# Analytical estimates of secular frequencies for binary star systems

## TL;DR

This paper develops analytical models to estimate the long-term orbital precession frequencies of planets in binary star systems, improving accuracy especially for high eccentricities and multiple perturbers.

## Contribution

It introduces a modified Laplace-Lagrange model for better frequency estimates and generalizes it to systems with multiple perturbers, including four-body scenarios.

## Key findings

- The modified model outperforms traditional models at high eccentricities.
- Application to four-body systems demonstrates the model's versatility.
- Discussion of model limitations and potential improvements.

## Abstract

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.

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Source: https://tomesphere.com/paper/1908.01048