The Moon and Earth rotate about their common center of mass, which is located about RCM = 4700 km from the center of Earth. (This is 1690 km below the surface.) Take the distance from the center of the earth to the center of the moon to be 3.84x108 m, and the mass of the moon to be 7.35x1022 kg.
a) Write an expression for the acceleration due to the Moon's gravity at their common center of mass using M as the mass of the moon and R as the distance between the center of the Earth and the center of the Moon.
b) Calculate the acceleration due to the Moon's gravity at their common center of mass in m/s2.
c) Calculate the centripetal acceleration of the center of Earth as it rotates about their common center of mass once each lunar month (about 27.3 d) in m/s2.