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 \(\sqrt8\) T.
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
\(T^2\propto R^3 \space\space\space\space.........(1)\)
now , when the distance of the planet from the star is 2R, then its period of revolution becomes
\(T_1^2\propto8R^3 \) ........(2)
Dividing equation 2 by 1
\(T_1^2= 8 T^2\)