A family of periodic solutions of the planar three-body problem, and their stability

Details A family of periodic solutions of the planar three-body problem, and their stability A family of periodic solutions of the planar three-body problem, and their stability

May 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..13..267h&link_type=abstract

Celestial Mechanics, vol. 13, May 1976, p. 267-285.

Other

39

Orbital Mechanics, Periodic Functions, Stellar Motions, Three Body Problem, Angular Momentum, Motion Stability, Orbit Perturbation, Triple Stars

Scientific paper

We describe a one-parameter family of periodic orbits in the planar problem of three bodies with equal masses. This family begins with Schubart's (1956) rectilinear orbit and ends in retrograde revolution, i.e., a hierarchy of two binaries rotating in opposite directions. The first-order stability of the orbits in the plane is also computed. Orbits of the retrograde revolution type are stable; more unexpectedly, orbits of the 'interplay' type at the other end of the family are also stable. This indicates the possible existence of triple stars with a motion entirely different from the usual hierarchical arrangement.

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