Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)

TL;DR

This paper applies Chirikov's diffusion theory to model the long-term orbital evolution of asteroids within the (5,-2,-2) resonance, combining analytical and numerical methods to estimate diffusion over hundreds of millions of years.

Contribution

It extends Chirikov's diffusion theory to a specific three-body asteroid resonance, providing new insights into orbital diffusion mechanisms in this context.

Findings

Diffusion along and across the resonance separatrices was quantified.

Estimated diffusion timescales reach up to 10^8 years.

The study links diffusion in phase space to changes in semi-major axis and eccentricity.

Abstract

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulations developed by Chirikov is applied to the Nesvorn\'{y}-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid system). In particular, we investigate the diffusion \emph{along} and \emph{across} the separatrices of the (5,-2,-2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to $10^{8}$ years.