Q4 of 15 Page 14

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.

By Kepler’s Third law of planetary motion;


Where ‘r’ is the distance of planet from the star; ‘T’ is the period of revolution.


Let T1 be the time period when planet was at a distance of ‘2R’ from the star.


By Kepler’s third law;



Since K is constant and its value is same therefore;




⇒


⇒



Hence Period of revolution will be times the period of revolution when planet was at distance ‘R’ from the star.


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