Tidal deceleration of the Moon's mean motion

The secular change in the mean motion of the Moon, ṅ, caused by the tidal dissipation in the ocean and solid Earth is due primarily to the effect of the diurnal and semidiurnal tides. The long-period ocean tides produce an increase in ṅ, but the effects are only 1 per cent of the diurnal and semidiurnal ocean tides. In this investigation, expressions for these effects are obtained by developing the tidal potential in the ecliptic reference system. The computation of the amplitude of equilibrium tide and the phase corrections is also discussed. The averaged tidal deceleration of the Moon's mean motion, nud, from the most recent satellite ocean tide solutions is −25.25 ± 0.4 arcseconds/century2. The value for nud inferred from the satellite-determined ocean tide solution is in good agreement with the value obtained from the analysis of 20 years of lunar laser ranging observations.