  The case of the planar circular restricted three-body problem where one of
the two primaries has a stronger gravitational field with respect to the
classical Newtonian field is investigated. We consider the case where two
primaries have the same mass, so as the the only difference between them to be
the strength of the gravitational field which is controlled by the power $p$ of
the potential. A thorough numerical analysis takes place in several types of
two dimensional planes in which we classify initial conditions of orbits into
three main categories: (i) bounded, (ii) escaping and (iii) collision. Our
results reveal that the power of the gravitational potential has a huge impact
on the nature of orbits. Interpreting the collision motion as leaking in the
phase space we related our results to both chaotic scattering and the theory of
leaking Hamiltonian systems. We successfully located the escape as well as the
collision basins and we managed to correlate them with the corresponding escape
and collision time of the orbits. We hope our contribution to be useful for a
further understanding of the escape and collision properties of motion in this
interesting version of the restricted three-body problem.
