Orbit injection of planet-crossing asteroids

Solar system Centaurs originate in transneptunian space from where planet orbit crossing events inject their orbits inside the giant planets' domain. Here, we examine this injection process in the three-body problem by studying the orbital evolution of transneptunian asteroids located at Neptune's collision singularity as a function of the Tisserand invariant, T. Two injection modes are found, one for T>0.1, or equivalently prograde inclinations far from the planet, where unstable motion dominates injection, and another for T<= 0.1, or equivalently polar and retrograde inclinations far from the planet, where stable motion dominates injection. The injection modes are independent of the initial semi-major axis and the dynamical time at the collision singularity. The simulations uncovered a region in the polar corridor where the dynamical time exceeds the solar system's age suggesting the possibility of long-lived primordial polar transneptunian reservoirs that supply Centaurs to the giant planets' domain.