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Analytic estimates and topological properties of the weak stability boundary

Ceccaroni, Marta and Biggs, James and Biasco, Luca (2012) Analytic estimates and topological properties of the weak stability boundary. Celestial Mechanics and Dynamical Astronomy, 114 (1-2). pp. 1-24. ISSN 0923-2958

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Abstract

The weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3 body problem (PCR3BP), 1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; 2) a precise description of the topology of the WSB; 3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB.