ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

In this contribution, we rebuilt and analyze the Weak Stability Boundary (WSB) algorithmic definition with the inclusion of the moon and earth collisional sets and the explicit construction and subclassification of the associated unstable set generated by this definition. The WSB concept associated to lunar ballistic capture in the final portion of the earth-moon transfer orbit was introduced by E. Belbruno (1987 and beyond) in the context of alternative techniques proposed to design low energy transfer orbits, by exploiting the intrinsic nonlinear dynamics of three and four body problems in a more natural way. With the aim of clarifying the applicability of the WSB in realistic mission design, a refined investigation of the several possible stable-unstable transitions is performed by considering elucidative criteria based on three-body problem dynamical elements.