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Doubly Asymptotic Orbits at the Unstable Equilibrium in the Elliptic Restricted Problem

Published online by Cambridge University Press:  12 April 2016

E. Perdios
E. Perdios*
Affiliation:
University of Patras, Patras, Greece

Abstract

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Outgoing asymptotic orbits at a collinear Equilibrium point of the elliptic restricted three-body problem are constructed analytically and numerically and those which intersect perpendicularly the axis of symmetry are selected by means of a numerical procedure of differential corrections. Due to the symmetry properties of the problem, the latter orbits terminate asymptotically back to the equilibrium point and therefore provide a kind of “asymptotic trapping” at the unstable equilibrium, a trapping mechanism based on "long duration of passage" rather than stability of motion.

Type
Part V - Trapped Motion in the Three-Body Problem
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 339 - 350
Copyright
Copyright © Reidel 1983

References

Bennett, A.: 1965, Icarus, 4, 177 CrossRefGoogle Scholar
Bennett, A.: 1966, in Duncombe, R.L. and Szebehely, V.G. (eds.), Methods in Astrodynamics and Celestial Mechanics, Academic Press, New York, p. 101.Google Scholar
Deprit, A. and Henrard, J.: 1965, Astron. J., 70, 271 Google Scholar