# Jacobi integral

## From Wikipedia, the free encyclopedia

In celestial mechanics, **Jacobi's integral** (also known as the **Jacobi integral** or **Jacobi constant**) is the only known conserved quantity for the circular restricted three-body problem.^{[1]} Unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases.

It was named after German mathematician Carl Gustav Jacob Jacobi.