  In this paper, the near-optimal capture problem is numerically investigated
to locate the optimal capture points around Charon using the Pluto-Charon
planar circular restricted three-body problem (PCRTBP). Capture orbits are
divided into the pre- and post-maneuver portions. In the pre-maneuver portion,
the gravitational capture conditions are discussed by backward numerical
integration. In the post-maneuver portion, the smaller alignment index (SALI)
is applied to numerically investigate the orbital characters of long-term
capture orbits around Charon. The initial conditions corresponding to three
types of motion: (i) bounded (regular or chaotic), (ii) escaping and (iii)
collisional are classified and studied. Combining results of the pre- and
post-maneuver portions, the near-optimal capture method is presented to find
optimal capture points by overlay figures, and then the corresponding capture
orbits are constructed in the PCRTBP. The different results between the
Pluto-Charon system and the Earth-Moon system are compared and analyzed. Our
results obtained in this paper, including the optimal capture points and the
corresponding capture orbits, could be applied in future space mission design.
