  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.
