New Formulation of de Sitter’s Theory of Motion for Jupiter I–IV. I. Equations of Motion and the Disturbing Function

Abstract

A brief discussion is given of the basic features of de Sitter’s theory. The main advantage of his theory is that it contains no small divisors, thanks to the use of elliptic rather than circular intermediate orbits in the first approximation. A 50-year extension of the satellite observations available to de Sitter makes it desirable to rederive the elements of his intermediate orbits, whose perijoves have a common retrograde motion. Furthermore, the theory suffers from a convergence problem, which can be avoided by reformulating the theory in terms of canonical variables, a task that is begun here. We adopt a formulation in Poincaré’s canonical relative coordinates rather than, as customary, in ordinary relative coordinates or in the Jacobian canonical coordinates. By means of the generalized Newcomb operators devised by Izsak, the disturbing function is expanded in a form that is very convenient for use with the modified Delaunay variables, G, L - G, H - G, ℓ + ω + Ω, ℓ, and Ω and their associated Poincaré variables.