Resonances in multiple planetary systems (Q1766260)

The authors investigate the dynamical stability of real extra-solar two-planet planetary systems HD 74156, HD 38529, HD 168443 and HD 169830. The reasons to choose these planets are: (a) they were not analyzed from the dynamical point of view before; (b) the two discovered planets of each system are far away from mean motion resonance; (c) the regions in-between may allow additional planets. The dynamical model used is the restricted four-body problem consisting of the star, two planets and mass-less test planets (in the same plane or in another experiment on inclined orbits). Two methods of establishing the dynamical stability are applied: (i) long-term (years) numerical integration; (ii) chaos indicators, i.e. relative Lyapunov indicators. The results obtained are discussed.