Perturbation Theory, Resonance, Librations, Chaos, and Halley’s Comet
The lectures given at the Advanced Study Institute began with a brief survey of quasi-ergodicity, wildness, and chaos-type phenomena in celestial mechanics, continued with a very brief outline of the development of solar system perturbation theory (itself very briefly indicated here), showing how resonance in orbital period leads to transitions between types of motion, so that, since rational values of the ratio of two orbital periods are everywhere dense, the motions in the solar system will show a complexity in which the eventual character of a particular orbit of the system may be expected to depend very finely on the initial conditions. The lectures ended with a description of some numerical investigations of resonant librations in the orbit of Halley’s comet.
KeywordsOrbital Period Secular Variation Planetary System Planetary Orbit Regular Orbit
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