Please help.?

Question

A satellite is in a circular orbit just above the surface of the Moon. What are the satellite's acceleration, speed, and the period of the orbit.

Answer 1

the moon does not rotate. The same side faces the earth all the time. The acceleration = 0. Speed = 0. Period = infinite.

Answer 2

Let's say the Moon has mass Mm and radius Rm. The satellite has mass Ms, speed Vs and acceleration As. G is the gravitational constant.
The force between the two:
F = G ( Mm Ms ) / (Rm^2) = Ms As
As = (G Mm ) / (Rm^2)
In fact we have
As = -(G Mm ) / (Rm^2) because the acceleration is directed toward the moon and the origin of coordinates is the center of the moon.
For the satellite to remain in orbit the centrifugal acceleration (Cs) must be of equal magnitude and opposite sign of As.
Cs = (Vs^2) / Rm = (G Mm ) / (Rm^2)
Vs^2 = (G Mm ) / Rm
Vs = Sqrt((G Mm ) / Rm)
The distance traveled is 2 Pi Rm at a speed of Vs
The period Ps = (2 Pi Rm) / Vs