Two satellites are monitored as they orbit the Earth;satellite X is four times as far from the Earth's center as is satellite Y.From Kepler's third law one may conclude that the period of revolution of X is what factor times that of Y?

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the period of revolution of a satellite is proportional to the cube of its distance from the center of the Earth. Let the distance of satellite Y from the center of the Earth be r. Then the distance of satellite X is 4r. Therefore, the period of revolution of X is proportional to (4r)^3, while the period of revolution of Y is proportional to r^3. 
Thus, the ratio of the periods of revolution of X and Y is:
(4r)^3/r^3 = 64
This means that the period of revolution of X is 64 times that of Y. Therefore, the factor by which the period of revolution of X is greater than that of Y is 64/8 = 8.0.

Two Satellites Are Monitored as They Orbit the Earth;satellite X