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For planets revolving round the sun, sho...

For planets revolving round the sun, show that `T^(2) prop r^(3)`, where T is the time period of revolution of the planet and r is its distance from the sun.

Text Solution

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(1) The centripetal force actiong on the planet revolving round the sun with orbital velocity 'v' is, `F = (mv^(2))/(r)`
(2) Substitute, `v = (2 pi r)/(T)`
where 'T' is the time period of revolution of the planet.
(3) The force of attraction between planet and sun is equal to `(GMm)/(R^(2))`
Equate (1) and (3). Then obtain the relation `T^(2) prop r^(3)` from the above solution.
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