In this dissertation we apply the Circular Restricted Three - Body Problem to the Earth -- Moon system both for astrodynamical and astronomical purposes. We take advantage of the hyperbolic invariant manifolds associated with the central invariant manifold of the collinear equilibrium point either L_1 and L_2 to construct transfers from either Moon and Earth to a nominal libration point orbit and to study some tracks leading to collisions events on the Moon. Also, we develop an effective methodology for the refinement of such trajectories into a more realistic vector field and we show the consequences of omitting the Sun. Throughout the work, we exploit the tools of Dynamical Systems Theory and optimal control strategies.
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