TITLE: THE QUASI-BICIRCULAR PROBLEM FOR THE EARTH-MOON-SUN PARAMETERS Authors: M.A. ANDREU, C. SIMO Dept. Matem\`{a}tica Aplicada i An\`{a}lisi, Univ. Barcelona, Gran Via 585, 08007 Barcelona, Spain. e-mails: mangel@maia.ub.es, carles@maia.ub.es ABSTRACT: The quasi-bicircular problem is a restricted four body problem where three masses are revolving in a quasi-bicircular motion (that is, a coherent motion close to circular), the fourth mass being small and not influencing the motion of the three primaries. A quasi-bicircular solution of the three body problem is computed for the Earth-Moon-Sun parameters. Then, the Hamiltonian governing the motion of the fourth particle under the gravitational influence of the first three masses is derived. Some resonant periodic orbits around L1 and L2 are shown. The system is reduced to an approximate center manifold and the periodic orbit found are used to check the range of validity of the approximation.