Dynamics of Extrasolar Planetary Systems: 2/1 Resonant Motion

Abstract

A systematic study of the dynamics of resonant planetary systems is made, based on the existence and stability character of families of periodic orbits of the planetary type. In the present study we consider planetary systems with two planets, moving in the same plane. We explore the whole phase space close to the 2/1 resonance, for the masses of the observed planetary system HD82943. We find four basic resonant families of periodic orbits at the 2/1 resonance, and show that large regions on the families correspond to stable motion, even for large values of the eccentricities of the two planets and for intersecting planetary orbits. The initial phase of the two planets plays a crucial role on the stability of the system. It is close to a periodic orbit that stable motion of a planetary system can exist. So, the study of the families of periodic orbits provides a systematic way to find all the regions of phase space where a resonant planetary system could exist in nature. Planetary systems with large eccentricities can exist in nature only if they are close to a resonance. Indeed, we show that the real planetary system HD82943 is close to a stable periodic orbit. The alignment of the line of apsides of the planetary orbits plays also a stabilizing role.