posted by Ron .
The exact mass of the moon was not determined until the Apollo lunar orbiter went into orbit around the moon. They used the period and the orbital radius to find the mass. But since you already know the mass of the moon, if the spaceship was orbiting 485 km above the surface of the moon, how long did it take for the lunar orbiter to make one complete orbit?
Set Gravitational force equal to centripetal force:
Gm1m2/r^2 = m2v^2/r
Notice m2 crosses out (as well as one of the r's)
solve for v.
Now find the circumference of the orbit (2pi r) and divide my the velocity.