Dynamics of three-dimensional capture orbits from libration region analysis

Low-energy trajectories take advantage of the mutual action of multiple celestial bodies on the spacecraft, and can conclude with ballistic capture about the arrival body, thus allowing significant savings in terms of propellant consumption, if compared to more traditional transfers. Because of the chaotic nature of multibody environments, the design of low-energy trajectories with given constraints can be complex and it is often obtained after a long, iterative, and eventually computationally expensive process. This work is aimed at identifying a limited set of characteristic parameters related both to the time behavior of three-dimensional ballistic capture orbits and to some osculating orbit elements (i.e., inclination, semimajor axis, and eccentricity), relative either to the departure or to the arrival body. The analysis is performed using the linear expansion of the Hamiltonian equations of motion in the equilibrium region around the collinear libration point L1 (or L2), in the dynamical framework of the 3 dimensional circular restricted 3-body problem. A correlation among some Hamiltonian parameters in the equilibrium region and the trajectory osculating orbital elements at capture is established. This result is used to design missions with ballistic capture having required orbital parameters at the arrival planet and it provides a strategy to control the target orbital elements at capture by small thrust maneuvers at the equilibrium region. Because of the long flight time, the solar perturbation is considered in the analysis, and suitable launch dates for the ballistically captured missions are determined.