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An analysis of Lunar Laser Ranging (LLR) observations from January 1972 until April 2001 has been performed, and a new solution for the lunar orbital motion and librations has been constructed that has been named S2001. With respect to prior solutions, improvements in the statistical treatment of the data, new nutation and libration models and the addition of the positions of the observing stations to the list of fitted parameters have been introduced. Globally, for recent observations, our rms (root mean square error) is within 2 to 3 centimeters in the lunar distance. Special attention has been paid to the determination of the correction to the IAU76 luni-solar constant of precession, and the value of the secular acceleration of the Moon's longitude due to the tidal forces. The main results are: –  correction to the constant of precession: $\Delta p$ = -0.302 ± $0.003 ''/{\rm cy}$, –  tidal acceleration of the lunar longitude: Γ = -25.858 ± $0.003 ''/{\rm cy}^{2}$. The positions and velocities of the stations have also been determined. The results are consistent with the ITRF2000 determinations from SLR observations. The lunar theory ELP is referred to a dynamical system and introduces the inertial mean ecliptic of J2000.0. The positioning of the reference system of the theory with respect to ICRS is performed (and also with respect to some useful JPL numerical integrations). Finally the orientation of the celestial axes with respect to the ICRS reference system has been derived as well as the offsets of the Celestial Ephemeris Pole.

A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements