The General Planetary Theory

Abstract

The construction of a general planetary theory (GPT), i.e. a theory representing the coordinates of the major planets in a purely trigonometric form and valid, at least formally, for an indefinite interval of time, has always been considered one of the most important problems of celestial mechanics. Laplace was the first to propose solving the equations of planetary motion in a purely trigonometric form with respect to time. But technical difficulties associated with a trigonometric form forced him to develop another form of planetary theory involving secular and mixed terms. Having failed to find efficient methods for the practical construction of a GPT, Le Verrier developed his famous analytical theories of motion of the planets in just the classical form first indicated by Laplace. A mathematical form of a GPT was rigorously proved for the first time by Newcomb (1876). Newcomb considered his technique to be only an existence theorem although he actually used Newton- type quadratic iterations underlying the present KAM theory (Section 8.4). Later on the trigonometric representation of GPT was advanced by Dziobek (1888), Poincaré (1905) and Charlier (1902, 1907).