ELP 2000-85: a semi-analytical lunar ephemeris adequate for historical times

New expressions for mean lunar arguments are obtained. With respect to ELP 2000-82, the main improvement consists in computing secular terms proportional to powers 3 and 4 of time. Such terms arise from secular variations of solar eccentricity and longitude of perigee, Earth figure effects and tidal effects. A semi-analytical solution for the lunar motion, ELP 2000-85, is presented which is valid over a time span of few thousand years and easily handled. Its estimated internal precision varies from 0".5 to about 10" over the time span (2000A.D. - 1500B.C.). A comparison of ELP 2000-85 with the JPL numerical integration LE 51, over a similar time span, has been performed. The leading point of the comparison is a secular drift of 0".0351/cy² in mean mean longitude between the two solutions. After removing this secular drift the differences have the same magnitude as the estimated internal precision of ELP 2000-85. For historical times, this secular drift as well as internal uncertainty of ELP 2000-85 are far below the uncertainties resulting from the tidal secular acceleration. For practical purpose, we give in an appendix, an abridged solution usable to compute a low precision lunar ephemeris (20") over a long time span for a given value of the tidal secular acceleration (-23".895/cy²).