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Math Trek

Celestial Atomic Physics

2:09pm, September 9, 2005

". . . it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon."

French mathematician Jules Henri Poincaré (1854–1912) made this observation in his 1908 essay "Science and Method." This remarkable insight aptly encapsulates a key feature of nonlinear dynamics (or what many people call, more loosely, "chaos" theory).

Sensitive dependence on initial conditions is a feature of the motion of three or more bodies that interact gravitationally. In the solar system, objects such as asteroids and comets, can follow chaotic trajectories, abruptly and unpredictably shifting their orbits from time to time. Numerical computations can pin down their paths only up to some finite time. The

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