Question
The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the surface.) (a) Calculate the magnitude of the acceleration due to the Moon's gravity at that point. (b) Calculate the magnitude of the centripetal acceleration of the center of Earth as it rotates about that point once each lunar month (about 27.3 d) and compare it with the acceleration found in part (a). Comment on whether or not they are equal and why they should or should not be.

a) $3.41 \times 10^{-5} \textrm{ m/s}^2$

b) $3.33 \times 10^{-5} \textrm{ m/s}^2$. These are nearly equal, which is expected since the moon is providing the centripetal force which causes the Earth's center to rotate about the center of mass of the Earth-Moon system.

Solution Video