Inclination pathways of planet-crossing asteroids

Abstract

ABSTRACT Long-term statistical simulations of the past evolution of high-inclination Centaurs showed that their orbits tend to be polar with respect to the Solar system’s invariable plane over a large semimajor axis range in trans-neptunian space. Here, we lay the analytical foundation of the study of the inclination pathways of planet-crossing asteroids that explains these findings. We show that the Tisserand relation partitions the inclination–semimajor axis parameter space of the three-body problem into distinct regions depending on the asteroid’s Tisserand parameter T or equivalently its orbital inclination I∞ far from the planet. The Tisserand relation shows that asteroids with I∞ > 110° (T < −1) cannot be injected inside the planet’s orbit. Injection on to retrograde orbits and high-inclination prograde orbits occurs inside the inclination corridor 45° ≤ I∞ ≤ 110° (−1 ≤ T ≤ 2). Inclination dispersion across the inclination pathway for moderate and high inclinations is explained by the secular perturbations from the planet and is smallest for polar orbits. When a planet-crossing asteroid temporarily leaves the inclination pathway, its long-term evolution still depends on its Tisserand parameter as evidenced by its eccentricity dispersion. Simulations of asteroid orbits using the equations of motion with Neptune as the perturbing planet confirm these results for moderate to high inclinations, forward and backward in time because the Tisserand relation is time-independent. The Tisserand inclination pathways will provide important constraints on comet delivery from the outer Solar system as well as on the possible presence of unknown planets in trans-neptunian space.