Question

A spacecraft orbits an unknown planet at a distance of 52 * 10 ^ 7 m from its center The period of its orbit is 52 hoursWhat is the mass of the planet ?

Answer 1

m V^2 / R = G M m / R^2

M = R V^2 / G balancing forces

V = 2 pi R / T speed of craft

M = 4 pi^2 R^3 / (G * T^2) substituting for V

M = 4 pi^2 * 52E21 / (6.67E-11 * 1.30E7) = 39.5 * 52 / (6.67 * 1.3) * 10^25 kg

M = 2.37E27 kg

note mass of earth = 5.98E24 kg - should check mass obtained