Secular effects of oceanic tidal dissipation of the moon's orbit and the earth's rotation

None of the four oceanic models presented in this study of the effects of tidal friction on orbital evolution leads to a Roche limit approach, when integrated back in time, and it is found that for the earth and moon to have ever been separated by less than about 35 earth radii requires that the M2 tide remain near resonance, on a global scale, throughout geological history. This is shown to be implausible, since an earth rotation of less than about 18 hours yields semidiurnal frequencies resonant only with the smaller-scale normal modes of the ocean. The calculated mean inclination parameter value at 4.5 billion years before the present ranged from three to 22 deg. depending on the relative contributions to the torque by major tidal constituents. These general conclusions, deduced from the idealized two-body problem, will not be substantially altered by the inclusion of a more realistic tide model or a generalized three-body orbit.