Abstract
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.
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