### 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.

(*mathematics,mechanics*)
**Further reading:**

http://en.wikipedia.org/wiki/Jacobi_integral

**Referenced by pages:**

N-body problem

Index