The difference in heights between the pole and equator can be found by expanding the potential from the Moon about the center of mass of the Earth. Define the coordinate system centered on Earth. Let the positive z-axis lie along the Earth-Moon line, and the x- and y-axes lie in the plane perpendicular to the moon-Earth line. The potential from the moon is then
The first term is constant, so it contributes no force. The second term produces a constant attractive force in the direction, so it is not tidal. The lowest higher order term is the quadrupole, which is this term responsible for tides.
which agrees with the exact result.
Tidal Acceleration, Tidal Heating, Tidal Torque
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