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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.

  1. 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.

Grade:10

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Dear student,

From Kepler’s law of planetary motion,

T^2\propto R^3
Hence(\dfrac{T_2}{T_1})^2=(\dfrac{2R}{R})^3
\implies \dfrac{T_2}{T}=2^{3/2}=\sqrt{8}
\implies T_2=\sqrt{8}T

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