宋代定朔计算精度分析

An Accuracy Analysis of the Real New Moon Algorithm in Song Dynasty

定朔是中国古代天文学中一个十分重要的概念。梳理了宋代历法中定朔推步的过程,严格按照历法术文将《纪元历》等11部历法的定朔算法编写成计算机程序,并计算出各部历法行用期间的所有定朔时刻,与定朔的真实值相比较,得出各部历法推算定朔的客观精度。使用古今两种观点对历法的精度进行分析,得到在古人眼中各部历法定朔的计算精度。利用周期函数法分析定朔误差的来源,得到各历法的经朔误差。

The real new moon is an extremely important concept in Chinese ancient astronomy. In this paper, the calculation process of real new moon in calendars of the Song Dynasty was introduced at first. Then the real new moon algorithms in 11 calendars including Jiyuan Calendar were compiled into computer programs strictly according to their prediction texts. The paper calculated all the real new moon moments by using the methods of each calendar. The objective accuracy of these calendars is estimated by comparing these calculations with true values, and the calculating accuracy is obtained from the perspectives of the ancients through the use of both ancient and modern viewpoints.Finally, the error of mean new noon of each calendar can be calculated by analyzing the sources of the real new moon error with a method of periodic function.