Question

On Apollo missions to the Moon, the command module orbited at an altitude of 222 km above the lunar surface. How long did it take for the command module to complete one orbit?

Answer 1

Moon mass and Apollo's please

Answer 2

balance gravitational force and centrifugal acceleration

\(\dfrac{GM_m \color{red}{M_A}}{r^2} = \color{red}{M_A} \omega^2 r\)

[you see that Apollo's mass is irrelevant]

use \(\omega = \dfrac{2 \pi}{\tau}\) to arrive at an expression for the period \(\tau\) of the orbit