On a global expansion of the disturbing function in the planar elliptic restricted three-body problem
The problem of obtaining an adequate expression for the disturbing function of the restricted three-body problem with as much range of validity as possible is considered. Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies the author has obtained a series expansion of the disturbing function of the planar elliptic tree-body problem which is valid for all points of the phase space outside the immediate vicinity of the collision points. Especially, the expansion found is valid for every high values of eccentricity of the perturbed body. Additionally, it is shown that in a case of interior mean-motion resonant configuration, the expression is easily averaged with respect to the sinodic period, yelding once again a global expansion of the disturbing function valid for every high eccentricities. A comparison between these results and the numerically computed exact function is presented. Orbits with different resonances and values of eccentricities are considered.
scientific article; zbMATH DE number 1046822