Stable Families of Ballistic Prograde Cyclers in the Restricted Three-Body Problem

Abstract

We report stable, ballistic cycler orbits in the circular restricted three-body problem: periodic trajectories that alternately undergo temporary capture about each primary. We construct continuous families of symmetric cyclers from intersections of the stable and unstable manifold tubes of the $L_1$ Lyapunov orbit and exhibit stable examples across more than two orders of magnitude in mass ratio, from the Sun--Jupiter regime to the equal-mass limit. Linear stability separates naturally into planar and out-of-plane components. The planar-stable branch of every computed family is created together with a hyperbolic branch in a saddle-center bifurcation of the return map at the family's maximal Jacobi constant, while out-of-plane instability occurs only through isolated parametric resonances. Every family examined contains a subfamily that is linearly stable to both planar and out-of-plane perturbations. We conjecture that saddle-center birth is universal among cycler families, implying that stable cyclers are a generic feature of the restricted three-body problem.