satellites I and II have circular orbits of radii R and 2R, respectively, about the same planet. The orbital velocity
of satellite I is v. In terms of v, what is the orbital velocity of satellite II?
11. A spacecraft of mass 1,000 kg is in an elliptical orbit about the Earth, as shown above. At point A, the spacecraft is at a
distance rA = 1.2 x 107 m from the center of the Earth and its velocity, of magnitude vA = 7.1 x 103 m/s, is perpendicular to
the line connecting the center of the Earth to the spacecraft. The mass and radius of the Earth are M E = 6.0 X 1024 kg and rE
= 6.4 X 106 m, respectively.
Determine each of the following for the spacecraft when it is at point A.
a. The total mechanical energy of the spacecraft, assuming that the gravitational potential energy is zero at an infinite distance from
the Earth.
b. The magnitude of the angular momentum of the spacecraft about the center of the Earth.
Later the spacecraft is at point B on the exact opposite side of the orbit at a distance r B = 3.6 X 107 m from the center of the Earth.
c. Determine the speed vB of the spacecraft at point B.
Suppose that a different spacecraft is at point A, a distance r A = 1.2 X 107 m from the center of the Earth. Determine each of the
following.
d. The speed of the spacecraft if it is in a circular orbit around the Earth
e. The minimum speed of the spacecraft at point A if it is to escape completely from the Earth
