Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..64..313b&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 64, Issue 4, pp.313-350
Astronomy and Astrophysics
Astronomy
7
Disturbing Function, High Eccentricity, Planar Three-Body Problem
Scientific paper
Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate 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 configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities. Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.
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