Tidal Effects on Earth’s Surface

where M is the earth mass, m is the perturber mass, R is the center-to-center distance between Earth and the perturber, a0 is the earth radius, ψ is the angle between the mass centers and the observer, ωL is the (siderial) rate of revolution of the two bodies, and θ is the co-latitude of the observer referenced to Earth’s center of mass. The last, rotational term, simply adds to the rotational potential of the earth, adding one part in ∼ 750 to the flattening of the earth (about 30 meters) in the case of the moon, but does not appear as a tidal perturbation. The second term is the term of importance, describing the tidal potential resulting in a prolate ellipsoidal deformation aligned along the center of mass line. This important term is designated