TITLE: Orbital dynamics of a Solar sail near L1 and L2 in the elliptic Hill problem AUTHORS: Ariadna Farres Universite de Bourgogne France Angel Jorba Departament de Matematica Aplicada i Analisi Universitat de Barcelona Gran Via 585 08007 Barcelona, Spain. E-mails: ariadna.farres@u-bourgogne.fr, angel@maia.ub.es ABSTRACT: In this paper we study the dynamics of a solar sail close to an asteroid. We have taken the Elliptic Hill problem adding the SRP due to the solar sail as a model. We first describe the dynamics of the system when the eccentricity of the asteroid orbit is neglected. The effect of the solar sail allows us to displace the Lagrangian points L1 and L2 . Moreover, we will find families of of periodic orbits for different sail orientations. Finally we will show how these invariant objects vary when we include the effect of the eccentricity.