中国古代五星定合算法的沿革与分期

A History of the Corrected Conjunction Algorithm of Five Stars in Ancient Chinese Planetary Theory

五星定合算法是中国传统行星理论中的一个重要算法.张子信之前的历法家均假定五星和太阳匀速运动,以此推算五星合日时刻及位置.唐代的《大衍历》最早在定合算法中考虑了行星中心差和太阳中心差,五星定合算法经过宋代《崇天历》改革而基本定型,此后一直到《授时历》未发生本质变化.梳理了中国古代五星定合算法的历史沿革,并根据五星定合算法的特征,以《大衍历》和《崇天历》为关节点,将五星定合算法的历史分为3个时期.

The corrected conjunction algorithm of Five Stars is one important algorithm in ancient Chinese planetary theory.When calendar-makers before Zhang Zixin calculated the moment and position of Planet-Sun conjunction,they supposed that the Sun and Five Stars were surrounded at a constant speed.Dayan Li of Tang Dynasty firstly considered the center equation of planets and Sun when they calculated the moment and position of corrected conjunction.The corrected conjunction algorithm of Five Stars was mature in Chongtian Li of Northern Song Dynasty.After the Chongtian Li,no substantial changes were made on the corrected conjunction algorithm of Five Stars in ancient Chinese mathematical astronomy.The history of the corrected conjunction algorithm of Five Stars was discussed and divide into three phases according to the features of corrected conjunction algorithm,and the critical points of three phases are Dayan Li and Chongtian Li.