Astronomy19 papers
Mean-motion resonances in the Solar system
A curated collection of essential papers on mean-motion resonances in the asteroid belt, TNO, and beyond.
ES
Evgeny Smirnov
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Diffusive chaos in the outer asteroid belt
N. Murray & M. Holman (1997)
- Published
- Sep 1, 1997
- Journal
- The Astronomical Journal · Vol. 114
At a GlanceAI
Analytic theory links chaotic resonance overlap to Lyapunov and asteroid removal times in Jupiter’s outer-belt resonances.
SummaryAI
This paper explains why many outer-belt asteroids show strong chaos (short Lyapunov times) yet can survive for billions of years. Murray and Holman build an analytic model of the planar elliptic restricted three-body problem showing that overlap among a single mean-motion resonance’s sub-resonances drives chaos, while eccentricity diffusion to a “planet-crossing” threshold sets the actual removal time. The theory predicts where chaotic zones (gap-like depletions) should occur in semimajor axis–eccentricity space and gives scaling formulas for both Lyapunov times and removal times that match long numerical integrations for most resonances. It also clarifies why previously reported simple power-law links between Lyapunov and escape times can arise in a different regime (first-order resonance overlap near a KAM boundary) and generally do not hold across the outer asteroid belt.
Method SnapshotAI
Hamiltonian resonance analysis of the planar elliptic restricted three-body problem combined with stochastic diffusion (Fokker–Planck/mapping) estimates and numerical checks.
BackgroundAI
Celestial mechanics (mean-motion resonances, disturbing function) plus basic Hamiltonian chaos concepts (resonance overlap, Lyapunov time, diffusion/KAM).
Sometimes one looks at the Lyapunov time of a main belt asteroid, and it’s minimal. But at the same time it’s not flying off anywhere... Thanks to stable chaos!
— ES