Stability criteria in many-body systems. III - Empirical stability regions for corotational, coplanar, hierarchical three-body systems

Details Stability criteria in many-body systems. III - Empirical stability regions for corotational, coplanar, hierarchical three-body systems Stability criteria in many-body systems. III - Empirical stability regions for corotational, coplanar, hierarchical three-body systems

Feb 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29..117w&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, Feb. 1983, p. 117-148. Research supported by the Science Research Council.

Physics

13

Equations Of Motion, Motion Stability, Numerical Integration, Orbital Mechanics, Systems Stability, Three Body Problem, Celestial Mechanics, Coplanarity, Gravitational Effects, Kepler Laws, Many Body Problem, Orbital Elements

Scientific paper

Previously established stability parameters are used to empirically determine regions of corotational, coplanar, and hierarchical three-body system stability by means of a numerical integration experiment. Attention is given to the initially circular cases of these systems, and their stability is studied by reference to the empirical stability parameters and the initial ratio of the semimajor axes of the orbit of the close binary to that of the third mass about the binary's mass center,which is less than unity. The way in which the stability of a system is affected by changes in the ratio of the semimajor axes is determined for given values of the stability parameters. It is noted that an upper limit exists for this ratio which determines the stability region for such systems. The extent to which a system will be unstable, in terms of the number of orbits it may execute before gross instability, is also determined. Also given is the effect of motion commensurabilities.

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