## 3. Equations of motion## 3.1. Basic equationsWe built our analytical solution resolving the following differential equations of the second order (Bretagnon et al., 1997) with and ## 3.2. Equations for numerical integrationWe used numerical integration to test our analytical development.
Eqs. (6) are transformed in the form
Eqs. (9) are strictly equivalent to the basic equations. ## 3.3. Model usedThe torques on the oblate rigid Earth due to the gravitational attraction of the Moon, the Sun and the planets from Mercury to Neptune are considered. The effects of the zonal harmonics with and of the tesseral harmonics , , , with , , are computed. ## 3.4. Construction of the analytical solutionFor the motion of the Sun and the planets we use the solution VSOP87A (Bretagnon, Francou, 1988). For the motion of the Moon we use the solution ELP 2000-82B which involves the theory ELP 2000-82 (Chapront-Touzé, Chapront, 1983) and the arguments of the theory ELP 2000-85 (Chapront-Touzé, Chapront, 1988). We use also the derivatives with respect to the different constants for obtaining the same physical constants and the same tidal model as in DE403/LE403. ## 3.5. Numerical integrationFrom Eqs. (9) we run two numerical integrations. The first one uses numerical solutions of the motion of the Moon, the Sun and the planets computed from VSOP87A et ELP 2000; the second one uses DE403/LE403. We put DE403/LE403 in the inertial ecliptic and dynamical equinox by the two following rotations: a) a rotation in the equator plane, b) a rotation The Euler angles are reckoned positively in positive rotation. The initial conditions of the numerical integrations, computed for (J2000) are © European Southern Observatory (ESO) 1998 Online publication: November 24, 1997 |