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Astron. Astrophys. 341, 928-935 (1999)

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The stable Kozai state for asteroids and comets

With arbitrary semimajor axis and inclination

G.F. Gronchi and A. Milani

Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, I-56127 Pisa, Italy (e-mail: gronchi@mail.dm.unipi.it; milani@dm.unipi.it)

Received 11 June 1998 / Accepted 2 October 1998

Abstract

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.

Key words: celestial mechanics, stellar dynamics – comets: general – minor planets, asteroids

Send offprint requests to: G.F. Gronchi

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© European Southern Observatory (ESO) 1999

Online publication: December 16, 1998
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