Chaos in high-order mean motion resonances in the outer asteroid belt

We present the results of an investigation into the origin of chaos near high-order mean motion resonances in the outer asteroid belt. First, we survey the variation of Lyapunov time with semimajor axis throughout the outer belt region with the elliptic restricted three body problem. Second, we develop an analytic theory based on resonance overlap that predicts the widths in semimajor axis and typical Lyapunov times of the chaotic zones associated with these resonances. Third, we examine the distribution of the known outer belt asteroids with more realistic models and show that, although most in fact have chaotic trajectories, they are distributed away from the chaotic zones with the shortest characteristic Lyapunov times. Even with the limited number of known outer belt asteroids the distribution shows distinct gaps at high-order mean motion resonances, similar to the Kirkwood gaps in the main asteroid belt. Our results identified gaps at fifth-order mean motion resonances, with hints of structure at higher-order resonances. Finally, we re-examined the orbital stability of Helga with 5 X 10(9) year numerical integrations. We show that Helga is not an example of ''stable chaos'' as conjectured by Milani & Nobili (1992), nor is it a long-lived remnant of a much larger initial population as conjectured by Murison et al. (1994). Instead, Helga has an orbital lifetime comparable to the current age of the solar system. (C) 1996 American Astronomical Society.