Journal Article

Dynamic portrait of the planetary 2/1 mean-motion resonance – II. Systems with a more massive inner planet

T. A. Michtchenko, C. Beaugé and S. Ferraz-Mello

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 391, issue 1, pages 215-227
Published in print November 2008 | ISSN: 0035-8711
Published online November 2008 | e-ISSN: 1365-2966 | DOI:
Dynamic portrait of the planetary 2/1 mean-motion resonance – II. Systems with a more massive inner planet

More Like This

Show all results sharing this subject:

  • Astronomy and Astrophysics


Show Summary Details


This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet.

As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution.

Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter–Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Keywords: celestial mechanics; planetary systems

Journal Article.  8894 words.  Illustrated.

Subjects: Astronomy and Astrophysics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.