Stability analysis of quintuple stellar and planetary systems using a symmetric five-body model

Shoaib [Shoaib, M., 2004. Many body symmetrical dynamical systems. Ph.D. Thesis, eprint arXiv:0709.0652, pp. 132-169] gave an analytical stability criterion for the Caledonian Symmetric Five-Body Problem valid for all time. This analytical stability criterion is verified numerically for the coplanar case. it is also shown numerically that the hierarchical stability and the Szebehely constant, C-0, are directly related to each other. We conclude that stable quintuple stellar systems should have large C-0 value, while planetary systems can be stabilised hierarchically by a massive central star even with relatively small C-0 value. This analysis can be used to study the stability of extrasolar planets and stellar systems.(C) 2008 Elsevier B.V. All rights reserved.