《大衍历》行星算法及精度分析

A Study on Planetary Theory and the Accuracy of Calculations of Planetary Positions in the Great Expansion System

行星理论是中国传统数理天文学的核心内容之一,我国第一部保存较为完整的历法《三统历》中就有比较完整的记载,此后各历中均有相关内容。在中国行星理论发展史上,《大衍历》因为有诸多创新而占有非常重要的地位。本文全面梳理了《大衍历》中的行星算法,并用Python语言对《大衍历》行星算法进行模拟,讨论了《大衍历》制定和颁行期间35年内的行星位置计算精度。研究结果表明,《大衍历》推算木星、火星、土星、金星和水星黄经的最大误差依次为3.93°、36.96°、7.99°、18.52°、32.5°。进一步的分析表明,《大衍历》中“五星爻象历”和“五星动态表”的设计及其误差、五星近日点黄经的测算误差和定合日期的推算误差,是影响《大衍历》行星计算误差的主要因素。

Planetary theory is one of the core contents of traditional Chinese mathematical astronomy.There is a relatively complete planetary algorithm in the Triple Concordance System,the first system which is well preserved in China,and related content is found in all subsequent systems.Since predicting the positions of the five planets was one of the criteria for judging whether a system was effective,the planetary theory was constantly improved.The Great Expansion System occupies a very important position in the development history of Chinese planetary theory because of its many innovations.This paper comprehensively explains the planetary algorithm in the Great Expansion System,simulates the planetary algorithm in the Great Expansion System using the computer program Python,discusses the accuracy of the calculations of planetary positions in the 35 years when the Great Expansion System was used,and concludes that the maximum error of the longitude of Jupiter,Mars,Saturn,Venus and Mercury calculated by the system is as follows:3.93°,36.96°,7.99°,18.52°,32.5°.Further analysis shows that the main factors affecting the error of the calculation of the planets in the Great Expansion System are as follows:the planetary Argument of Aspectual and Interval Count(the table of planetary equations of the center),the precision of planetary perihelion longitude,the date of conjunction of the planet with the sun and the constant of the planetary synodic period.