The Planetary Theories and The Precession of the Ecliptic

Abstract

In this paper, I give the present state of the analytical planetary theories by describing the general theories and the secular variation theories, the variations of the ecliptic with respect to the ecliptic J2000, the utilization of the analytical planetary theories in the calculation of the precession-nutation of the equator and in the calculation of the expressions of transformation between the barycentric and geocentric reference systems. At last, I describe the construction of new planetary theories undertaken at the Bureau des longitudes.The analytical planetary theories arise in two forms: the general theories give, with a low accuracy, the variations of the elements of the planets over several million years; the secular variation theories reach a high accuracy over time spans of a few thousands of years.In all these solutions, the motion of the planets is represented with 6 elements: a, the semi major axis, λ, the mean longitude and the variables k = e cos ϖ, h = e sin ϖ, q = sin ½ cos Ω, p = sin ½ sin Ω where e represents the eccentricity of the orbit, w the longitude of the perihelion, i the inclination of the orbit about the ecliptic J2000 and Ω the longitude of the node.