宋代的日月食起讫算法  

Algorithm of the Moment of First Contact and Last Contact of an Eclipse in Calendars of the Song Dynasty

作　　者：滕艳辉[1,2] 

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000 [2]咸阳师范学院自然科学史研究所,陕西咸阳712000

出　　处：《咸阳师范学院学报》2014年第2期74-78,共5页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11073016);咸阳师范学院科研基金项目(12XSYK009)

摘　　要：梳理了宋代历法中的日月食起讫算法。详细分析《纪元历》《崇天历》《乾元历》日食泛用分和定用分算法,进而分析中国古代历法中处理时间和距离换算问题的两种不同思路。指出《崇天历》以前的历法使用线性插值算法处理日月食初亏到食甚的时间,《崇天历》以后的历法则采用二次内插法来处理;《纪元历》及其以后的历法为了简化运算,在对食延进行月亮不均匀性修正的过程中使用了近似算法。文中对《纪元历》的月食时差算法进行了讨论。This paper reviewed the algorithm for calculating the moment of first contact and last contact of an eclipse in ancient Chinese calendars of Song dynasty. A detailed analysis of Dingyongfen and Fanyongfen algorithms of Jiyuanli, Chongtianli and Qianyuanli had been made, and then two dif- ferent ways to deal with the problem of conversion in distance and time in ancient Chinese calendars had been analyzed. The paper pointed out that calendar makers caculated time from the early round loss to the middle of an eclipse using linear interpolation algorithm before Chongtianli, and quadratic inter- polation method used after that, Jiyuanli and other calendars after it used the approximate algorithm in order to simplify the calculation of the moon inhomogeneity correction. Finally, the paper discussed the shicha algorithm of lunar eclipse in Jiyuanli.

关 键 词：日食 初亏 复圆 《崇天历》 《纪元历》 

分 类 号：N09[自然科学总论—科学技术哲学]