TITLE: On the Lagrangian points of the real Earth-Moon system AUTHORS: Angel Jorba, Enric Castella Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain E-mail: angel@maia.ub.es ABSTRACT: In this note we discuss the motion of a particle near the Lagrangian points of the real Earth-Moon system. We use, as real system, the one provided by the JPL ephemeris: the ephemeris give the positions of the main bodies of the solar system (Earth, Moon, Sun and planets) so it is not difficult to write the vectorfield for the motion of a small particle under the attraction of those bodies. Numerical integrations show that trajectories with initial conditions in a vicinity of the equilateral points escape after a short time. On the other hand, the Restricted Three Body Problem is not a good model for this problem, since it predicts a quite large region of practical stability. Therefore, we introduce an analytic model that can be written as a quasi-periodic perturbation of the Restricted Three-Body Problem, that tries to account for the effect on the Sun and the eccentricity of the Moon. Then, we compute some families of normally elliptic 3-D invariant tori at some distance from the triangular points, that give rise to regions of effective stability. By means of numerical simulations, we show that these regions seem to persist in the real system, at least for time spans of 1000 years. This is a summary of a plenary talk at the Equadiff meeting held in Hasselt, Belgium, July 22-26, 2003.