Solving the Oumuamua and 3i/Atlas Anomalies via Hyperbolic Scale Relativity: A Scale-Gradient Approach

This paper provides a quantitative solution to the non-gravitational accelerations observed in interstellar objects 'Oumuamua and 3I/ATLAS. While traditional models rely on unobserved outgassing or radiation pressure, we propose that these anomalies are kinematic effects emerging from Hyperbolic Scale Relativity. By applying the Universal Constant of Scale (α=0.9), we demonstrate that the "ghost thrust" is a result of the object's high velocity (v2 dependency) interacting with the solar system’s temporal density gradient. Our calculations yield an anomalous acceleration of 4.62×10−6m/s2 for 'Oumuamua, showing remarkable agreement with NASA observational data. This framework suggests that interstellar anomalies are not due to external propulsion but are relativistic scale effects occurring as bodies transition between different scalar environments. Note: Full derivation of the Universal Constant of Scale (α=0.9) and temporal density equations are available here:https://doi.org/10.5281/zenodo.18890819