Question

The Apollo 8 mission in 1968 included a circular orbit at an altitude of 111 km above the Moon’s surface. What was the period of this orbit? The Moon’s mass is Mm=7.35E22 kg and its radius is Rm= 1.74E6 m

Answer 1

You need the orbit radius, and that is
R = 1.74*10^6 m + 0.111*10^6 m
= 1.85*10^6 m

Gravity pull = centripetal force

G*Mm*m/R^2 = m*V^2/R

Satellite mass m cancels out.

V = sqrt(G*Mm/R)

Period = 2 pi R/V

Substitute the previous equation for R.