Stability criteria in many-body systems. V - On the totality of possible hierarchical general four-body systems

Details Stability criteria in many-body systems. V - On the totality of possible hierarchical general four-body systems Stability criteria in many-body systems. V - On the totality of possible hierarchical general four-body systems

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29..267w&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, March 1983, p. 267-294. Research supported by the Science and Engineering Researc

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3

Celestial Mechanics, Dynamic Stability, Four Body Problem, Hierarchies, Kepler Laws, Orbit Perturbation, Binary Stars, Equations Of Motion, Graphs (Charts), Many Body Problem, Planets

Scientific paper

Attention is given to the parameters that are a measure of the perturbation imposed on the disturbed Keplerian orbit of each member of a system by the other bodies present. It is shown that if these parameters are small enough, then the initial hierarchical order will be undisturbed for some time; that is, the status quo will be maintained and to that extent stability will exist. In the light of this criterion, the appropriate parameters for the general four-body problem are treated. Two distinct hierarchical arrangements of four-body systems are possible. These are classified and an examination of the relevant stability parameters is made in each case. The way in which regions may be determined within which real four-body systems can exist and be stable is demonstrated. In addition, it is shown how the various types of possible systems within these regions may be identified. These include Star-Star-Star-Star and Star-Planet-Planet-Star systems.

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