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Energy conservation in the restricted elliptical three-body problem

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Abstract

The energy conservation law for the elliptical three-body problem is derived using an invariant relation corresponding to the Jacobi integral in the circular problem. The minimum-energy surfaces are constructed, which transform in the case of zero eccentricity into zero-velocity surfaces. Some astronomical applications of the results are considered. In particular, it is shown that Roche-lobe overflow displays pulsational behavior in the elliptical three-body problem.

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Authors and Affiliations

  1. Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119992, Russia

    L. G. Luk’yanov

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  1. L. G. Luk’yanov
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__________

Translated from Astronomicheski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Zhurnal, Vol. 82, No. 12, 2005, pp. 1137–1147.

Original Russian Text Copyright © 2005 by Luk’yanov.

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Luk’yanov, L.G. Energy conservation in the restricted elliptical three-body problem. Astron. Rep. 49, 1018–1027 (2005). https://doi.org/10.1134/1.2139818

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