《崇天历》行星算法及精度分析

Planetary Theory in the Reverence for Heaven System and Its Accuracy

行星理论是中国传统历法中的重要内容,行星视位置的计算精度更是检测历法优劣的重要标准之一。《崇天历》是宋朝行用时间最长的官方历法,该历中的步五星术将中国古代行星理论推向了一个全新的高度。文中利用python语言模拟《崇天历》步五星算法,并讨论了《崇天历》颁布初期30年的行星计算精度。研究结果表明,《崇天历》推算木星、火星、土星、金星、水星黄经的最大误差依次为4.58°、7.47°、2.36°、7.87°、15.88°,《崇天历》的行星计算精度尚未达到北宋天文学家“差天二度”的期望,精度不足的主要原因是由《崇天历》步五星的算法结构以及盈缩历和动态表的误差造成的。

Planetary theory is an important part of the traditional Chinese mathematical system,and the calculation accuracy of the apparent position of the planet is one of the important criteria for testing the pros and cons of the system.Reverence for Heaven System is the official system with the longest travel time in the Song dynasty.The planetary theory in the Reverence for Heaven System has pushed the ancient Chinese planetary theory to a whole new level.The author uses python programming to simulate the planetary theory and discusses the accuracy of planetary calculations in the first 30 years of the Reverence for Heaven System,then compares it with the theoretical longitude extracted from Skymap software.The results show that the maximum error of the longitude of Jupiter,Mars,Saturn,Venus and Mercury of the System is:4.58°,7.47°,2.36°,7.87°,15.88°.Research result shows that the system accuracy of the planetary apparent position in the Reverence for Heaven System did not meet the expectations of astronomers in the Northern Song dynasty that“the accuracy is more than two degrees”.The main reason for the lack of accuracy is the algorithm structure of the five planets in the Reverence for Heaven System,the Yingsuoli table,and the dynamic table.