We study homoclinic transport to Lyapunov orbits around a collinear librationpoint in the planar restricted three body problem. A method to computehomoclinic orbits is first described. Then we introduce the scattering map forthis problem (defined on a suitable normally hyperbolic invariant manifold) andwe show how to compute it using the information already obtained for thehomoclinic orbits. An example application to Astrodynamics is also proposed.