Efficient two-body approximations of impulsive transfers between halo orbits

This contribution presents an efficient method to compute direct transfers between Halo orbits from two circular restricted three-body problems. Owing to the remarkable impulse given over the past two decades to the plans for the robotic exploration of the Jovian system, the envisaged application of this work is the design of low-energy spacecraft transfers between Galilean moons. The basis of the method were set in a previous work in which planar Lyapunov orbits of two Galilean moons were connected by approximating their stable and unstable hyperbolic invariant manifolds with two-body elliptical orbits with focus at Jupiter. The propellant cost at the intersection (impulsive manoeuvre) between ellipses departing from and leading to each moon turned out to depend on the relative orbital phase between the moons, and the minimum ΔV was found to correspond to the orbital configuration in which the ellipses were mutually tangent. The identification of such configuration was entirely analytical and, hence, computationally very fast. Here, we extend the method to the more interesting and scientifically useful case of Halo orbits. These orbits offer a three-dimensional (3D) view of the moons, thus providing a wider coverage of their surface. The two-body approximation of the stable and unstable invariant manifolds of the Halo orbits still consists in sets of ellipses, but their intersection must be determined in 3D space. Under appropriate conditions, the existence of the intersections and the associated manoeuvre cost depend on the difference between the right ascensions of the ascending nodes of the two ellipses, and this in turn shapes the initial orbital configuration. The method adopted to compute the intersections and identify the minimum-cost solution will be illustrated. Finally, the benefits of this methodology when applied to the design of a 3D lunar tour are discussed.