How Are the Terms of the Angular Distance between Celestial Bodies Defined in Korean Historical Records?

Korean historical literatures offer numerous records on astronomical phenomena such as eclipses, comets, and close approaches, etc. Records of close approaches often use specific terms to describe the angular distance, which lack translation into modern numerical values. We study the usage of the five commonly used terms, namely, Entry (入, En), Invasion (犯, In), Occultation (掩, Oc), Eclipse (食, Ec), as well as the unit Chi (尺). Our analysis is based on more than 2,300 records from Goryeo (918–1392 CE) and Joseon (1392–1910 CE) Dynasties. Through statistical analysis, we determine their quantitative definitions. We convert the lunisolar calendar to the Julian and Gregorian date and utilize the modern ephemeris DE431 to calculate the angular distance between celestial bodies. We find that the angular distances of the terms En, In, Oc, and Ec correspond to respectively 1.78^◦+2.36 −1.11^, 0.89^◦+3.54 −0.51^{,0.44◦+1.15}−0.31, and 0.29◦+2.61−0.16 for the Goryeo Dynasty and 1.36◦+1.15−0.64^{,0.51◦+1.11}−0.32^{,0.25◦+0.27}−0.17, and 0.21◦+0.25−0.11 for the Joseon Dynasty. Additionally, we determine the angular size of the unit Chi by using the records from Korean chronicles along with the drawings of comets’ tails in the Daily Log (天變謄錄). We estimate the unit Chi to be 1.11^◦+0.46 −0.40 and find that the numerical definition was consistent throughout the two dynasties in Korea. Furthermore, we find that the terms were used to describe the closest approach and that there is no observational bias in the angular distances against the apparent magnitudes of the objects. We show that the terms En, In, Oc, and Ec represent decreasing angular distance in that order and this ordering was consistent in both dynasties.