Stable Ballistic Prograde Cyclers in the Three-Body Problem
Abstract
We report the first continuous families of stable, ballistic, prograde cycler orbits in the circular restricted three-body problem: periodic trajectories that alternately undergo temporary capture and orbit each primary. We construct continuous families of symmetric cyclers from intersections of the stable and unstable manifold tubes of the L1 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. A planar-stable branch of every computed family is created simultaneously 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 computed family contains a subfamily that is linearly stable to both planar and out-of-plane perturbations. These stable cyclers persist into the full three-body problem for sufficiently small third mass. We conjecture that saddle-center birth is universal among cycler families, suggesting that stable cyclers are a generic feature of three-body dynamics.
Versions
Related
- Planar Three-Body Problem: theoretical predictions and simulation results
- Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum, IV: Octupole for Librating Kozai-Lidov Cycles
- Families of relative periodic orbits in the planar three-body problem via consecutive alignments
- Ballistic mixing: Stellar mergers drive internal mixing in extremely massive stars with implications for proto-globular cluster pollution
- Ballistic mixing: stellar mergers drive internal mixing in extremely massive stars, with implications for proto-globular cluster pollution
BibTeX
@misc{ross2026stable,
title = {{Stable Ballistic Prograde Cyclers in the Three-Body Problem}},
author = {Shane D. Ross and Michael Roberts-Tsoukkas},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.29189},
eprint = {2606.29189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29189},
}
RIS
TY - UNPB
TI - Stable Ballistic Prograde Cyclers in the Three-Body Problem
AU - Shane D. Ross
AU - Michael Roberts-Tsoukkas
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.29189
UR - https://arxiv.org/abs/2606.29189
AB - We report the first continuous families of stable, ballistic, prograde cycler orbits in the circular restricted three-body problem: periodic trajectories that alternately undergo temporary capture and orbit 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. A planar-stable branch of every computed family is created simultaneously 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 computed family contains a subfamily that is linearly stable to both planar and out-of-plane perturbations. These stable cyclers persist into the full three-body problem for sufficiently small third mass. We conjecture that saddle-center birth is universal among cycler families, suggesting that stable cyclers are a generic feature of three-body dynamics.
ER -