Trajectories: A Geometric Analysis of Interstellar Object 3I/ATLAS with Definitive Implications for Deep-Space Navigation, Galactic Structure Determination, and Solar System Baryonic Field Effects

This geometric analysis of interstellar object 3I/ATLAS (C/2025 N1) uses astrometric data to December 26, 2025, revealing trajectory residuals aligned with the Milky Way's galactic center. The method examines sky-plane orientations without nongravitational models, showing perihelion continuity and validation through daily positions with ~14° offsets. This confirms hierarchical barycentric influences, determining the 'king' barycenter with CFK baryonic refinements. Implications include improved deep-space navigation, trajectory forecasting, and solar system compression effects near Neptune (~31.6 AU, March 2028), redefining space as structured.