A Geometric Framework for Solar-System Orbital Dynamics

We examine Solar-System orbital dynamics within the Curvature-Field Framework (CFF), in which gravitational acceleration is expressed through the spatial variation of a curvature field associated with the geometry of tangent directions. For stationary spherical configurations, the CFF acceleration depends on the radial logarithmic gradient of the curvature field. We show that the Newtonian inverse-square law corresponds to a particular radial curvature-field profile, from which Keplerian circular-orbit dynamics follows as a consequence. More general radial profiles provide a systematic description of possible departures from the Newtonian-correspondence regime and lead to characteristic modifications of orbital periods, velocities, and perihelion motion. As an observational test, we derive the supplementary perihelion precession produced by an inverse-power curvature correction and confront it with Mercury ephemeris constraints, obtaining an upper bound on the corresponding curvature-correction amplitude. The results establish a direct connection between the CFF curvature-field description and precision Solar-System orbital dynamics, while keeping phenomenological curvature profiles distinct from independently derived CFF predictions.