Question

A satellite is launched into a circular orbit of radius R while a second satellite is launched into an orbit of radius 1.02R. What is the percentage change in the time periods of the two satellites?

(a) 0.7

(b) 1

(c) 1.5

(d) 3

This question was posed to me in a national level competition.

Origin of the question is Gravitation in division Gravitation of Physics – Class 11

Answer 1

Right option is (d) 3

Best explanation: The time periods (T) of a satellite revolving around the earth of radius R and at height h is:

T = 2 x pi x [(R + h)^3 / (G X M)]^1/2

Hence, the time period is directly proportional to (R + h)^3/2

From this, we have the ratio of the time periods as 1.03.

1.03 x 100 = 103. Hence, there is a 3% change in the time period.