The effect of Poynting-Robertson drag on the triangular Lagrangian points

TL;DR

This paper analyzes how Poynting-Robertson drag affects the stability of particles near the L4 and L5 Lagrangian points in a three-body system, combining analytical models with numerical simulations.

Contribution

It introduces a simplified resonant model to study the effect of Poynting-Robertson drag on Lagrangian point stability, extending previous asymmetry results to more realistic force conditions.

Findings

Temporary stability duration depends on beta, semi-major axis, and mean motion.

Stability asymmetry between L4 and L5 is confirmed under realistic force models.

Numerical simulations support analytical predictions for Jupiter-like systems.

Abstract

We investigate the stability of motion close to the Lagrangian equilibrium points L4 and L5 in the framework of the spatial, elliptic, restricted three- body problem, subject to the radial component of Poynting-Robertson drag. For this reason we develop a simplified resonant model, that is based on averaging theory, i.e. averaged over the mean anomaly of the perturbing planet. We find temporary stability of particles displaying a tadpole motion in the 1:1 resonance. From the linear stability study of the averaged simplified resonant model, we find that the time of temporary stability is proportional to beta a1 n1 , where beta is the ratio of the solar radiation over the gravitational force, and a1, n1 are the semi-major axis and the mean motion of the perturbing planet, respectively. We extend previous results (Murray (1994)) on the asymmetry of the stability indices of L4 and L5 to a more realistic force model. Our analytical results are supported by means of numerical simulations. We implement our study to Jupiter-like perturbing planets, that are also found in extra-solar planetary systems.