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Imagine a light planet revolving around ...

Imagine a light planet revolving around a very massive star in a circular orbit of radius r with direction T. On what power of r, will the square of time period depends if the gravitational force of attraction between the planet and the star is proportional to `r^(-5//2)` .

Text Solution

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The gravitational force provides necessary centripetal force
`(mV^2)/r=K/r^(5//2) rArr V^2=K/(mr^(3/2))`
So that `T=(2pir)/V=2pirsqrt((mr^(3//2))/K)`
So `T^2 prop r^(7//2)`
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