ABSTRACT
This chapter provides a few elementary notions on the following arguments: perturbations of the planetary movements including the relativistic precession of the perihelion of Mercury; the case of a planet plus a small moon; the inequalities of the lunar movement. The Jupiter–Saturn interaction, the restricted circular 3-body problems, the 2-bodies of which one with finite dimensions, and the librations. The mathematical model used at Jet Propulsion Laboratory (JPL) includes: point mass interactions among the Sun, planets, and moons; general relativity; Newtonian perturbations of selected asteroids. The first planet would then follow a two-body trajectory whose initial conditions were also determined by the perturbation due to the other planet. The situation was, so to speak, the reverse of the one previously discussed: from the observed perturbations of a given body, the mass, position, and orbital elements of a still unseen perturbing body were inferred. An immediate application of the theory of perturbations was the discovery of Neptune in 1846.
