  We numerically investigate the orbital dynamics of a spacecraft, or a comet,
or an asteroid in the Pluto-Charon system in a scattering region around Charon
using the planar circular restricted three-body problem. The test particle can
move in bounded orbits around Charon or escape through the necks around the
Lagrangian points $L_1$ and $L_2$ or even collide with the surface of Charon.
We explore four of the five possible Hill's regions configurations depending on
the value of the Jacobi constant which is of course related with the total
orbital energy. 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) escaping and (iii) collisional. In
particular, we locate the different basins and we relate them with the
corresponding spatial distributions of the escape and collision times. Our
results reveal the high complexity of this planetary system. Furthermore, the
numerical analysis shows a strong dependence of the properties of the
considered basins with the total orbital energy, with a remarkable presence of
fractal basin boundaries along all the regimes. Our results are compared with
earlier ones regarding the Saturn-Titan planetary system.
