Tidal evolution of hierarchical and inclined systems

  • Alexandre C. M. CorreiaEmail author
  • Jacques Laskar
  • François Farago
  • Gwenaël Boué
Original Article


We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems.


Restricted problems Extended body Dissipative forces Planetary systems Rotation HD 11964 HD 80606 HD 98800 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Alexandre C. M. Correia
    • 1
    Email author
  • Jacques Laskar
    • 2
  • François Farago
    • 2
  • Gwenaël Boué
    • 3
  1. 1.Department of PhysicsI3N, University of Aveiro, Campus Universitário de SantiagoAveiroPortugal
  2. 2.Astronomie et Systèmes DynamiquesIMCCE-CNRS UMR 8028, Observatoire de ParisParisFrance
  3. 3.Centro de AstrofísicaUniversity of PortoPortoPortugal

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