When two objects attract each other then gravitational force of attraction applied by the first object on the second object is same as the force applied by the second object on the first object.
As we know also,
L=mvr (angular momentum helps the body revolve) along with the help of gravity
F=GM1M2R2 , and centripetal force act on the body , Fc=mv2r
Newton's Third Law of Motion explains that forces always come in action-reaction pairs. The Third Law states that for every action force, there is an equal and opposite reaction force. The two forces create an interaction pair on different objects and are equal in strength and opposite in direction. So, the force of attraction of Earth on Moon is equal and opposite to the force of attraction of Moon on Earth