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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) 3This question was posed to me in a national level competition.Origin of the question is Gravitation in division Gravitation of Physics – Class 11

Answer»

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.



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