2/1 resonant periodic orbits in three dimensional planetary systems

K. I. Antoniadou, G. Voyatzis

    Research output: Contribution to journalArticlepeer-review


    We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic orbits of the system given in a suitable rotating frame. The stability of periodic orbits characterize the evolution of any planetary system with initial conditions in their vicinity. Stable periodic orbits are associated with long term regular evolution, while unstable periodic orbits are surrounded by regions of chaotic motion. We compute many families of symmetric periodic orbits by applying two schemes of analytical continuation. In the first scheme, we start from the 2/1 (or 1/2) resonant periodic orbits of the restricted problem and in the second scheme, we start from vertical critical periodic orbits of the general planar problem. Most of the periodic orbits are unstable, but many stable periodic orbits have been, also, found with mutual inclination up to 50–60, which may be related with the existence of real planetary systems.

    Original languageEnglish
    Pages (from-to)161-184
    Number of pages24
    JournalCelestial Mechanics & Dynamical Astronomy
    Issue number2
    Publication statusPublished - 18 Jan 2013


    • 2/1 resonance
    • 3D general three body problem
    • periodic orbits
    • planetary systems
    • vertical critical orbits
    • vertical stability


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