  The halo orbits of the spatial circular restricted three-body problem are
largely considered in space-flight dynamics to design low-energy transfers
between celestial bodies. A very efficient analytical method for the
computation of halo orbits, and the related transfers, has been obtained from
the high-order resonant Birkhoff normal forms defined at the Lagrangian points
L1-L2. In this paper, by implementing a non-linear Floquet-Birkhoff resonant
normal form, we provide the definition of orbits, as well as their manifold
tubes, which exist in a large order approximation of the elliptic three-body
problem and generalize the halo orbits of the circular problem. Since the
libration amplitude of such halo orbits is large (comparable to the distance of
L1-L2 to the secondary body), and the Birkhoff normal forms are obtained
through series expansions at the Lagrangian points, we provide also an error
analysis of the method with respect to the orbits of the genuine elliptic
restricted three-body problem.
