A Keplerian Solution to the Precession of the Equinoxes: Modeling a Binary Solar–Neutron Star Orbit Using Archaeo-Astronomical Anchors

The anomalous long-term variations in the Earth's orientation, traditionally described as axial precession, are modeled here as a literal orbital motion of the Sun around a shared barycenter with a 2.15 M ⊙ neutron star. Using textual constraints from classical Sanskrit astronomical treatises—specifically the Aryabhatiya and the Surya Siddhanta— chronological epoch markers (Kali Yuga and Krita Yuga) are extracted to define historical orbital configurations. The system's dynamics place the historical solar apoapsis at the vernal equinox of 232 CE, with periapsis passages calculated at 11,804 BCE and 12,267 CE with an orbital period of 24,070 tropical years. A purely mathematical Keplerian fit was executed against the recorded precession of the equinoxes. The resulting model resolves a stable binary system with an eccentricity of 0.037876. To find total precession in degrees at the vernal equinox of a given year t (in CE), calculate the eccentric anomaly E by E + 0.037876 sin E = 0.01495638 ∘ ∙ t and apply to v(t) = 2 ∙ arctan [0.962804 ∙ tan (E/2)]. The precessional velocity ( dv/dt ) at that moment is given by dv/dt = 53.80435 / (1 + 0.037876 cos v) 2 arcseconds per year. At the J2000.0 epoch, the calculated true anomaly of the Sun is 24.59°. Under this configuration, the Sun moves along a semi-major axis of 833.65 AU, and the hypothesized 2.15 M ⊙ neutron star, occupies a companion orbit with a semi-major axis of 388.12 AU. This manuscript outlines the strict mathematical derivation of these orbital parameters, demonstrating how ancient textual datasets can be reconciled with celestial mechanics to provide an alternative geometric solution to equinoctial precession and celestial perturbations.