TITLE:
Periodic and Quasi-Periodic Motions of a Solar Sail close to $SL_1$ in
the Earth-Sun System

AUTHORS:
Ariadna Farres, Angel Jorba
Universitat de Barcelona
Departament de Matematica Aplicada i Analisi
Gran Via 585, 08007 Barcelona, Spain

E-mails: ari@maia.ub.es, angel@maia.ub.es

ABSTRACT: 
Solar sails are a proposed form of spacecraft propulsion using large
membrane mirrors to propel a satellite taking advantage of the solar
radiation pressure.  To model the dynamics of a solar sail we have
considered the Earth~-~Sun Restricted Three Body Problem including the
Solar radiation pressure (RTBPS).  This model has a 2D surface of
equilibrium points parametrised by the two angles that define the sail
orientation. In this paper we study the non-linear dynamics close to
an equilibrium point, with special interest in the bounded motion. We
focus on the region of equilibria close to $SL_1$. For different fixed
sail orientations we find families of planar, vertical and Halo-type
orbits. We have also computed the centre manifold around different
equilibria and used it to describe the quasi-periodic motion around
them. We show how the geometry of the phase space varies when we vary
the sail orientation. These kind of studies can be very useful for
future mission applications.