How does the moons pull affect the Earth, grossly?
The moon causes the tides. There should be a bulge on the side of Earth facing the moon and a bulge on the opposite side. This is because the moon pulls on the water on the near side more than it pulls on the solid earth (because the solid earth is further away), but it pulls on the solid earth more than it pulls on the water on the far side. One might expect a difference in the pressure with depth profile. water pressure in the ocean increases with depth because the pressure has to balance with gravity (hydrostatic equilibrium). However, at high tide you have a deeper column of water and consequently a larger mass of water weighing down, potentially increasing the pressure at depth, but the gravitational pull from the moon means the net force on the ocean towards the center of the Earth is slightly reduced.