We study the topology of the unbounded region of the invariant manifolds with fixed values of the Jacobi constant C of the two-body problem, when C>3 . We describe the hamiltonian flow on this manifolds. TWo main consequences have been given : (i) a clarifyina result about the curves of zero velocity ; (ii) using the fact that the circular,planar and restricted three-body problem is a little perturbation of the two-body problem, when m or C-1 is sufficiently small, we prove the stability of the first kind of periodic orbits .