Migration of Jupiter-family comets and resonant asteroids to near-Earth space

The orbital evolution of about 26,000 Jupiter-crossing objects and 1,500 resonant asteroids under the gravitational influence of planets was investigated. The rate of their collisions with terrestrial planets was estimated by computing the probabilities of collisions based on random-phase approximations and the orbital elements sampled with a 500 yr step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results for orbital evolution, but sometimes give different collision probabilities with the Sun. For orbits close to that of Comet 2P, the mean collision probabilities of Jupiter-crossing objects with terrestrial planets were greater by two orders of magnitude than for some other comets. For initial orbital elements close to those of Comets 2P, 10P, 44P, and 113P, a few objects (about 0.1%) entered Earth-crossing orbits with semi-major axes a < 2 AU and aphelion distances Q < 4.2 AU, and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myr). Some of them even got inner-Earth orbits (Q < 0.983 AU) and Aten orbits. A few comets achieve typical asteroidal orbits for hundreds of Myr. Most former trans-Neptunian objects that have typical near-Earth object orbits moved in such orbits for millions of years; thus, during most of this time they were extinct comet, if they did not disintegrate.