Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP

TL;DR

This paper introduces a semi-analytical method for calculating the trapped orbits of satellites near a planet within the elliptic restricted three-body problem, accounting for quasi-periodic motion.

Contribution

A novel ansatz and solving procedure are developed to derive semi-analytic solutions for satellite orbits in ER3BP, capturing their quasi-periodic behavior.

Findings

Coordinates depend on true anomaly and a quasi-periodic function.

The third coordinate varies quasi-periodically with true anomaly.

The method provides semi-analytic solutions for trapped satellite orbits.

Abstract

In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem of three bodies, ER3BP (with Keplerian elliptic trajectories of primaries Sun and planet around each other). A new type of the solving procedure is implemented here to obtain the coordinates of the infinitesimal mass (satellite) with its orbit located near the planet. The system of equations of motion was applied for obtaining of the semi-analytic and analytic solutions. It is obtained that two cartesian coordinates (in a plane of mutual rotation of primaries Sun and planet around each other) depend on the true anomaly and a function which determines the quasi periodic character of solution, while the third coordinate (perpendicular to the plane of rotation of primaries) is quasi-periodically varying with true anomaly.