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Orbital Stability in the Elliptic Restricted Three Body Problem

Published online by Cambridge University Press:  12 April 2016

C.A. Williams  and
J.G. Watts
C.A. Williams
Affiliation:
Dept. of Astronomy, University of South Florida, Tampa, Fla. Fla. 33620
J.G. Watts
Affiliation:
Dept. of Astronomy, University of South Florida, Tampa, Fla. Fla. 33620

Abstract

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Based on the concept of orbital stability introduced by G. W. Hill, a method is presented to facilitate the determination of the orbital stability of solutions to the planar elliptic restricted problem of three bodies. The invariant relation introduced by Szebehely and Giacaglia (1964) contains an integral which is expanded here about a Keplerian solution to the problem. If the expansion converges, it can be used to determine the conditions for Hill stability. With it one can also define stability in a periodic sense.

Type
Part V. Gravitational Problem of three or more bodies
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 333 - 337
Copyright
Copyright © Reidel 1978

References

Hill, G. W. 1905, Collected Mathematical Works of Hill, G. W., 1, Carnegie Inst, of Washington, Washington, D.C. Google Scholar
Szebehely, V. and Giacaglia, G. 1964, A. J.Google Scholar
Szebehely, V. 1967, Theory of Orbits, Acad. Press.Google Scholar
Szebehely, V. and Williams, C. A. 1964, A. J. 69, 460.Google Scholar