The fractal dynamics of satellite capture in the circular restricted three-body problem

The structures of periodic orbit families in the circular restricted three-body problem are fractal-like. Thus, satellite capture can be thought of as a competition between two primary masses for the possession of the third particle, the boundary regions of the struggle being fractal. In addition, it is shown that an important mechanism of satellite capture involves the particle coming in (being captured) on a trajectory near the stable manifold of a hyperbolic fixed point near the inner Lagrangian point. The stable and unstable manifolds intersect transversally, resulting in chaotic motions and subsequent escape. Thus, gravitational capture is intimately associated with chaotic motion.