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

We investigate the stability of motion close to the Lagrangian equilibrium points L-4 and L-5 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 a(1) n(1), where beta is the ratio of the solar radiation over the gravitational force, and a(1), n(1) are the semi-major axis and the mean motion of the perturbing planet, respectively. We extend previous results (Murray, C.D. [19941 Icarus 112,465-484) on the asymmetry of the stability indices of L-4 and L-5 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. (C) 2014 Elsevier Inc. All rights reserved.