Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1 R_E and Satellite Two is at an altitude of 2 R_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? A)1/2 B) 2/3 C) 3/2 D)1/4 E) 2

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Quizplus · Accepted Answer

The potential energy of a satellite in orbit around Earth is given by:$$U = -\frac{GMm}{r}$$where:* G is the gravitational constant* M is the mass of Earth* m is the mass of the satellite* r is the distance from the satellite to the center of EarthSince the two satellites have the same mass, the ratio of their potential energies is:$$\frac{U_1}{U_2} = \frac{r_2}{r_1}$$where:* r1 is the distance from Satellite One to the center of Earth* r2 is the distance from Satellite Two to the center of EarthSubstituting the given values, we get:$$\frac{U_1}{U_2} = \frac{2R_E}{R_E} = 2$$Therefore, the ratio of the potential energy of Satellite One to Satellite Two is 3/2.

Two Satellites of the Same Mass Are Placed in Orbits