Two satellites of the same mass are placed in orbits around Earth.Satellite One is at an altitude of 1R_E and Satellite Two at an altitude of 2R_E where R_E = 6370 km is the radius of Earth.What is the ratio of the potential energy of Satellite One to Satellite Two? B)2/3 C)3/2

Question

Quizplus · Accepted Answer

The potential energy of a satellite in a circular orbit is given by U = (-GMm)/(2r), where G is the gravitational constant, M is the mass of Earth, m is the mass of the satellite, and r is the distance from the center of Earth to the satellite. The mass of the satellites is the same, so the ratio of their potential energy is simply the ratio of their distances from the center of Earth:

U1/U2 = (-GMm)/(2r1) / (-GMm)/(2r2) = r2/r1

Plugging in the values, we get:

U1/U2 = (6370+1) / (6370+2) = 3185.5 / 3186
U1/U2 ≈ 0.9997 ≈ 1/1.0003 ≈ 3/2

Therefore, the ratio of potential energy of Satellite One to Satellite Two is 3/2.

Two Satellites of the Same Mass Are Placed in Orbits