The star catalogue of Wilhelm IV, Landgraf von Hessen-Kassel: Accuracy of the catalogue and of the measurements

TL;DR

This study evaluates Wilhelm IV's 1586 star catalogue, demonstrating it has higher measurement accuracy than Brahe's, especially after correcting for known equinox offset, with precise altitudes and angles measurements.

Contribution

The paper provides a detailed accuracy analysis of Wilhelm IV's star catalogue, showing it surpasses Brahe's in precision after correction for equinox offset.

Findings

Measurement accuracy averages 26 arcsec for fundamental stars.

Catalogue accuracy improves by a factor of two after correction.

Conversion computations are highly accurate with negligible errors.

Abstract

We analyse a manuscript star catalogue by Wilhem IV, Landgraf von Hessen-Kassel, from 1586. From measurements of altitudes and of angles between stars, given in the catalogue, we find that the measurement accuracy averages 26 arcsec for eight fundamental stars, compared to 49 arcsec of the measurements by Brahe. The computation in converting altitudes to declinations and angles between stars to celestial position is very accurate, with errors negligible with respect to the measurement errors. Due to an offset in the position of the vernal equinox the positional error of the catalogue is slightly worse than that of Brahe's catalogue, but when correction is made for the offset -- which was known to 17th century astronomers -- the catalogue is more accurate than that of Brahe by a factor two. We provide machine-readable Tables of the catalogue.