A satellite moves in a circular orbit of radius R with time period T. What is the time period of another satellite orbiting in a circular orbit of radius 9R?

9 T
27 T
12 T
3 T

Correct answer: 27 T

Solution

By Kepler's third law, T² is proportional to r³. So T2/T1 = (r2/r1)^(3/2). With r2 = 9R and r1 = R: T2/T = (9)^(3/2) = 9 * sqrt(9) = 9 * 3 = 27. So T2 = 27T.

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