Journal Article

On the 2/1 resonant planetary dynamics – periodic orbits and dynamical stability

G. Voyatzis, T. Kotoulas and J. D. Hadjidemetriou

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 395, issue 4, pages 2147-2156
Published in print June 2009 | ISSN: 0035-8711
Published online May 2009 | e-ISSN: 1365-2966 | DOI:
On the 2/1 resonant planetary dynamics – periodic orbits and dynamical stability

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The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the restricted to the general problem is studied in a systematic way. Starting from the Keplerian unperturbed system, we obtain the resonant families of the circular restricted problem. Then, we find all the families of the resonant elliptic restricted three-body problem, which bifurcate from the circular model. All these families are continued to the general three-body problem, and in this way we can obtain a global picture of all the families of periodic orbits of a two-planet resonant system. The parametric continuation, within the framework of the general problem, takes place by varying the planetary mass ratio ρ. We obtain bifurcations which are caused either due to collisions of the families in the space of initial conditions or due to the vanishing of bifurcation points. Our study refers to the whole range of planetary mass ratio values [ρ∈ (0, ∞)] and, therefore we include the passage from external to internal resonances. Thus, we can obtain all possible stable configurations in a systematic way. As an application, we consider the dynamics of four known planetary systems at the 2/1 resonance and we examine if they are associated with a stable periodic orbit.

Keywords: celestial mechanics; planetary systems

Journal Article.  8191 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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