A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ r = K r 2 . Identify the current relation between the radius R of the particle’s orbit and its period T :

Step-by-step solution

M = ∫ ρ 4 π r 2 d r = ∫ 0 R K r 2 4 π r 2 d r = 4 π K R Satellite velocity = G M R = 4 π K Time period, T = 2 π R v = 2 π R 4 π K Now, T R = 2 π 4 π K = constant