A Pure Kinematic Helical Model of the Solar System: Deriving VSOP87 Coefficients via Vector Geometry in an External Frame

This study presents a purely kinematic mathematical framework for planetary orbits, focusing strictly on the geometric description of motion independently of gravitational dynamics (mass and the gravitational constant). Adopting an external observer's frame of reference (the Galaxy), we demonstrate that orbital trajectories are three-dimensional helices resulting from the vector addition of the Solar System's translational velocity (240 km/s) and the planet's local orbital velocity. We introduce a novel geometric metric: the "Angular Curvature per Kilometer" (\kappa). Applying this model to the inner planets yields a perfect 100% numerical match with the primary amplitude coefficients in the empirical VSOP87 astronomical tables. This match demonstrates that traditional "orbital perturbations" are merely 2D geometric projections of a true 3D helical path in a moving space, providing a deeper geometric understanding of planetary motion.