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


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.


Opposite Direction Periodic Solution Periodic Orbit Planar Problem Equal Mass 
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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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