On the stability of satellites at unstable libration points of sun-planet-moon systems

TL;DR

This paper investigates the stability of satellites at unstable libration points in sun-planet-moon systems, considering the effects of moon-induced perturbations and employing transition state theory to identify stable periodic orbits.

Contribution

It introduces a novel application of transition state theory to celestial mechanics, analyzing the stability of satellites near libration points under perturbations.

Findings

Satellites can be stabilized at libration points using time-periodic transition state trajectories.

Moon perturbations influence the stability of libration point orbits.

A specific orbit near L2 can remain stable indefinitely under certain conditions.

Abstract

The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory -- which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time -- and investigate the stability properties of that orbit.