Secular terms of classical planetary theories using the results of general theory
Abstract
Using the methods of the general theory given in Laskar (1985), the differential system giving the secular variations of the orbital elements for eight major planets, at the order 2 with respect to the masses and up to degree 5 in the eccentricityinclination variables with a relative precision of 10 to the 6th is analytically computed. Relativistic and lunar perturbations are included. The entire system is integrated numerically over 10,000 years, and then developed in Taylor expansion around J2000. New polynomial secular terms for the inner planets up to the power 10 of the time are obtained. Comparisons are made with Bretagon's (1982) theory VSOP82 and with the numerically integrated JPL ephemeris, DE102 (Newhall et al., 1983). The global accuracy is approximately 0.04202 arcsec/1000 yr for the inclination of the earth. Using the theory of the rotation of the rigid earth of Kinoshita (1977), new formulas for the precessional quantities, up to t to the 10th, and valid over 10,000 years, are derived.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 March 1986
 Bibcode:
 1986A&A...157...59L
 Keywords:

 Celestial Mechanics;
 Computational Astrophysics;
 Numerical Integration;
 Orbital Elements;
 Planetology;
 Secular Variations;
 Eccentric Orbits;
 Lunar Effects;
 Orbit Perturbation;
 Planetary Mass;
 Planetary Orbits;
 Precession;
 Relativistic Effects;
 Taylor Series;
 Lunar and Planetary Exploration