The Apple and the Moon II
Newton showed that the total force the Earth exerts on an object near its surface can be calculated by taking all the mass of the Earth to be concentrated at its center.
Therefore, Fg = mag = mg = GMearth m/ Rearth2
The acceleration due to gravity at the surface of the earth is: g = GMearth / Rearth2
The acceleration of the moon is: amoon = GMearth / Rmoon2