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.