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 β a 1 n 1 , where β 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. [1994]. 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.