东汉到刘宋时期历法五星会合周期数源

THE SOURCE OF THE SYNODIC PERIOD OF FIVE PLANETS IN CHINESE CALENDARS FROM EAST HAN TO LIU SONG DYNASTY

刘宋何承天元嘉历(公元443年)以前,历家皆用分数M/N来刻划其五星会合周期,意即:日率M个回归年内,行星与太阳相合为周率N次,通过《东汉到刘宋时期历法上元积年计算》一文的实例考察,我们得出此间历法五星会合周期均不具备参与其上元推算条件的结论,因此,M/N需要某种特别的选择方能与上元配合。

This paper provides the method of synodic period selection of five planets in calendars and the way how these data match with heir determined superior epoch during the period from East Han to Liu Song Dynasty. The error analyses for some calendars in this period may pro- vide answers to the following questions: whydid the Jing Chu Calendar choose some rough synodic periods of five planets? why did five planets have nothing to do with their superior tpoch in the Yuan Jia Calendar? And why did Zu Chongzhi change the forms of synodic periods in his Da Ming Calendar?