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

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'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' 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' 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 {\Delta}T constraints of -492 s =< {\Delta}T =< 200 s in 1560 and 140 s =< {\Delta}T =< 151 s in 1567 to satisfy Clavius' descriptions, considering the lunar limb profile and assuming Auwers' canonical R_Sun.

This study constrains the R_Sun margin of 1567, utilising three scenarios to interpret Clavius' account.

The local totality requires an upper R_Sun limit of 1567 as R_Sun =< 696200 km in absolute size (959.92" 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" within 3 centuries, even beyond the capacity of extreme shrinking-Sun hypotheses.