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 = $\frac{1}{9}$ FA.
B)FB = $\frac{1}{3}$ FA.
C)FB = FA.
D)FB = 3FA.
E)FB = 9FA.

Question

Quizplus · Accepted Answer

According to Newton's law of gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Since both satellites are in geosynchronous orbit, they are at the same distance from the center of the Earth. Therefore, the force of gravity between the Earth and each satellite depends only on their masses. Since Satellite B has three times the mass of Satellite A, the gravitational force on B will be three times that on A. Therefore, FB = 3FA.

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