On the general planetary perturbations in rectangular coordinates

Abstract

A new theory of general planetary perturbations in rectangular coordinates is developed. Expansion of the potential in terms of multipoles and application of operator calculus yield a direct and automatic way of forming the equations for the perturbations of any order. The perturbations in the position vector are decomposed along the instantaneous position and velocity vectors of the undisturbed motion and along the normal to the plane of the undisturbed motion. This decomposition leads to a direct method of integration and final formulas that are in a convenient form for programming.