Does the Moon's orbital inclination follow the wobble in the Earth's rotation?

Question

As the Earth wobbles during rotation, does the higher gravity at the equator tend to pull the moon toward an equatorial orbit even as the earth does that thousands of years wobble cycle? It would seem to me that the higher gravity, due to the larger diameter at the equator, would keep the Moon's orbit close to the equator. Or does the orbit of the moon with respect to the earth stay relatively stable with respect to the solar plane around the sun?

Answer 1

The Earth and moon orbit around their common barycenter
I don't think the differential torque of the equator has very much effect on the plane of the moon's orbit - it takes a lot of energy to move the plane of an orbit!