中国古代的行星运动理论

中国传统数理天文学的行星运动理论的主要目的，是计算任意给定时刻行星的地心真黄经。具体算法由两个步骤组成：首先，按照行星与地球绕日匀速运动的假设，来推算行星视运动的地心平黄经；然后，对平黄经进行修正，由此获得所求时刻行星的地心真黄经。根据构建的行星地心平黄经的理论模型，分析了传统历法中对行星的平视运动推算的精度；又利用行星之地心真黄经的理论模型，探讨了中国古代行星算法模型的天文意义。由此得到的传统历法的行星理论之沿革，大体如次：在南北朝末期张子信发现行星公转与太阳视运动不均匀现象之前（约公元550年），传统历法仅仅推算行星的平黄经。从隋代刘悼的《皇极历》以迄唐代一行的《大衍历》，逐步完善并确立了行星中心差的修正模型。在边冈的《崇玄历》之后，进一步加入了太阳视运动之中心差的修正，从而在理论上考虑到了行星视运动的全部主要因素，为高精度的行星预测奠定了基础。

Planetary Theory in Ancient China

The aim of planetary theory in traditional Chinese astronomical mathematics is to calculate the true geocentric longitude at arbitrary given time. The theory consists of two parts: ( 1) Making use of an astronomical table in a synodic period and interpolation, the mean geocentric longitude of a planet will be determined. This step is permitted under such a hypothesis that both the planet and the Earth are in mean motion around the Sun. (2) Making use of a function to calculate the deviation between the true and mean geocentric longitudes of the planet. For analyzing the precision of traditional Chinese algorithm for the mean geocentric longitude of planet, its theoretical model is established by the author. Taking Mars in the Jiyuan Li (1106) as an example, the result shows that the average error of its mean geocentric longitude in a synodic period is about 4'. According to its theoretical model of the true geocentric longitude, the astronomical meaning of planetary theory in ancient China is revealed. Its evolution, in brief, could be described as follows: Before the phenomena of irregular movement of the Earth's and planet's revolution were discovered by Zhang Zixin in around 550, only its mean geocentric longitude of planet was calculated by calendar-makers. From Liu Zhuo's Huangji Li (600) to Yixing's Dayan Li (724) , an algorithm for the deviation between the true and mean longitude of planet was put to use. This deviation was supposed to be caused by the equation of center of planet only. Based on the method of Liu Zhuo and Yixing, a new algorithm was developed by Bian Gang in his Chongxuan Li (892). It incorporated the equation of center of the Earth in the deviation between the true and mean geocentric longitudes. After the Jiyuan Li ( 1106) , no substantial changes were made on the planetary theory in traditional Chinese mathematical astronomy.