A Keplerian Orbital Model for the Mechanism of General Precession

Abstract Context. Modern astrometric models (e.g., IAU 2000/2006) and long-term variations such as the Laskar polynomial precessional rate represent the precession of the equinoxes using high-order empirical polynomials. While highly accurate over short intervals, these formulations exhibit significant cumulative divergence and instability over macro-historical timescales, highlighting the limitations of the traditional torque-induced Newtonian rigid-rotator model. Aims. This paper presents a standalone Keplerian orbital model as a closed-form kinematic alternative. By mapping the long-term sweep of the Earth's rotational axis onto a closed elliptical loop, we investigate whether multi-millennial variations in the precessional rate can be explained natively through the conservation of areal velocity (Kepler's Second Law) rather than complex, ad-hoc gravitational torque adjustments. Methods. A rigorous 24,070-year timeline was constructed, anchored to twelve archaeoastronomical milestones derived from classical Vedic treatises (Siddhantas). The apoapsis (minimum velocity vector; v =0°) was fixed at the zero-offset Ayanamsha epoch of 21 March 232 CE (Aryabhatiya). The periapsis vertices (v=180°) were bound to major planetary configurations in 11804 BCE (Surya Siddhanta) and 12267 CE. The orbital trajectory was constrained by ten intermediate historical milestones determined via synodic planetary conjunctions. A global optimization routine utilizing a high-precision Newton-Raphson engine was deployed to fit the transcendental Kepler equation across the independent unanchored datasets. Results. The optimized model yields a highly stable precessional eccentricity of e = 0.0364877 with a mean motion vector of n = 0.014956° year-1. At the current epoch, the model naturally recovers the modern observed precessional rate of 50.3'' year-1. The long-term velocity envelope varies smoothly, bounded strictly between a global minimum of 50.0854'' year-1 at apoapsis and a global maximum of 57.9596'' year-1 at periapsis. Statistical diagnostics confirm the framework's mathematical integrity (R2 = 0.999997), with tracking residuals successfully clearing Shapiro-Wilk normality testing (p = 0.2164) and remaining entirely within the 95% confidence interval (0.366°). Conclusions. These findings demonstrate that ancient chronological boundaries and planetary alignments operate as a unified, mathematically consistent celestial system rather than isolated historical artifacts. By shifting the precessional framework to a closed Keplerian envelope, the model completely eliminates macro-historical coordinate drift and directly challenges the necessity of traditional Newtonian torque-driven models. This alternative paradigm provides a robust, mathematically stable foundation for macro-historical chronologies, paleoclimate tracking, and long-term geodetic projections.