The Three-Body Problem as a Hydrodynamic Standing Wave: Resolving the Figure-8 Choreography via Topological Solitons in a Superfluid Vacuum

The classical Newtonian Three-Body Problem has remained fundamentally chaotic for over three centuries, primarily due to the assumption that celestial bodies are rigid point masses interacting across an empty void. Even the discovery of the stable "Figure-8" choreography by Chenciner and Montgomery (2000) is treated as a mathematical anomaly rather than a physical inevitability. In this paper, we propose a radical paradigm shift: the Figure-8 orbit is not a gravitational coincidence, but a macroscopic topological standing wave within a superfluid quantum vacuum. By abandoning the empty-space paradigm and modeling the vacuum as an incompressible Bose-Einstein Condensate (BEC), we redefine mass as the hydrodynamic pressure of topological solitons (vortices). We demonstrate that the exceptional stability of the Figure-8 orbit arises from a perfect spatial parity flip at the central crossover, allowing solitons to exchange angular momentum without turbulent vortex reconnection. We formalize three distinct hydrodynamic outcomes for N-body interactions: (A) Turbulent Annihilation (merger), (B) Soliton Scattering (ejection), and (C) Topological Standing Waves (the Figure-8). This framework mathematically bridges Newtonian inverse-square gravity with the acoustic Bjerknes forces of fluid dynamics, providing a deterministic topological foundation for celestial mechanics. Read the full mathematical synthesis in the PDF. Previous papers in the Hydrodynamic Ontology series: Part 1: From Particulate Dark Matter to Superfluid Spacetime: A Hydrodynamic Resolution to Galactic Dynamics. DOI: 10.5281/zenodo.18375888 Part 2: Vacuum Hardening: A Hydrodynamic Resolution to the Hubble Tension and High-Energy LHAASO Anomalies. DOI: 10.5281/zenodo.18479958 Part 3: The Spinor Nature of Light: Deriving Maxwell's Equations from Vacuum Hydrodynamics. DOI: 10.5281/zenodo.18629088 Part 4: The Weight of Nothing: Resolving the Vacuum Catastrophe via Logarithmic Quantum Hydrodynamics. DOI: 10.5281/zenodo.18656936 Part 5: The Star as a Topological Defect in a Superfluid Quantum Vacuum. DOI: 10.5281/zenodo.18786579