TITLE Consecutive quasi-collisions in the planar circular RTBP} AUTHORS Joaquim Font, Ana Nunes and Carles Sim\'o J.F. Departament de Matem\`atica Aplicada i An\`alisi Universitat de Barcelona Gran Via 585, 08007 Barcelona e-mail:quim@maia.ub.es A.N. MAFUL/DFFCUL Universidade de Lisboa Av. Prof. Gama Pinto 2, 1619-003 Lisboa e-mail:anunes@lmc.fc.ul.pt C.S. Departament de Matem\`atica Aplicada i An\`alisi Universitat de Barcelona Gran Via 585, 08007 Barcelona e-mail:carles@maia.ub.es ABSTRACT: In this paper we consider the planar circular restricted three body problem and, in particular, the existence of orbits which undergo consecutive close encounters with the small primary. The number of revolutions of the small bodies around the larger one between successive encounter can be chosen to be two arbitrary sequences of natural number, with constraints depending on the Jacobi constant. We prove that such orbits exist as a consequence of the fact that, when the mass parameter $\mu $ is small, the first return map defined on a region of phase space whose projection is a circle around the small primary is a 'horseshoe' map. The proof is constructive, in the sense that it is based on the computation of an approximate expression for this return map. When $\mu $ is small, the approximate return map contains the essential information about the dynamics from the quantitative as well as from the qualitative point of view. Using this information, we have been able to carry out a numerical study of this problem for $\mu $ up to $10^{-3}$.