南宋历法中的交食算法及其计算精度  

Eclipse algorithm and its calculation accuracy in the Southern Song Dynasty calendars

作　　者：滕艳辉[1] 王鹏云[1] 刘娅娅[2] TENG Yanhui;WANG Pengyun;LIU Yaya(School of Mathematics and Information Science,Xianyang Normal University,Xianyang 712000,China;Department of Statistics,Xi′an University of Finance and Economics,Xi′an 710100,China)

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]西安财经学院统计学院,陕西西安710100

出　　处：《西北大学学报（自然科学版）》2018年第2期311-316,共6页Journal of Northwest University（Natural Science Edition）

基　　金：国家社会科学基金重大项目(15ZDB029);国家自然科学基金资助项目(11603017);陕西省教育厅专项科研计划基金资助项目(15JK1797)

摘　　要：南宋的历法多是根据北宋历法修订而来的。正史仅记载了它们的历法常数,而对历法的具体推算术文则略去不记。分析现存的部分历法术文和史载的历法推算日月交食的记录,并进行回推计算和比较,得出《统元历》、《乾道历》、《淳熙历》和《会元历》使用《崇天历》的交食推算方法,而《统天历》、《开禧历》和《成天历》可能使用了《纪元历》的交食推算方法。使用南宋的七部历法的算法分别计算了它们各自行用前后100年间的所有可见日食,并与真实的天象作比较,得到这些历法的推算精度。结论是:历法推算日食食甚的平均误差大约是0.5小时,食分误差是1.5分。Calendars of the Southern Song Dynasty are always revised according to the Calendars of Northern Song Dynasty.Their astronomical constants record in official history,but the complete calculation methods are not kept.In this paper,the existing text in the calendars and the historical records of eclipses calculated by algorithm are analyzed.According to recalculation and comparison,it is concluded that"tongyuan li","qiandao li","chunxi li"and“huiyuan li”in the Southern Song Dynasty used the same calculation method of solar eclipse with“chongtian li”,while“tongtian li”,”kaixi li”and“chengtian li”may use the method in“jiyuan li”.In this paper,all visible solar eclipses before and after 100 years within each calendar enactment are calculated.Comparing with the real astronomical phenomena,the calculation accuracy of the calendars is obtained.The conclusion is that the average error of the middle of a solar eclipse of all the calendars is about 0.5 hours and the error of magnitude of eclipse is 1.5.

关 键 词：日食 精度 《纪元历》 《崇天历》 交食算法 

分 类 号：N09[自然科学总论—科学技术哲学] P1-092[天文地球—天文学]