Dreikörperproblem

the Dreikörperproblem of celestial mechanics consists of it finding a solution for the course process of three bodies under the influence of its mutual attraction (gravitation). The Dreikörperproblem applied since the discoveries of Johannes Kepler and Nikolaus Kopernikus as one of the most difficult mathematical problems, alsoin the course of the centuries many well-known mathematicians such as Leonhard Euler, Joseph Louis lying rank, Thorvald Nicolai Thiele, George William Hill and Henri Poincaré were occupied. Karl Frithiof Sundman could indicate an analytic solution of the restringierten Dreikörperproblems as the first in form of a convergent power series.

The Zweikörperproblem is strictly solvable by the Kepler laws. On the other hand the more general case of three heavenly bodies is not with simple formulas solvable, there that System integrabel is not. The stability of a three-body system is described by the coming theorem. Approximation solutions are possible, if the mass one that Heavenly body is small:

One solves general many-body problems as mechanical simulation.

See also: Hill sphere

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