> Q. Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $ R^{-5/2} $ , then – LIVE ANSWER TODAY

Q. Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $ R^{-5/2} $ , then

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Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $ R^{-5/2} $ , then

Solution:

$frac{mv^2}{R} propto R^{-5/2}$

$ therefore , , , , , , , , v propto R^{-3/4}$

Now , $ , , , , , , , , , T=frac{2 pi R }{v} , , , or , , , T^2 propto bigg(frac{R}{v}bigg)^2 $

$ or , , , , , , , T^2 propto bigg( frac{R}{R^{-3/4}} bigg)^2 , , , or , , T^2 propto R^{7/2}$

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