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4. Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be 8 T.

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Thus, when the period of revolution of the planet at a distance R from a star is T, then from kepler's  third law of planetry motion, we have

T2R3    .........(1)

now , when the distance of the planet from the star is 2R, then its period of revolution becomes

T12(2R)3

T128R3    ........(2)

Dividing equation 2 by 1

T12T2=8R3R3

T12=8T2

T1=8T

 

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