Resonant Asteroidal Motion in the Kirkwood Gaps: A Three-Dimensional Study

Resonant asteroidal motion is investigated over 17 000 years in a three-dimensional elliptical model Sun-Jupiter-Asteroid averaged by Schubart's method à la Poincarè. Orbits remain trapped in the resonance over this period. The various stability mechanisms are discussed. With respect to their behaviour of ω and ῶ, our resulting orbits reveal 5 distinct classes. These 5 classes can be described in Schubart's topology for the planar problem. As compared to the planar case, eccentricities of orbits in the three-dimensional model vary more strongly. This is an important result for the problem of the delivery of meteorites.

Asteroidal Motion at Commensurabilities Treated in Three Dimensions

This paper consists of a review about work done on three-dimensional motion at commensurabilities of either the mean motions, or of secular periods, and of a report on the author's recent results on some special cases. Real and fictitious asteroidal orbits and the corresponding long-period effects are the main subject of interest. At first, methods are listed.