EXPANSION OF THE SECULAR AND RESONANCE PARTS OF THE PERTURBING FUNCTION IN THE THEORY OF MOTION OF LONG-PERIOD COMETS

A method is proposed for expansion of the perturbing function in the r estricted circular three-body problem for cometary orbits. A formula i s derived for representing functions of elliptical motion as power ser ies in epsilon = (1-e)/2 (where e is the eccentricity of the cometary orbit). It is found that for long-period comets the domain of converge nce of these series extends to distances such that planetary perturbat ions may be ignored. Formulae and recursion relations are found for co mputing the secular and resonance parts of the perturbing function.