The secular accelerations of the moon's orbital motion and the earth's rotation

The results and methods of determining the secular accelerations of the Moon's orbital motion and the Earth's rotation from astronomical observations are critically reviewed. In particular, the effect on these results is considered should Spencer Jones' value for the secular acceleration of the Moon be revised. General relationships are deduced between these accelerations, the rate of dissipation of energy in the Earth and the fractional change in the rate of rotation of the Earth. It is shown that the theory of tidal torques alone does not completely account forany of the wide range of results for the retardation of the Earth deduced from astronomical observations.Presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971.