# Secular Orbit Evolution in Systems with a Strong External Perturber - A Simple and Accurate Model

## TL;DR

This paper introduces a semi-analytical correction to the classical secular orbit model, improving its accuracy for systems with strong external perturbers by using polynomial correction factors validated against numerical simulations.

## Contribution

A simple, accurate correction model for secular orbit evolution that enhances Heppenheimer's classical solution using polynomial functions based on system parameters.

## Key findings

- Corrected secular equations match numerical simulations more closely.
- Model applicable across a wide range of parameters.
- Provides limits of applicability for the correction.

## 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.