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Grade 1010 grade science

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.

Vijay mohite

8 Years agoGrade 10

1 Answer

Eshan

8 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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