Long-term perturbations due to a disturbing body in elliptic inclined orbit

TL;DR

This paper develops a double-averaged analytical model to study long-term third-body perturbations in elliptic inclined orbits, validated through comparisons with full models and applied to lunar and Martian systems.

Contribution

The paper introduces a new double-averaged model including perturbing body inclination, improving long-term prediction accuracy for celestial orbit perturbations.

Findings

The model accurately predicts lunar satellite behavior considering lunar obliquity.

The model effectively forecasts Martian spacecraft long-term dynamics.

Comparison shows the model's efficiency over full elliptic restricted three-body simulations.

Abstract

In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68\degree is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.