The acceleration of the moon with respect to the earth is 0.0027 m/s ^2 , whereas the acceleration of an apple falling on the earth's surface is approximately 10 m/s ^2 . Taking the radius of the moon to be one fourth of the earth's radius, suppose the moon is momentarily stopped and then released so that it falls towards the earth. The moon's initial acceleration towards the earth will be

Step-by-step solution

The acceleration of the moon with respect to the earth in its orbit is provided by the mutual gravitational force between them. According to Newton's law of gravitation, the gravitational force is given by: F = G M_e M_m r^2 The relative acceleration of the moon with respect to the earth is: a_ rel = a_m + a_e = G M_e r^2 + G M_m r^2 = G(M_e + M_m) r^2 This acceleration depends only on the masses of the earth and the moon, and the distance r between their centers. It is independent of the moon's tangential velocity