In ELP, the computation of planetary perturbations is about 20 years old. A better knowledge of lunar and planetary parameters, new planetary solutions under construction and progresses in numerical tools, are factors that should contribute to their improvements. The construction of planetary perturbations takes widely its inspiration from Brown’s method. In a first step, we only consider the main problem (Earth, Moon, and Sun with a Keplerian motion). The solution of the main problem is actually of a high precision and is used as a reference (Chapront-Touzé, 1980). This solution is expressed in Fourier series of the 4 Delaunay arguments, with numerical coefficients, and partials with respect to integration constants.

The method based on the variation of arbitrary constants is described in (M.Chapront-Touzé, J.Chapront, 1980). Equations of Moon’s motion are written in a rotating frame where the reference plane is the mean ecliptic. In this frame, the absolutec acceleration is expressed by means of disturbing forces acting on the Moon, by the Sun, the Earth and a planet. It is the gradient of F which can be divided into several components: Fc related to the main problem, FD and FI giving rise to direct and indirect planetary perturbations.