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Suppose gravity varies inversely as the n-th power of the distance between two bodies. For a planet moving in a circular orbit of radius R around the Sun, the orbital time period T is proportional to which power of R?

1. Rⁿ
2. R^((n+1)/2)
3. R^((n-1)/2)
4. R^(-n)

Correct answer: R^((n+1)/2)

Solution

Equate gravitational and centripetal forces to get v as a function of R, then express the period T = 2*pi*R/v.

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