Celestial Mechanics and Dynamical Astronomy

, Volume 124, Issue 4, pp 405–432 | Cite as

Secular dynamics of S-type planetary orbits in binary star systems: applicability domains of first- and second-order theories

  • Eduardo Andrade-Ines
  • Cristian Beaugé
  • Tatiana Michtchenko
  • Philippe Robutel
Original Article


We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio between the planet and the binary. We show that each model has both advantages and limitations. While the first-order analytical model is algebraically simple and easy to implement, it is only applicable in regions of the parameter space where the perturbations are sufficiently small. The second-order model, although more complex, has a larger range of validity and must be taken into account for dynamical studies of some real exoplanetary systems such as \(\gamma \) Cephei and HD 41004A. However, in some extreme cases, neither of these analytical models yields quantitatively correct results, requiring either higher-order theories or direct numerical simulations. Finally, we determine the limits of applicability of each analytical model in the parameter space of the system, giving an important visual aid to decode which secular theory should be adopted for any given planetary system in a close binary.


Secular dynamics Binary star Second-order Perturbation theory Planets in binaries 



Part of this work was developed during a visit of E.A-I. to the Universidad Nacional de Cordoba. We wish to express our gratitude to FAPESP (Grants 2010/01209-2 and 2013/17102-0), CNPq, CONICET and Secyt/UNC for their support.

Supplementary material

10569_2015_9669_MOESM1_ESM.dat (352 kb)
Supplementary material 1 (dat 351 KB)
10569_2015_9669_MOESM2_ESM.dat (63 kb)
Supplementary material 2 (dat 62 KB)


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Eduardo Andrade-Ines
    • 1
    • 2
  • Cristian Beaugé
    • 3
  • Tatiana Michtchenko
    • 2
  • Philippe Robutel
    • 1
  1. 1.Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE)ParisFrance
  2. 2.Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG)Universidade de São PauloSão PauloBrazil
  3. 3.Observatorio Astronómico de Cordoba (OAC)Universidad Nacional de CórdobaCórdobaArgentina

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