The earth keeps the moon fixed at one orbit only because of it's(the earth's) gravity. The moon's gravity affects the tides on earth.We know that the moon's gravity is 1/6 times as that of the earth. But then how is it possible that the moon's gravity causes an effect on the eath?
The gravitational force between the earth and the moon is because of the masses of both the earth and the moon. The force with which the earth pulls the moon is equal to the force with which the moon pulls the earth. Since, the mass of earth is very large compared to the mass of the moon, the acceleration of the earth is negligible. So, only moon moves along with the revolution of the earth around the sun. But, the gravitational force of the moon is strong enough to pull water bodies on the surface of the earth which constitutes a small fraction of the mass of the earth.