Abstract
A family of rectilinear periodic solutions of the three-body problem, in which the central body collides alternately with each of the two other bodies, is investigated numerically for all values of the three masses. It is found that for every mass combination there exists just one solution of this kind. The linear stability of the orbits with respect to arbitrary three-dimensional perturbations is also investigated. Domains of stability and instability are displayed in a triangular mass diagram. Their boundaries form one-parameter families of critical orbits, which are tabulated. Limiting cases where one or two masses vanish are studied in detail. The domains of stability cover nearly one half of the total area in the mass diagram: this reinforces the conclusion that real triple stars might have motions of a kind entirely different from the usual hierarchical arrangement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hénon, M.: 1973,Astron. Astrophys. 28, 415.
Hénon, M.: 1974,Celes. Mech. 10, 375.
Hénon, M.: 1976,Celes. Mech. 13, 267.
Schubart, J.: 1956,Astron. Nachr. 283, 17.
Standish, E. M.: 1972,Astron. Astrophys. 21, 185.
Szebehely, V.: 1971,Celes. Mech. 4, 116.
Szebehely, V.: 1972,Proc. Nat. Acad. Sci. U.S.A. 69, 1077.
Waldvogel, J.: 1972,Celes. Mech. 6, 221.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hénon, M. Stability of interplay motions. Celestial Mechanics 15, 243–261 (1977). https://doi.org/10.1007/BF01228465
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01228465