Secular Orbit Evolution in Systems with a Strong External Perturber - A Simple and Accurate Model
Abstract
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the co-planar restricted three-body problem. The correction is given in the form of a polynomial function of the system's parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secular equations are simple, straight forward to use and improve the fidelity of Heppenheimer's solution well beyond higher-order models. The quality and convergence of the corrected secular equations are tested for a wide range of parameters and limits of its applicability are given.
Cite
@article{arxiv.1701.03425,
title = {Secular Orbit Evolution in Systems with a Strong External Perturber - A Simple and Accurate Model},
author = {Eduardo Andrade-Ines and Siegfried Eggl},
journal= {arXiv preprint arXiv:1701.03425},
year = {2017}
}
Comments
13 pages, 6 figures, accepted for publication in The Astronomical Journal