Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth-Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = cent, da/dt = 38.30 +/- 0.08 mm/year, and di/dt = -0.5 +/- 0.1 as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives /year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = /year. For total dn/dt, there is 1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is /cent or 87.5 s/cent for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.