(9.12) | ||
(9.13) |
(9.14) |
We can rearrange Equation (9.10) to give
where is the energy (per unit mass) of mass , the angular momentum (per unit mass) of mass , and the orbital angular velocity of the other two masses. Note, however, that is not a constant of the motion. Hence, is not a constant of the motion either. In fact, the Jacobi integral is the only constant of the motion in the circular restricted three-body problem. Incidentally, the energy of mass is not a conserved quantity because the other two masses in the system are moving.