  The theory of the post-Newtonian (PN) planar circular restricted three-body
problem is used for numerically investigating the orbital dynamics of a test
particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar
Sun-Jupiter system with a scattering region around Jupiter. For determining the
orbital properties of the test particle, we classify large sets of initial
conditions of orbits for several values of the Jacobi constant in all possible
Hill region configurations. The initial conditions are classified into three
main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the
smaller alignment index chaos indicator (SALI), we further classify bounded
orbits into regular, sticky or chaotic. In order to get a spherical view of the
dynamics of the system, the grids of the initial conditions of the orbits are
defined on different types of two-dimensional planes. We locate the different
types of basins and we also relate them with the corresponding spatial
distributions of the escape and collision time. Our thorough analysis exposes
the high complexity of the orbital dynamics and exhibits an appreciable
difference between the final states of the orbits in the classical and PN
approaches. Furthermore, our numerical results reveal a strong dependence of
the properties of the considered basins with the Jacobi constant, along with a
remarkable presence of fractal basin boundaries. Our outcomes are compared with
earlier ones, regarding other planetary systems.
