The stable Kozai state for asteroids and comets - With arbitrary semimajor axis and inclination

Semianalytical averaging is used to compute secular perturbations on the orbits of asteroids and comets; the method is applicable even for planet-crossing orbits. We prove that for every value of the asteroid/comet semimajor axis, and for an arbitrary number of perturbing planets, there is a stable region of orbits free from node crossings; it corresponds to either circulation or libration of the argument of perihelion. This has implications on the possibility of collisions with the planets and also, when encounters are possible, on the algorithms to compute the probability of collision.