《纪元历》五星定合算法及其精度研究

A Discussion on the Corrected Conjunction Algorithm of Five Planets of Jiyuan Li

考察了《纪元历》五星定合算法,构建了五星定合算法的数学模型,分析了《纪元历》五星定合算法的合理性,计算了《纪元历》五星定合算法的精度,木星、火星、土星、金星和水星的定合时刻误差的绝对值平均值分别为0.92,1.20,0.81,1.00和3.93日,定合时刻五星地面视赤经误差的绝对值平均值分别为木星0.54°,火星1.05°,土星0.59°,金星1.02°,水星4.18°.木星、土星定合算法的精度较高,火星和金星次之,水星最低.《纪元历》五星定合时刻及位置误差曲线呈现出有规律的波动,其波动周期约为行星和地球绕日公转时间的最小公倍数.

In this paper, the corrected conjunction algorithm of Five Stars in Jiyuan Li are investigated and recovered by studying the offical texts of Songshi. Mathematical model of corrected conjunction algo- rithm of Five Stars is constructed and the reasonability of corrected conjunction algorithm in Jiyuan Li is dis- cussed. The calculated accuracies of planetary corrected conjunction algorithm are obtained. For Jupiter, Mars, Saturn, Venus and Mercury, the average values of absolute errors of corrected conjunction moment are 0.92, 1.20, 0.81, 1.00 and 3.93 clays and that of planetary locations at corrected conjunction moment are 0.54°, 1.05°, 0.59°, 1.02° and 4. 18°. Jupiter and Saturn have relatively higher accuracies, Mars and Ve- nus come second and Mercury the third. The error curves of planetary corrected conjunction algorithm in Jiyuan Li show regular rising and falling and their wave cycles are about the least common multiple of the revolution cycle of earth and that of planet.