An asymptotic solution for the stellar case of the non-planar three-body problem

Details An asymptotic solution for the stellar case of the non-planar three-body problem An asymptotic solution for the stellar case of the non-planar three-body problem

Jul 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..24..289d&link_type=abstract

Celestial Mechanics, vol. 24, July 1981, p. 289-327.

Physics

1

Asymptotic Methods, Binary Stars, Kepler Laws, Orbital Mechanics, Stellar Motions, Three Body Problem, Circular Orbits, Equations Of Motion, Expansion, Stellar Mass, Systems Integration

Scientific paper

A simplified model of the nonplanar three-body problem is considered in which two particles, forming a close binary, orbit a distant point. A small parameter epsilon, related to the distance separating the binary and the remaining mass, is defined. Time is eliminated from the equations of motion and an angular variable is used instead. A three-variable expansion procedure is used to find an asymptotic solution of the problem. It is possible to obtain a solution up to the order six in epsilon without secular terms only if the mutual inclination of the unperturbed orbits is less than a critical inclination approximately 39 deg.

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