An astronaut stands at a position on the Moon such that Earth is directly over h

Question

An astronaut stands at a position on the Moon such that Earth is directly over head and releases a Moon rock that was in her hand.
(a) Which way will it fall? answer toward moon

What is the gravitational force exerted by the Moon on a 1.4-kg rock resting on the Moon's surface? answer is 2.27 N

What is the gravitational force exerted by the Earth on the same 1.4-kg rock resting on the surface of the Moon? answer is 3.78 mN

What is the net gravitational force on the rock? answer is 2.26N towards the moon

please show work to get answers

Explanation / Answer

a ) Mass of the rock is m = 1.4 kg mass of the moon is M = 7.35*10^22 kg distance is r = 1.74 *10^6 m gravitational force is F = G m M / r^2                                        = 6.67*10^-11 * 1.4 kg *  7.35*10^22 kg / ( 1.74*10^6m)^2                                         = 2.27N b) mass of the rock is m = 1.4 kg mass of the earth is M = 5.7*10^24 kg distance r = 3.84*10^9 m      gravitational force is F = G mM /r^2                              = 6.67*10^-11 * 1.4 kg * 5.97*10^24 kg / ( 3.84*10^8 m)^2                               = 3.78 m N c ) Net gravitational force on rock is F_net = F _moon                                                                      = 2.27 N

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