Identical satellites X and Y of mass m are in circular orbits around a planet of mass M. The radius of the planet is R. Satellite X has an orbital radius of 3R, and satellite Y has an orbital radius of 4R. The kinetic energy of satellite X is Kx.
1) In terms of Kx, the gravitational potential energy of the planet-satellite X system is
(A) - 2Kx
(B) - Kx
(C) - Kx/2
(D) Kx/2
(E) 2Kx
2) Satellite x is moved to the same orbit as satellite Y by a force doing work on the satellite. In terms of Kx, the work done on satellite X by the force is
(A) - Kx/2
(B) - Kx/4
(C) 0
(D) + Kx/4
(E) + Kx/2
Show the work for each question.
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