A Study of Planetary Theory in the Great Expansion System(Dayan li大衍历,727 CE):The Case of Mars

《大衍历》(727)中的行星理论研究--以火星为中心的考察

The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different planets had important astrological significance.Thus,planetary theory is an important part of Chinese mathematical astronomy.The Great Expansion System,which was compiled by Yixing一行of the Tang唐dynasty(618–907 CE),provided many innovations in planetary theory.Based on the extant Treatises on Mathematical Harmonics and Astronomy(Lüli zhi律历志)in Chinese official histories,the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet.It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet,which was the basis for calculating the true position of the planet.In addition,Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China.The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems.Mars is taken as a case study to investigate the planetary theory in the Great Expansion System,including the astronomical constants related to Mars,two important astronomical tables,namely the table of the equation of center and the table of the phase motion of Mars in one synodic period,and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center.Two questions are addressed.First,how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars?Second,how did Yixing calculate the true position of Mars on any given day?The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.

本文以火星为例,详细考察《大衍历》(727)中的行星运动理论。在中国古代星占学中,一个行星的位置和不同行星的相对位置具有重要的星占学意义。因此,行星理论是中国数理天文学中的重要内容之一。唐代一行的《大衍历》在行星理论中有许多创新。根据现存中国正史中的《律历志》,《大衍历》是第一部设计行星中心差算表并利用该算表计算行星位置的中国历法,也是第一部设计五星动态表计算行星平位置的中国历法,行星平位置是计算行星真位置的基础。此外,一行还提出了行星近日点进动的概念并首次给出了行星近日点进动的数值。《大衍历》在行星理论方面的诸多创新奠定了它在历法史上的重要地位。本文考察的内容主要包括与火星有关的天文常数,火星的中心差表和火星在一个会合周期内的动态表这两个重要的天文算表,以及利用行星中心差和太阳中心差计算火星在任意一天的位置的算法。本文主要阐明两个问题。一是一行是如何用行星中心差修正火星平合时刻以及火星在任意时刻的平位置的?二是一行是如何计算火星在任意一天的位置的?通过分析《大衍历》的原始文本,本文展示了一行是如何发展隋代及初唐的行星理论,并建立起一套完整的预报行星位置的算法的。