Low-Energy Sub-Optimal Low-Thrust Trajectories to Libration Points and Halo-Orbits

The paper considers the problem of calculating direct and low-energy, low-thrust trajectories to the libration points of the Earth-Moon system and to halo-orbits. A method for solving the problem is proposed. It consists of calculating stable manifolds of libration points or halo-orbits and calculating a low-thrust trajectory from an initial circular Earth orbit to the given point of this manifold using sub-optimal feedback control. With a fixed final mass of a spacecraft, the last stage of calculations is reduced to solving the Cauchy problem. The numerical examples are given for the calculation of direct and low-energy trajectories to libration points and to halo-orbits and the optimization of entry points to stable manifolds for low-energy trajectories.