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Imagine a light planet revolving around ...

Imagine a light planet revolving around a massive star in a circular orbit of radius r with a period of revolution T. If the gravitaional force of attraction between planet and the star is proportional to `r^(-3//2)`, find the relation between `T & r`.

Text Solution

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Force of gravitation on the planet = centripetal force.
`kr^(-3//2) = mrw^(2) = mr ((2pi)/(T))^(2)`
`T^(2) = (4 pi m r)/(kr^(-3//2)) = (4pi^(2)m)/(k) cdot r^(5//2)`
`:. T^(2) prop r^(5//2)`
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