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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)` .

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The gravitaitonal force provides necessary centripetal force
`(mV^(2))/(r) = (K)/(r^(5//2)) rarr V^(2) = (K)/(m r^(3//2))`
So that `T = (2pir)/(V) = 2pi rsqrt((mr^(3//2))/(K))`
So `T^(2) prop r^(7//2)`
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