The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values.A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.

Abstract. The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill's equations, describing the relative motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained for the linearised equations and also of the third-order solution computed by D.L. Richardson and J.W. Mitchell (2003). With the algorithm presented, those orbits can be computed in a fast and efficient way up to a high-order in the in-plane and out-of-plane amplitudes.

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In this paper we study the manoeuvres to be done by a spacecraft in order to correct the error in the execution of the injection manoeuvre in the transfer trajectory. We will consider the case in which the nominal trajectory is a halo orbit around the collinear equilibrium point L 1 . The results can be easily extended to the L 2 point and to other kinds of libration point orbits, such as Lissajous and quasi-halo orbits. For our study we use simple dynamical systems concepts related with the invariant manifolds of the target orbit, and we compare our results with those obtained by Serban et al. 14 using optimal control.

In this paper we study the manoeuvres to be done by a spacecraft in order to correct the error in the execution of the injection manoeuvre in the transfer trajectory. We will consider the case in which the nominal trajectory is a halo orbit around the collinear equilibrium point L 1 . The results can be easily extended to the L 2 point and to other kinds of libration point orbits, such as Lissajous and quasi-halo orbits. For our study we use simple dynamical systems concepts related with the invariant manifolds of the target orbit, and we compare our results with those obtained by Serban et al. 14 using optimal control.