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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Stable Chaos in the Asteroid Belt
A. Milani et al. (1997)
- Published
- Jan 1, 1997
- Journal
- Icarus · Vol. 125 · No. 1
At a Glance
Explains how high-order resonances can cause strong chaos in asteroid orbits without long-term instability (“stable chaos”).
Summary
The paper resolves an apparent paradox: many asteroids have very short Lyapunov times (strong chaos) yet remain dynamically stable over millions of years. Focusing on the Veritas family, it shows that high-order mean-motion resonances with Jupiter, modulated by secular perihelion dynamics, repeatedly switch critical arguments between circulation and libration, producing irregular behavior and slow diffusion. This yields large short-term chaos but bounded semimajor axis evolution and only gradual changes in proper eccentricity and inclination. The result reframes Lyapunov time as a poor proxy for removal/instability when chaos is driven by high-order resonances far from low-order, encounter-enabling resonances.
Method Snapshot
Long-timescale N-body numerical integrations of real asteroid orbits with Lyapunov-exponent estimation and proper-element time-series analysis near resonances.
Background
mean-motion/secular resonances, Lyapunov exponents, and proper elements.
An essential manuscript on the concept of stable chaos driven by mean-motion resonances (short Lyapunov time but more-or-less stable orbits).
— ES