Anomalous Astrodynamics, Metric Impedance Mismatch, and Deep-Space Orbital Mechanics: An Exact Geometric Framework for the Flyby Anomaly, Trans-Neptunian Clustering, and Interstellar Trajectories

This preprint resolves three long-standing anomalies in astrodynamics and deep-space celestial mechanics using geometric scale invariance and spatial information bounds. We provide an exact, parameter-free derivation of the planetary flyby velocity anomaly observed in spacecraft trajectories like NEAR and Galileo. Furthermore, we explain the orbital clustering of extreme trans-Neptunian objects as an intrinsic secular precession effect at low accelerations, eliminating the need for an undiscovered Planet Nine. Finally, the non-gravitational radial acceleration of the interstellar interloper 'Oumuamua is derived from metric refraction and its observed geometric aspect ratio without requiring cometary outgassing.