Celestial Mechanics and Dynamical Astronomy

, Volume 124, Issue 3, pp 311–334 | Cite as

Dynamics of the 3/1 planetary mean-motion resonance: an application to the HD60532 b-c planetary system

  • A. J. AlvesEmail author
  • T. A. Michtchenko
  • M. Tadeu dos Santos
Original Article


In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance. The case where the outer planet is more massive than its inner companion is considered. We show that the resonant dynamics can be described using two fundamental parameters, the total angular momentum and the spacing parameter. The topology of the Hamiltonian function describing the resonant behaviour is investigated on a large domain of the phase space without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The families of the Apsidal Corotation Resonances (ACR) parameterized by the planetary mass ratio are obtained and their stability is analyzed. The main dynamical features in the domains around the ACR are also investigated in detail by means of spectral analysis techniques, which allow us to detect the regions of different regimes of motion of resonant systems. The construction of dynamical maps for various values of the total angular momentum shows the evolution of domains of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems.


Exoplanetary systems Resonant dynamics Periodic orbits Apsidal corotation resonance (ACR) Spacing parameter Libration 



This work has been supported by the Brazilian National Research Council - CNPq (Grant 153713/2010-0). The authors are grateful to Prof. Dr. S. Ferraz-Mello, Dr. J. Correa-Otto, Dr. E. Andrade-Ines, and Dr. C. Beaugé, for numerous suggestions and corrections to this paper. This work has made use of the facilities of the Computation Center of the University of São Paulo (LCCA-USP) and of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (Grant 2009/54006-4) and the INCT-A.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • A. J. Alves
    • 1
    Email author
  • T. A. Michtchenko
    • 1
  • M. Tadeu dos Santos
    • 1
  1. 1.Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG)Universidade de São PauloSão PauloBrazil

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