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 each the system bodies comprising the system are not conserved separately, and a general analytical solution is not possible. With the gravitational force being conservative, the total energy (hamiltonian), the linear moment and the angular momentum of an isolated three-body system (the problem being either restricted or not) are conserved.
It was named after German mathematician Carl Gustav Jacob Jacobi.
- ^ Bibliothèque nationale de France. Jacobi, Carl G. J. (1836). "Sur le movement d'un point et sur un cas particulier du problème des trois corps". Comptes Rendus de l'Académie des Sciences de Paris. 3: 59–61.