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Jacobi integral

(method of solving some three-body problems)

The Jacobi integral is a mathematical device useful for analysis and solution of some three-body problems. Three-body problems, like other N-body problems, have no general solution. Essentially it is a formula of incorporating various parameters of the system with some variants for particular cases. In cases where it can be used, it produces an associated constant, i.e., a conserved quantity, sometimes called its Jacobi constant. The three-body problems for which it can be used are restricted circular three body problems, problems in which two of the bodies are in a circular orbit and the third body has a mass too small to affect them significantly, and Jacobi integral produces an approximation that depends upon this insignificance. Short-term insignificance may not hold over the long term (secular motion) so the Jacobi integral has more use regarding short-term situations.

Further reading:

Referenced by pages:
N-body problem