Bureau des Longitudes, Paris, France
In view of a comparison to lunar-laser observations of the analytical theory of the lunar orbital motion ELP associated with the libration theory obtained by M. Moons, we have studied 3 complementary aspects of the problem: to construct numerical complements to ELP which allow fits to a centimeter level, to improve the solution for the libration, and to develop a numerical tool to compute O-C.
Several comparisons of ELP have been made with JPL ephemerides: DE200/LE200, DE245/LE245 and DE403/LE403. The tool which consist of ELP plus its numerical complement makes possible precise comparisons between various models (fitting of the constants, test of the physical models), keeping the analytical character of the solution. The numerical accuracy of this technic is illustrated by the evidence of different tidal models between ELP200082B (and DE200) and DE245, where, after a fit of the constants, periodic inequalities of an amplitude less than 0.''0006 are detected in the longitude. Hence we have been led to adopt a new tidal model in ELP.
The lunar libration of M. Moons consistent with ELP (constants and fundamental arguments) has been compared to DE245. By a frequency analysis of the residuals, we have determined the coefficients of the so-called ''free libration'', and improved the frequencies.
A program of computation of the O-C has been tested with DE245 which provides the orbital motion, the libration and the barycentric ephemerides of the Earth and Sun, necessary to the corrections. Normal points of Mac Donald, Haleakala and CERGA have been used.