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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.

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

From Kepler’s law of planetary motion,

$\dpi{80} T^2\propto R^3$
Hence$\dpi{80} (\dfrac{T_2}{T_1})^2=(\dfrac{2R}{R})^3$
$\dpi{80} \implies \dfrac{T_2}{T}=2^{3/2}=\sqrt{8}$
$\dpi{80} \implies T_2=\sqrt{8}T$