Stochasticité parmi les orbites planétaires stables dans des systèmes d'étoiles doubles

In the frame of the Restricted Three-Body Problem (plane elliptic case), orbital stability of fictitious planets orbiting one of the two components of a binary star system (known the mass ratio of the two stars and the eccentricity of their orbit) is systematically explored, varying initial coordinates and velocities of the planet. For the first 5 binaries we studied, the main result is that stable planetary orbits exist at large distance from their “sun” ; for 3 of these binaries, some of these stable planetary orbits are nearly circular and, among these latter, several lie inside the habitable zone.

Moreover, extrapolating to exoplanets the known dynamics of the Solar System, we may suspect that a subset of these orbits could be chaotic (and, sometimes, chaos may be bounded). A method to study this possible chaos is to compute Lyapunov Indicators; results of a numerical simulation - over Solar System age - are presented here for a fictitious exoplanet orbiting η CrB A, a planet for which the trajectory reveals bounded chaos caracteristics (during the simulation time span).