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Three-Body Stability Criteria

Published online by Cambridge University Press:  12 April 2016

J.R. Donnison
J.R. Donnison*
Affiliation:
Department of Mathematical and Computing Sciences, Goldsmiths College, University of London, New Cross, London SE14 6NW, UK

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Progress has been made in understanding the stability of hierarchical three-body systems where the third body moves on an approximately Keplerian orbit about the centre of mass of the binary, at a distance large compared to the binary separation. Harrington (1968,1969) showed analytically that provided the third body was sufficiently distant from the binary no secular terms appeared in the semi-major axis and the system was stable. Harrington (1972,1975,1977) established numerically a critical minimum separation distance (or period) for a stable system in terms of the masses, unaffected by the relative inclinations of the orbits, except for angles close to 90°. Most subsequent investigations have therefore used planar configurations. Graziani & Black (1981), Black (1982) and Pendleton & Black (1983) again using long-term integration of the orbits obtained a criterion for high and low mass binaries. Donnison & Mikulskis (1992,1994,1995) carried out numerical integrations on prograde, retrogade, planetary and stellar triple systems and found for prograde systems very good quantitative agreement with the c2H method. Eggleton & Kieselva (1995) suggested a critical distance ratio approximation determined by the masses in the system. Systems with eccentric orbits are covered using the period ratio determined by Kepler’s third law.

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 441 - 442
Copyright
Copyright © Kluwer 1999

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