Supplemental Material for "Astronomical Fidelity in Historical Coordinate Systems of Celestial Partitioning: Quantitative Comparison of Linear vs. non-Linear Measurements"

SCOPE AND FOUNDATIONAL PRINCIPLES

This volume of supplemental material provides the necessary celestial mechanics, data sets, and spherical geometry proofs underpinning the computational findings of the paper “Astronomical Fidelity […] Quantitative Comparison.” The visual evidence and comprehensive data tables are essential for the reader to verify the celestial mechanics and the calculated temporal errors of the linear methods compared to the non-linear method, specifically RGM compared to PTM/PLC.

Please note that the celestial geometry discussed herein operates exclusively within the framework of Ecliptic segments, i.e., the Zodiacal signs, which are the twelve uniform 30º divisions of Ecliptic Longitude (λ) that are fixed relative to the Vernal Equinox and, therefore, precess simultaneously with said point. This mathematical or geometric framework (rooted in Ptolemy’s Tetrabiblos) is distinct from the Zodiacal Constellations, which are the physically defined, irregular star groupings from which the ecliptic segments inherited their names. The former (signs) are uniform, geometric markers required for mathematical local horizon partitioning, whereas the latter are non-uniform bodies that have no geometric role in the calculation of cusps. Also, inasmuch as the Ecliptic constitutes the path of the sun, signs of delayed or long ascension in the northern hemisphere (from Cancer to Sagittarius, or λ 90º–270º) are the signs of rapid or short ascension in the southern hemisphere, and vice versa, the signs of rapid or long ascension in the northern hemisphere (from Capricorn to Gemini, or λ 270º–90º), are the signs of delayed or long ascension in the southern hemisphere.

Unless otherwise made explicit, all artistic illustrations were produced by the author.