# 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 the Dreikörperproblem then iterative, nowadays with computers, or
- computes orbit/trajectory disturbances, which suffers the smallest (easiest) body by the larger (heavier).
- Accurately solvable it is however with
*equilibrium*of the force of gravity between the large (heavier) bodies - into that Points of lying rank L1 to L5. The internal point L1 is used for example in space travel for the sun research. The SOHO - Sonnenobservatorium is there.

One solves general many-body problems as *mechanical simulation*.

*See also:* Hill sphere

## Web on the left of

## video

- material video:
*Can one park in the universe?*(From the television broadcast alpha Centauri)- note for gehörlose ones, Schwerhörige and blind ones: The video has a length of 14 minutes and shows only a speaking man. It does not contain visualRepresentations or explanations to the topic.