On a global expansion of the disturbing function in the planar elliptic restricted three-body problem
type: Item
instance of: scholarly article
title: On a global expansion of the disturbing function in the planar elliptic restricted three-body problem
zbMATH Open document ID: 0967.70504
DOI: 10.1007/BF00054551
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1997-09-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 70F07
zbMATH DE Number: 1046822
zbMATH Keywords: three-body problem
zbMATH Keywords: planar elliptic three-body problem
zbMATH Keywords: disturbing function
zbMATH Keywords: high eccentricity
author: Cristian Beaugé
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00054551
OpenAlex ID: W2097167813
description: scientific article; zbMATH DE number 1046822