Geometry of Weak Stability Boundaries

Details Geometry of Weak Stability Boundaries Geometry of Weak Stability Boundaries

2012-04-06

arxiv.org/abs/1204.1502v1

Mathematics

Dynamical Systems

Scientific paper

The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has been investigated in a number of studies, where partial results have been obtained. We propose a generalization of the weak stability boundary. We prove analytically that, in the context of the planar circular restricted three-body problem, under certain conditions on the mass ratio of the primaries and on the energy, the weak stability boundary about the heavier primary coincides with a branch of the global stable manifold of the Lyapunov orbit about one of the Lagrange points.

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