《开禧历》日食算法及计算精度  

Eclipse Algorithm and Its Calculation Accuracy of Kaixili

作　　者：滕艳辉[1] 王鹏云[1] 刘娅娅[2] TENG Yan- hui;WANG Peng -yun;LIU Ya -ya(School of Mathematics and Information Science,Xianyang Normal University,Xianyang 712000,Shaanxi,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：《内蒙古师范大学学报（自然科学汉文版）》2018年第3期259-264,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11603017);陕西省教育厅科研计划项目(15JK1797)

摘　　要：根据《开禧历》现存日食推算过程名称及天文常数,推断其日食计算方法与《纪元历》相同.给出了《开禧历》完整的日食推算公式以及使用《开禧历》计算淳祐五年七月朔日食的过程.将《开禧历》的日食算法编写为计算机程序,计算出1112至1303年间杭州的所有日食.与真实的天象作比较,得到《开禧历》日食计算精度为:日食食甚的平均误差0.46h,食分误差1.65分;有近20%的推算达不到当时的标准.According to astronomical constants and the solar eclipse calculation process existed in Kaixili,it is infered that the method of solar eclipse calculation in kaxili is the same as Jiyuanli.This paper gives a complete formula of solar eclipse caculation and a caculating example,the solar eclipse in the seventh month of the lunar year of the fifth year of Chunyou.A computer program according to eclipse algorithm is written to calculate all eclipses from 1 112 to 1 303 in Hangzhou.Compared with the true celestial phenomena,the calculation accuracy of the solar eclipse is obtained.The average error of the middle eclipse calculation is 0.46 hour and the error of magnitude of eclipse calculation is 1.65 min.Nearly 20% of the projections of eclipse failed to meet the ancient standards.

关 键 词：开禧历 纪元历 日食 精度 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]