The Illusion of Curved Space-time: A 3D Euclidean Derivation of Gravitational Precession

Abstract

We present a geometric framework for gravitational interaction based on the concept of energy-shadow regions generated by finite-sized bodies embedded within a background energy medium. The model introduces active shadow-cone masses and associated spherical-cap corrections arising from the three-dimensional geometry of interacting bodies. Starting from this geometric construction, closed-form expressions are derived for a baseline inverse-square force and an additional perturbative term associated with orbital precession.
The framework reproduces the classical inverse-square dependence in the limiting cone approximation while introducing a volumetric correction linked to the physical curvature of spherical bodies. A dimensionless volumetric ratio is shown to generate a precessional contribution that scales with the kinematic factor v²/c². Application of the model to Solar System planets and binary pulsars yields values consistent with observed precessional shifts over a wide range of orbital velocities and eccentricities. The results suggest that certain gravitational and precessional phenomena may admit an alternative geometric interpretation based on finite-body volumetric effects. Further observational and experimental tests will be required to assess the physical validity and predictive power of the proposed framework.