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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The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem
J. Wisdom (1980)
- Published
- Aug 1, 1980
- Journal
- The Astronomical Journal · Vol. 85
- DOI
- 10.1086/112778
At a GlanceAI
Introduces the resonance-overlap criterion linking overlapping resonances to the onset of chaotic motion in the restricted three-body problem.
SummaryAI
This paper formulates and applies the resonance-overlap criterion to explain how overlapping mean-motion resonances produce stochastic (chaotic) behavior in the restricted three-body problem. It identifies a clear mechanism for the transition from regular to chaotic orbital dynamics. The result provides a theoretical basis for predicting instability zones in planetary and small-body systems, with implications for long-term orbital stability.
Method SnapshotAI
Analytical development and application of a resonance-overlap criterion in celestial dynamics.
BackgroundAI
Basic celestial mechanics and dynamical-systems concepts (resonances, perturbation theory, chaos).
Theoretical paper on the application of Chirikov's criterion to the three-body problem (which led to an explanation of the chaos in 3J-1). Nice if you want to understand the fundamentals.
— ES