A new solution for the planetary perturbations of the Moon is being built in the frame of ELP 2000, using Bretagnon's planetary theories, and achieved at the first order. It contains the two actions commonly distinguished: direct and indirect. The internal precision of computation is 2×10−6 arcsec. First-order planetary perturbations, in the direct case (Venus & Mars), have been compared to Standaert's solution. The major discrepancy reaches 70 cm in the longitude of Venus. Perturbations of the second order with respect to planetary masses, have been undertaken and illustrations are given. Finally, new values for the perigee and node motions are proposed.

Planetary perturbations of the Moon in ELP 2000

Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine with the help of an algebraic processor. Brown's results are first recovered and refined. The solution is then expanded to include most terms of order nine. The terms in the series for the longitude and latitude are listed with an accuracy of 0.000 01“ and of 0.000 001” for the parallax.

The Main Problem of Lunar Theory Solved by the Method of Brown

In a previous paper (Standaert, 1980) we have described an algorithm to compute the direct perturbation of the planets on the Moon's motion. A short summary of this algorithm is presented in Section 2 of this paper. Our first results permit us to present some complements and comments about these computations.

Comments about the direct perturbations of Venus and Mars on the Moon's motion

SALE and ELP, analytical theories of the main problem of the Moon, are developed by Henrard (1979) and Chapront-Touze (1980), respectively Both theories are compared with numerical integration over one year, which covers about 13 revolutions of the Moon’s orbit The root-meansquare residuals in the distance of SAL| truncated at 10−5 arcsecond is about 10 cm for geries truncated at 10−5 arcsecond and 12 cm for series truncated at 10−6 arcsecond ELP is also compared with 20 years of numerical integration and the root-mean-square residuals in the distance is about 15 cm

Comparison of Lunar Ephemerides (SALE and ELP) with Numerical Integration

Comparison of sale with numerical integration

The principal problem of the motion of the moon - Comparison between two theories

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The principal problem of the motion of the moon - Comparison between two theories