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Analytical estimates of secular frequencies for binary star systems

Binary and multiple star systems are extreme environments for the formation and long-term presence of extrasolar planets. Circumstellar planets are subject to gravitational perturbations from the distant companion star, and this interaction leads to a long-period precession of their orbits. We investigate analytical models that allow to quantify these perturbations and calculate the secular precession frequency in the dynamical model of the restricted three-body problem. These models are applied to test cases and we discuss some of their shortcomings. In addition, we introduce a modified Laplace-Lagrange model which allows to obtain better frequency estimates than the traditional model for large eccentricities of the perturber. We then generalize this model to any number of perturbers, and present an application to the four-body problem.