Analyses on Christoph Clavius' Reports of Total Solar Eclipses in 1560 and 1567: Key References for the Centennial Variations of the Earth's Rotation Speed and the Solar Radius

Abstract

Variations in solar radius (hereafter R_Sun) is a key reference for solar magnetic activity in time. The sunlight amount may have varied with R_Sun and had an effect on the Earth&#39;s climate in the past. Eclipse observations offer a unique opportunity to measure the absolute R_Sun value before modern direct observations. The scientific community has discussed a possible long-term R_Sun variability from 1715 onward. Prior to their coverage, Clavius&#39; eclipse reports had been subjected to qualitative debates regarding the local eclipse visibility and a possible secular R_Sun trend. This study leverages the recent dramatic developments of lunar topography data and ephemeris data to provide an effective resolution of this debate. Clavius&#39; eclipse reports described an explicit totality in 1560 at Coimbra and a &#34;slender circle&#34; around the eclipsing Moon in 1567 at Rome. Our study revised the ΔT constraints of -492 s =< ΔT =< 200 s in 1560 and 140 s =< ΔT =< 151 s in 1567 to satisfy Clavius&#39; descriptions, considering the lunar limb profile and assuming Auwers&#39; canonical R_Sun. This study constrains the R_Sun margin of 1567, utilising three scenarios to interpret Clavius&#39; account. The local totality requires an upper R_Sun limit of 1567 as R_Sun =< 696200 km in absolute size (959.92&#34; in angular size), indicating no linear secular R_Sun shrinkage but possible R_Sun oscillations on a centennial timescale. Conversely, the annularity scenario is considered unlikely because it requires an R_Sun decrease of 7.5&#34; within 3 centuries, even beyond the capacity of extreme shrinking-Sun hypotheses.