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Question

What is the mass of the planet that has a satellite whose time period is T and orbit radius is r?

[Assume, satellite revolves around the planet in a circular orbit]

A
4π2r2GT2
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B
4π2r0GT2
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C
4π2r3GT2
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D
4π2r3GT2
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Solution

The correct option is C 4π2r3GT2
Suppose a satellite of mass m describes a circular orbit around a planet of mass M.
The gravitational force provides the necessary centripetal force, hence
GMmr2=mω2r Where, r is the radius of circular path and G is gravitional constant for the planet.

GMr2=(2πT)2r [ω=2πT]

M=4π2r3GT2

Hence, option (c) is the correct answer.

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