Mathematical Description of the Oscillations of the Radius Difference Modulus at Symmetrical Orbital Points

This paper introduces an original kinematic approach for analyzing planetary orbits, specifically focusing on the perihelion precession of Mercury. The study presents the "Method of Symmetrical Differences," a mathematical apparatus that allows for the extraction of precession parameters from a single orbital revolution. By analyzing the modulus of radius differences (R2 – R1) at points symmetrical to the line of apsides, the author derives analytical expressions for the "envelope waves" (beats) that characterize precessing orbits. Unlike classical methods that require secular observations over decades or centuries, this approach demonstrates that the magnitude of precession is geometrically "imprinted" within the data of one orbital period. The methodology is rigorously validated using high-precision ephemeris data from NASA HORIZONS. The results provide a new tool for verifying orbital perturbations and offer a fresh perspective on the kinematic interpretation of relativistic effects in the Solar System.