Secular tidal changes in lunar orbit and Earth rot

Authors: James G Williams Dale H Boggs

Publish Date: 2016/06/29

Volume: 126, Issue: 1-3, Pages: 89-129

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Abstract

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 = 2597pm 005 /cent2 da/dt = 3830 ± 008 mm/year and di/dt = −05 ± 01 upmu as/year Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives sim 3times 1012/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 = 150 pm 010times 1011/year For total dn/dt there is le 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 1316 /cent2 or 875 s/cent2 for UT1AT a 2395 ms/cent increase in the length of day and an obliquity rate of 9 upmu as/year For evolution during past times of slow recession the eccentricity rate can be negativeWe thank the lunar laser ranging stations at McDonald Observatory Texas Observatoire de la Côte d’Azur France Haleakala Observatory Hawaii Apache Point Observatory New Mexico and Matera Italy that provided the data sets that make LLR analyses possible LLR data are available from the International Laser Ranging Service archive at http//ilrsgsfcnasagov/ We acknowledge extensive conversations with D Pavlov about tidal modeling that benefited this paper C F Yoder contributed to the early development of the solar perturbation scaling factors for LLR results M Efroimsky provided a valuable review The research described in this paper was carried out at the Jet Propulsion Laboratory of the California Institute of Technology under a contract with the National Aeronautics and Space Administration Government sponsorship acknowledged

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