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1. Resonance

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   In orbital dynamics, resonance occurs when two or more orbiting bodies exert periodic gravitational perturbations on each other that are commensurable (related by a ratio of small integers). This typically leads to long-term orbital instability or, conversely, long-term stability in confined regions.
   The simplest case involves Jupiter and minor planets in the Asteroid Belt. A $3:1$ resonance means that for every one orbit completed by the asteroid, Jupiter completes exactly …