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Question
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 \[\sqrt{8}\] T.
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Solution
From Kepler's third law of planetary motion, we have
or
\[ T_1^2 \propto 8 R^3 . . . . . \](iii)
\[ \Rightarrow T_1 = \sqrt{8}T\]
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