Construction of a consistent semianalytic theory of a planetary or moon orbiter perturbed by a third body

The third body perturbation of an orbiter of a planet or moon is considered. A very convenient form of the Lagrange equations is given allowing an easy derivation of the various terms of the expansion of the perturbed elements. A careful analysis of the order of magnitude of these terms indicates which ones are required for a consistent theory. It follows that in many practical cases the main term of the disturbing function has to be carried to the second order of the perturbation theory.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.Dedicated to V. Szebehely on the occasion of his 60th birthday