Dynamical properties of the weak stability boundary and associated sets

Abstract

In this contribution the weak stability boundary algorithmic definition was numerically accomplished with the inclusion of lunar and earth collisional sets and a subclassification of the unstable set. Then, the associated sets to WSB definition were analyzed and characterized according to relevant dynamical properties in order to clarify their applicability in earth-moon transfer orbit design. The obtained stable, unstable, and collisional sets are defined as a function of the osculating ellipse eccentricity for prograde and retrogade initial conditions. The stable sets, candidates to ballistic capture transfers, are subclassified according to chosen specific criteria, namely, the Jacobi constant intervals defined by distinct classes of Hill regions, the location of the final state after a complete cycle with respect to the Hill sphere, the permanence in the lunar sphere of influence in a full cycle around the moon, and exit basins for retrograde evolution. By the first time, with this investigation, elucidative criteria based on three-body problem elements are employed to identify initial condition subsets with required properties to design ballistic capture transfers.