The Trojan manifold is defined as the analytical manifold of periodic orbits which contains the triangular equilibrium L4 as a singularity. Two branches emanate from L4 : the branch ℒ4ι of long period orbits and the branch ℒ48 of short period orbits. ℒ4ι terminates on a bifurcation orbit which is a short period orbit; ℒ48 terminates on a symmetrical periodic orbit which belongs both to the branch ℒ58 of short period orbits emanating from the equilibrium L 5 and to the branch ℒ3 of periodic librations around the collinear equilibrium L3 .