Speed-Error Cross-Correlation Dating of Ancient Star Catalogues, with Application to the Almagest

TL;DR

The paper introduces SESCC, a novel method for dating ancient star catalogues by analyzing cross-correlations between stellar proper-motion speeds and positional residuals, validated on historical catalogues and applied to the Almagest.

Contribution

SESCC is a new technique that accurately estimates the epoch of star catalogues using cross-correlation, with robustness against offsets and application to the Almagest.

Findings

SESCC accurately dates Tycho Brahe and Ulugh Beg catalogues.

Applied to the Almagest, the method suggests a pre-Christian origin.

The method is invariant under positional offsets and confirms Ptolemaic precession corrections.

Abstract

We present SESCC (Speed-Error Signals Cross-Correlation), a method for dating ancient star catalogues from the cross-correlation between stellar proper-motion speeds and positional residuals. At the true epoch, residuals are independent of proper-motion speed; the epoch estimate is the trial date that minimises this cross-correlation. For ecliptic latitudes, SESCC applies the dot product between speeds and residuals across all catalogue stars without subset selection or linear modelling. For ecliptic longitudes, SESCC-pairs uses pairwise longitude differences between neighbouring stars, making the method immune to any global longitude offset by algebraic construction. Validated against Tycho Brahe (1547 CE, true ~1580 CE) and Ulugh Beg (1452 CE, true 1437 CE), and confirmed invariant under offsets of +-6 deg, the method is applied to the Almagest. Both coordinates yield bootstrap distributions with 74% pre-Christian minima, consistent with a Hipparchan origin and inconsistent with a Ptolemaic one. The near-absence of quarter-degree fractions in the Almagest longitudes, explained as the deterministic consequence of Ptolemy's precession correction, provides independent corroboration.