In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to :

Step-by-step solution

According to Kepler's third law of planetary motion, the square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit. For a circular orbit, the semi-major axis is equal to the radius of the orbit R . Therefore, T^2 R^3 Taking the square root on both sides, we get: T R^ 3/2 Alternatively, equating the gravitational force to the required centripetal force: GMm R^2 = mv^2 R v = GM R The time period T is given by: T = 2 R v = 2 R