ON A GLOBAL EXPANSION OF THE DISTURBING FUNCTION IN THE PLANAR ELLIPTIC RESTRICTED 3-BODY PROBLEM

Starting with a simple Taylor-based expansion of the inverse of the di stance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic ca se) which is valid for all points of the phase space outside the immed iate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configur ation, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of [R] v alid for very high eccentricities. Comparisons between these results a nd the numerically computed exact function are presented for various r esonances and values of the eccentricity. Maximum errors are determine d in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.