Analyses on Christoph Clavius’s 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

Variations in solar radius (hereafter R ⊙ ) is a key reference for solar magnetic activity over time. The sunlight amount may have varied with R ⊙ and had an effect on the Earth’s climate in the past. Eclipse observations offer a unique opportunity to measure the absolute R ⊙ value before modern direct observations. The scientific community has discussed a possible long-term R ⊙ variability from 1715 onward. Prior to their coverage, Clavius’s eclipse reports had been subjected to qualitative debates regarding the local eclipse visibility and a possible secular R ⊙ trend. This study leverages the recent dramatic developments of lunar topography data and ephemeris data to provide an effective resolution of this debate. Clavius’s eclipse reports described an explicit totality in 1560 at Coimbra and a “slender circle” around the eclipsing Moon in 1567 at Rome. Our study revised the Δ T constraints of −492 s ≤ Δ T ≤ 200 s in 1560 and 140 s ≤ Δ T ≤ 151 s in 1567 to satisfy Clavius’s descriptions, considering the lunar topography data and assuming Auwers’s canonical R ⊙ . This study constrains the R ⊙ margin of 1567, utilizing three scenarios to interpret Clavius’s account. The local totality requires an upper R ⊙ limit of 1567 as R ⊙ ≤ 696200 km in absolute size (959 . ″ 92 in angular size), indicating no linear secular R ⊙ shrinkage but possible R ⊙ modulations on a centennial timescale. Conversely, the annularity scenario is considered unlikely because it requires a R ⊙ decrease of 4 . ″ 7 within three centuries, even beyond the capacity of Eddy's extreme shrinking-Sun hypotheses.