《明天历》日食算法分析  

The solar eclipse algorithm of Mingtian Li and its analysis

作　　者：袁敏[1] 滕艳辉[2] 

机构地区：[1]西北大学数学系,陕西西安710127 [2]咸阳师范学院数学与信息科学学院,陕西咸阳712000

出　　处：《西北大学学报（自然科学版）》2012年第4期688-692,共5页Journal of Northwest University（Natural Science Edition）

基　　金：教育部人文社科青年基金资助项目(10YJCZH208);国家自然科学基金资助项目(11073016;11171271)

摘　　要：目的用数学公式将《明天历》的日食算法表达出来,并指出其天文学意义。方法文献分析与数学建模。结果《明天历》先求得合朔时交点离开冬至点的距离以及太阳到冬至点的距离,两者的差值就是"去交度分";常数中的"朔差"是一个朔望月中交点退行的距离;它以恒星年而不以回归年入算以及用太阳的去交分代替月亮的去交分都是其去交度分算法的不足之处。《明天历》的食甚时刻仅是对经朔时刻加入日月不均匀运动有关的修正,没有进行时差的修正。其他算法与主流算法基本相同。结论《明天历》的日食算法在宋代是比较特殊的,这些特殊之处大部分是正确的、合理的,但某些算法中仍存在不足。Aim To research the algorithms of the solar eclipse in Mingtian Li and to express it with mathematical formula completely, then to point out its astronomical significance. Methods Analysis of the original literatures and mathematical modeling. Results In Mingtian Li the distance between the winter solstice and the node was cal- culated at first. Then the distance between the winter solstice and the sun can be calculated at the time of the new moon. The difference between the two distances is the distance to the node. Shuocha is the distance of regression of nodes in one synodic month in Mingtian Li. Calculating with the sidereal year but not tropical year and substituting the distance between the node and the sun for the moon are the algorithm＇s shortcomings. The middle solar eclipse of Mingtian Li is got only by the correction about irregularity of the sun and moon but not shicha. Other algorithms and the mainstream algorithms are basically same. Conclusion The solar eclipse algorithms in Mingtian Li are special algorithms in the Song Dynasty. Most pant of them are right and reasonable, but some algorithms still exist deficiencies.

关 键 词：《明天历》 日食 去交度分 朔差 时差 

分 类 号：N09[自然科学总论—科学技术哲学] P194.3[天文地球—天文学]