Global dynamics of the Gliese 876 planetary system

The Gliese 876 planetary system consists of two Jupiter-like planets having a nearly commensurate 2:1 orbital periods ratio. Because the semimajor axes of the planets are very small (of the order 0.1 au and 0.2 au, respectively), and the eccentricity of the inner companion is ?0.3, the mutual perturbations are extremely large. However, many authors claim the long-term orbital stability of the system, at least over 500 Myr for initial conditions found by Rivera & Lissauer. Results of investigations of a migration of initially separated planets into the close 2:1 mean motion resonance lock from Lee & Peale also support the conclusion that the system should be stable for the lifetime of the parent star. Initial conditions of the system, found from non-linear N -body fits by Laughlin & Chambers and Rivera & Lissauer, to the radial velocity curve, formally allow for a variety of orbital configurations of the GJ 876 system, e.g. coplanar, with planetary inclinations in the range ?30°, 90°], and with relative inclinations of orbital planes as high as 80°. Our work is devoted to the stability investigation of the systems originating from the fitted initial conditions. We study neighbourhoods of these initial states in the orbital parameter space. We found estimations of the 2:1 mean motion resonance width and dynamical limitations on the planetary masses. We also obtain a global representation of the domains of the orbital parameters space in which initial conditions leading to stable evolutions can be found. Our results can be useful in localization of the best, stable fits to the observational data. In our investigations we use the MEGNO technique (the Mean Exponential Growth factor of Nearby Orbits) invented by Cincotta & Simó. It allows us to distinguish efficiently and precisely between chaotic and regular behaviour of a planetary system.