Trajectory and stability of Lagrangian point $L_2$ in the Sun-Earth system

TL;DR

This study analyzes the trajectory and stability of the Lagrangian point L2 in the Sun-Earth system, considering additional gravitational effects and perturbations, to aid in satellite and space station positioning.

Contribution

It introduces a modified three-body model including belt potential, radiation pressure, and Earth's oblateness to analyze L2 stability and trajectory.

Findings

L2 is asymptotically stable up to certain time thresholds.

The model helps in precise satellite placement around L2.

Stability depends on specific parameter values and initial conditions.

Abstract

This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the model for the Sun-Earth system. The effect of radiation pressure of the Sun and oblate shape of the Earth are considered. The point $L_2$ is asymptotically stable upto a specific value of time $t$ correspond to each set of values of parameters and initial conditions. The results obtained from this study would be applicable to locate a satellite, a telescope or a space station around the point $L_2$.