Models of Solar and Lunar Motions in the Chinese Chongxiu-Daming Calendar

The Chongxiu-Damingli (Revised Great Enlightenment Calendar) of the Jin dynasty (A.D. 1115–1234) was developed in 1171 and used until 1280 in China. It had also been used since the reign of King Sejong (A.D. 1418–1450) in Korea to supplement calculations of the eclipse times. In this study, we investigate solar and lunar motions in this calendar. Referring to the Garyeong (Example Supplement for the Calculations of Solar and Lunar Eclipses Occurred in 1447) preserved in Korea, we first investigate sunrise and sunset times by the Chongxiu-Damingli to estimate the observation sites of these times. We then analyze the calculation methods of solar and lunar motions and of the maximum eclipse time using the calendar. We find that a cubic equation was utilized to calculate sunrise and sunset times. Compared with the results of modern calculations, we also find that the sunrise and sunset times are more suitable at Kaifeng (capital of the Northern Song dynasty) than Beijing (capital of the Jin dynasty). This finding confirms the record of the Jinshi (History of the Jin Dynasty) that the Chongxiu-Damingli was made based on the calendar of the Northern Song dynasty. Regarding solar and lunar motions, we find that the mean absolute difference values between the Chongxiu-Damingli and modern calculations are ∼0.005 and ∼0.145 degrees, respectively. Lastly, we find that the difference in the time of maximum solar eclipse that occurred on 1447 September 10 in Seoul (capital of the Joseon dynasty) is approximately 1 min between the calendar and modern calculation. We believe that this study will contribute to understanding the Chongxiu-Damingli and comparing the accuracy with other Chinese calendars such as the Shoushili.