Computation of weak stability boundaries: Sun-Jupiter system

Astronomy and Astrophysics – Astronomy

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Restricted Three-Body Problem, Weak Stability Boundary, Ballistic Capture, Invariant Manifolds, Lyapunov Orbits, Stable Sets

Scientific paper

We compute the weak stability boundary in the planar circular restricted three-body problem starting from the algorithmic definition, and its generalization by García and Gómez. In addition, we consider a new set of primaries, Sun-Jupiter, to replace the case of Earth-Moon considered in previous studies. Numerical enhancements are described and compared to previous methods. This includes defining the equations of motion in polar coordinates and a modified numerical scheme for the derivation of both stable sets and their boundaries. These enhancements decrease the computational time. New results are obtained by considering the Sun-Jupiter case which we compare to the Earth-Moon case.

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