What keeps the moon in a stationary orbit, with no relative motion to earth?
Gravity, of course. Gravity acts like a rubber band connecting the two bodies in space. The earth-moon pair have a center of mass. That center of mass is connected to the sun by gravity. The earth-moon pair rotates about the center of mass of the two. The sun-earth/moon pair rotate about the center of mass between the sun and the earth moon pair center of mass. You can link an analogy here, of a rock on the end of a string that you swing in a circle. Gravity is like the string, keeping the moon in orbit. And like you do, wobble to maintain your position as you swing the mass of the rock, so does the earth wobble in response to the movement of the moon and the sun wobble because of the motions of the planets. We know there are planets in orbit about distant stars because the stars wobble in response to the planet moving and the gravity between the two. Newton’s 3rd law says that for every action, there is an equal and opposite reaction. It does not matter if that is gravity or a string
