Title:

                  Three-Body Mean Motion Resonances and the Chaotic Structure of the Asteroid Belt
 Authors:

                  Nesvorný, D.; Morbidelli, A.
 Affiliation:

                  AB(Observatoire de la Côte d'Azur-Nice, B.P. 4229, Le Mont-Gros, F-06304 Nice Cedex 4, France)
 Journal:

                  The Astronomical Journal, Volume 116, Issue 6, pp. 3029-3037. (AJ Homepage)
 Publication Date:

                  12/1998
 Origin:

                  AJ
 AJ Keywords:

                  CELESTIAL MECHANICS, STELLAR DYNAMICS, MINOR PLANETS, ASTEROIDS
 Abstract Copyright:

                  (c) 1998: The American Astronomical Society
 Bibliographic Code:

                  1998AJ....116.3029N
 

                                            Abstract

We discuss the existence and the properties of a new type of mean motion resonance populated by a large number of asteroids, the
resonant angle being defined as a linear combination (with integer coefficients) of the mean longitudes of asteroid, Jupiter, and
Saturn. We call these resonances the three-body mean motion resonances. In the present paper, we show that the anomalous large
oscillation of the mean semimajor axis of about 250 numbered asteroids is associated with some of the most prominent three-body
mean motion resonances, and we conjecture that the actual number of the resonant asteroids is much larger. The positive Lyapunov
exponent detected for the majority of resonant bodies in our numerical integrations suggests the chaotic nature of their orbits.
Moreover, we show, using frequency analysis, that orbits in the three-body mean motion resonances may slowly and chaotically
diffuse in eccentricity. The existence of such diffusion may have major consequences for our present understanding of the
long-term evolution of the asteroidal belt and the delivery of objects to near-Earth orbits.