Find the velocity of the planet given by description below.

Question

Consider a planet of mass m, moving in a circular orbit of radius r, around a star of mass M. From a = v²/r, the force of gravity and Newton’s second law, find the velocity of the planet. Assume that the mass of the star is much larger than the mass of the planet, so that you can neglect the star’s motion.

Answer 1

The centripetal force F_c must be equal the gravitational force F_g.

F_c = m.v²/r (from Newton's second law)

F_g = G.M.m/r² (from Newton's gravitational law)

m.v²/r = G.M.m/r²

v = sqrt(G.M/r)