A methodology for the computation of constrained orbits and its application to the design of Solar System trajectories

The purpose of this paper is the development of a procedure for the determination of constrained trajectories of spacecraft in the Solar System and its application to thecomputation of orbits, such as heteroclinic connections in the Sun-Earth-Moon system, that cannot becomputed using only a two or three-body problem approach. Starting from a nominal trajectorycomputed in a simplified force model, the aim is tocompute a new one, close to the original, but satisfying more realistic equations of motion. The formulation adopted allows for the existence of discontinuities in velocity and specific constraints for the states of the orbit, including boundary conditions. The continuity requirement of the orbit is accomplished in position by a differential correction process. The discontinuities in velocity are minimized using an optimization procedure. Some significant applications are presented, mainly regarding libration point orbit missions. It will be shown how using the initial input, the constraints and weights, an orbit, initially determined in the Circular Restricted Three-Body Problem, can be refined in order to fulfill the equations of motion of the Restricted n-Body Problem and specific scopes. In all the cases, an accurate initial guess is a key point.