  Consider the Restricted Planar Circular 3 Body Problem with both realistic
mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence
of all possible combinations of past and future final motions. In particular,
we obtain the existence of oscillatory motions. All the constructed
trajectories cross the orbit of Jupiter but avoid close encounters with it. The
proof relies on the method of correctly aligned windows and is computer
assisted.
