Homoclinic and heteroclinic connections between planar Lyapunov orbits of the Sun-Earth and Earth-Moon models can be found by using their hyperbolic invariant manifolds and Poincare section representations. These connections can be classified in bifurcation families according to the range of values of the associated Jacobi constant. In the formalism of invariant manifolds (as the aforementioned Jacobi constant changes) the foliation of all Lyapunov orbits is a Normally Hyperbolic Invariant Manifold. In this context, the homoclinic connections correspond to the so called Scattering map of this NHIM into itself. In this work, the Scattering map is studied as a possible way to formally describe the asymptotic connections arising from the natural dynamics of the Sun-Earth and Earth-Moon problems.