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Boundaries for the Equipotential Curves in the Elliptic Restricted Three-Body Problem

Published online by Cambridge University Press:  12 April 2016

Magda Delva
Magda Delva*
Affiliation:
Institut für Astronomie, Universität Graz, Austria

Abstract

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In the elliptic restricted three body problem an invariant relation between the velocity square of the third body and its potential is studied for long time intervals as well as for different values of the eccentricity. This relation, corresponding to the Jacobian integral in the circular problem, contains an integral expression which can be estimated if one assumes that the potential of the third body remains finite. Then upper and lower boundaries for the equipotential curves can be derived. For large eccentricities or long time intervals the upper boundary increases, while the lower decreases, which can be interpreted as shrinking respectively growing zero velocity curves around the primaries.

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. 317 - 323
Copyright
Copyright © Reidel 1983

References

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