D. Nesvorny et A. Morbidelli, Three-body mean motion resonances and the chaotic structure of the asteroid belt, ASTRONOM J, 116(6), 1998, pp. 3029-3037
We discuss the existence and the properties of a new type of mean motion re
sonance populated by a large number of asteroids, the resonant angle being
defined as a linear combination (with integer coefficients) of the mean lon
gitudes of asteroid, Jupiter, and Saturn. We call these resonances the thre
e-body mean motion resonances. In the present paper, we show that the anoma
lous large oscillation of the mean semimajor axis of about 250 numbered ast
eroids is associated with some of the most prominent three-body mean motion
resonances, and we conjecture that the actual number of the resonant aster
oids is much larger. The positive Lyapunov exponent detected for the majori
ty of resonant bodies in our numerical integrations suggests the chaotic na
ture of their orbits. Moreover, we show, using frequency analysis, that orb
its in the three-body mean motion resonances may slowly and chaotically dif
fuse in eccentricity. The existence of such diffusion may have major conseq
uences for our present understanding of the long-term evolution of the aste
roidal belt and the delivery of objects to near-Earth orbits.