The hierarchical stability of quadruple stellar and planetary systems using the Caledonian Symmetric Four-Body Model

A. Széll, B. Steves, B. Érdi

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The hierarchical stability and evolution of a symmetrically restricted four-body model called the Caledonian Symmetric Four-Body Problem (CSFBP) is studied. This problem has two dynamically symmetric pairs of masses m and M with mass ratio μ = m/M. The analytical stability criterion derived for the CSFBP by Steves & Roy (2001) is verified numerically for the coplanar case. It is shown numerically that there exists a direct relationship between the hierarchical stability of the system and the Szebehely constant C0, a combination of the total energy and angular momentum of the system. For C 0 > Ccrit2. where Ccrit2 is a critical value dependent only on μ, the system undergoes no change in its hierarchical arrangement, and is therefore considered to be hierarchically stable. It is also shown that for large mass ratios μ the double binary configurations are the dominant hierarchical configuration, while for smaller mass ratios μ it is the configuration containing a single binary with two outer bodies that is the dominant configuration.

Original languageEnglish
Pages (from-to)1145-1154
Number of pages10
JournalAstronomy and Astrophysics
Issue number3
Publication statusPublished - Dec 1 2004



  • Celestial mechanics

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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