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Celestial mechanics

, Volume 13, Issue 3, pp 267–285 | Cite as

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

  • M. Hénon
Article

Abstract

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.

Keywords

Opposite Direction Periodic Solution Periodic Orbit Planar Problem Equal Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1976

Authors and Affiliations

  • M. Hénon
    • 1
  1. 1.Observatoire de NiceNiceFrance

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