The design of system -to -system transfer arcs using invariant manifolds in the multi-body problem

Recent complex spacecraft missions in multi-body regimes represent a significant step in expanding space exploration and science options. From the engineering perspective, the Genesis mission, for example, highlighted the benefits of preliminary transfer trajectory design using the invariant manifolds associated with halo orbits in the Circular Restricted Three-Body Problem. As a result, a number of researchers initiated a systematic development of transfer trajectory design strategies based on manifolds and dynamical systems theory. One design problem that remains unsolved is that of transfer between different three-body systems. The main purpose of this work is to develop a methodology that employs the dynamical properties of the three-body problem to systematically produce low ΔV transfer trajectories in multi-body problems. The basis of this methodology is the capability to identify unstable manifolds that depart one three-body system and arrive along a stable manifold in a second three-body system. More specifically, the method initially seeks near-crossing manifolds using the dynamical properties of two different three-body problems (Sun-Planet1-Spacecraft and Sun-Planet 2-Spacecraft) to reduce the search space. These candidate solutions are then linked and the trajectories along each manifold are blended into one smooth low-cost transfer. During this investigation, a well established method involving differential corrections to generate an initial trajectory arc between two points in the three-body problem is used extensively and an interesting property of the solution is observed. Perhaps not surprisingly, as the time of flight between the two points is varied, the solutions form a continuous surface. In addition, two solutions are available for each time of flight. These two separate surfaces join as the time of flight is reduced and the trajectory between the two points approaches a straight line. This result is, in effect, a numerical three-body Lambert solution. It is applied in a variety of problems throughout this work