His paper studies the dynamics of stable regions for relatively long time intervals (practical stability) in the vicinity of the triangular equilibrium points of a binary asteroid with mass ratio µ larger than Rouths critical mass ratio µ R = (9 - v 69) / 18 . The study is based in a detailed analysis of the Poincaré map for values of the Jacobi constant associated to stable periodic orbits around the triangular points. Solar perturbation is then taken into consideration and the evolution of the stable region is presented