On the Secular Resonances Occured in Planetary Systems

We present different orbital topologies for extrasolar planetary systems including a 2:1 mean motion resonance namely the Gliese 876 HD 82943 and HD 160691 planetary systems as well as the pair Io-Europa in our solar system. Using a new technique called MEGNO we show that the orbital parameters may allow the existence of a stability zone in the semi-major axes parameter space preserved by a mechanism of apsidal secular resonances. Moreover our global dynamics analysis in the 3-D orbital parameter space allows us to make into evidence new resources of the 2 :1 orbital resonances : a stable orbital topology requires aligned or anti-aligned apsidal lines according to the characteristics of these different planetary systems. These configurations coupled with adequate relative positions of the planets on their orbits avoid close approaches. For instance in the HD 160691 system the apsidal lines are anti-aligned and the stabilizing mechanism avoids close approaches at their periapses (high outer eccentricity of the second planet helps). In the pair Io-Europa conjunctions occur when Io is near periapse and Europa near apoapse whereas conjunctions of the GJ 876 companions occur when both planets are near periapses