  The case of the planar circular restricted three-body problem is used as a
test field in order to determine the character of the orbits of a small body
which moves under the gravitational influence of the two heavy primary bodies.
We conduct a thorough numerical analysis on the phase space mixing by
classifying initial conditions of orbits and distinguishing between three types
of motion: (i) bounded, (ii) escape and (iii) collisional. The presented
outcomes reveal the high complexity of this dynamical system. Furthermore, our
numerical analysis shows a remarkable presence of fractal basin boundaries
along all the escape regimes. Interpreting the collisional motion as leaking in
the phase space we related our results to both chaotic scattering and the
theory of leaking Hamiltonian systems. We also determined the escape and
collisional basins and computed the corresponding escape/collisional times. We
hope our contribution to be useful for a further understanding of the escape
and collisional mechanism of orbits in the restricted three-body problem.
