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?
A)FB = FA.
B)FB = FA.
C)FB = FA.
D)FB = 3FA.
E)FB = 9FA.

Question

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?
A)FB = FA. 
B)FB = FA. 
C)FB = FA. 
D)FB = 3FA. 
E)FB = 9FA.

Quizplus · 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.

Two Satellites Are Placed in Geosynchronous Orbits, Orbits with a Period