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 , 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, C0, are directly related to each other. We conclude that stable quintuple stellar systems should have large C0 value, while planetary systems can be stabilised hierarchically by a massive central star even with relatively small C0 value. This analysis can be used to study the stability of extrasolar planets and stellar systems.