Consider a light planet revolving around a massive star in a circular orbit of radius ' r ' with time period ' T '. If the gravitational force of attraction between the planet and the star is proportional to r^ - 7 2 , then T^2 is proportional to

Step-by-step solution

For the planet to orbit around the star, the centripetal force must be provided by gravitational force. Hence, F _ d = F _ a . F _ a - r ^ -7 / 2 ...(Given) (-ve sign indicates force is towards the centre of orbit) array ll & Hence, a - r ^ -7 / 2 & - ^2 r - r ^ -7 / 2 & ^2 r ^ -9 / 2 & 4 ^2 ~T ^2 r ^ -9 / 2 & T ^2 r ^ 9 / 2 array