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

EDUARDO ANDRADE-INES; C. BEAUGÉ; T.A. MICHTCHENKO; PHILIPPE ROBUTEL

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

SPRINGER

Lugar: Berlin; Año: 2016 vol. 124 p. 405 - 432

0923-2958

We analyse the secular dynamics of planets on S-type coplanar orbits intight binary systems, based on first- and second-order analyticalmodels, and compare their predictions with full N-body simulations. Theperturbation parameter adopted for the development of these modelsdepends on the masses of the stars and on the semimajor axis ratiobetween the planet and the binary. We show that each model has bothadvantages and limitations. While the first-order analytical model isalgebraically simple and easy to implement, it is only applicable inregions of the parameter space where the perturbations are sufficientlysmall. The second-order model, although more complex, has a larger rangeof validity and must be taken into account for dynamical studies of somereal exoplanetary systems such as γ Cephei and HD 41004A. However,in some extreme cases, neither of these analytical models yieldsquantitatively correct results, requiring either higher-order theoriesor direct numerical simulations. Finally, we determine the limits ofapplicability of each analytical model in the parameter space of thesystem, giving an important visual aid to decode which secular theoryshould be adopted for any given planetary system in a close binary.