On the Non-Structural Nature of Chaos in the Three-Body Problem

This work presents a theoretical framework to stabilize the three-body problem. It demonstrates that the chaos associated with the classical Newtonian model is not an inescapable structural property, but rather a consequence of the mathematical singularities of the point-mass model. To this end, a modified Hamiltonian is introduced that is analytically tractable and more physically realistic, using two key mechanisms: A Plummer potential to regularize collisions and eliminate singularities. A harmonic confinement to ensure the system's stability on a large scale. Main Results: Global Stability: An explicit and constructive threshold (γ + Ω² > B(m, ε)) is derived that guarantees the system's convexity. Under this condition, the KAM and Nekhoroshev theorems become applicable, ensuring the system's behavior is stable and predictable for exponentially long times. Exact Local Integrability: It is shown that by adjusting the model's parameters to satisfy the Bertrand-Darboux conditions near relative equilibria (Lagrange points), it's possible to cancel the primary chaotic resonance. This gives rise to an additional integral of motion, making the system exactly and locally integrable. This approach provides an analytical solution for "taming" chaos in one of the fundamental problems of celestial mechanics and is successfully applied as a proof of concept to the Sun-Earth-Moon system.