Question

4. 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.

Answer 1

Thus, when the period of revolution of the planet at a distance R from a star is T, then from kepler's  third law of planetry motion, we have

$T^2\propto R^3.........(1)$

now , when the distance of the planet from the star is 2R, then its period of revolution becomes

$T_1^2\propto (2R{)}^3$

$T_1^2\propto 8R^3$    ........(2)

Dividing equation 2 by 1

$\frac{T_1^2}{T^2}=\frac{8R^3}{R^3}$

$T_1^2=8T^2$

$\therefore T_1=\sqrt{8}T$

 

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