《授时历》五星推步的精度研究

The Accuracy of the Five-planet Locations Calculated by the Chinese Ancient Calendar Named Shoushi Li

着重考察了《授时历》的步五星术,考校、复原了其推步方法.(1)推步了1299年木星历,并与已有研究进行比对,从而确认恢复方法的正确性.(2)得出《授时历》在1280～1650年间推步五星黄经的精度,木星、火星、土星、金星和水星的误差的绝对值平均分别为0.49°、1.91°、0.70°、2.82°和5.01°,木星、土星的精度较高.(3)指出将现代天文方法获取的《授时历》五星参数(周率、历率、度率、合应及历应)精确值代入《授时历》推步模型,木星、土星的推步精度并未提高,误差分别为1.83°和1.21°,而水星、金星和火星的误差却大幅加大,结果分别为30.04°、54.86°和10.82°.说明某些重要参数的修正并不能改善推步结果.

The calendar Shoushi Li is one of the most famous calendars in ancient China, which was recorded in the Lizhi （ancient calendar book of China） of Yuanshi （annals of the Yuan Dynasty from 1279 to 1367）. There are seven important calculation parts, including solar terms, syzygies, corrections of the sun and the moon, eclipses and so on. The locations of the five-planet are also in the list. Almost every part has a corresponding section in the modern astronomical year book. It is the last calendar formulated only by Chinese astronomers and its period of usage （from 1281 to 1644） is the longest one in ancient China. It was also a new calendar system which cast off the traditional method by which calculations were carried out from the epoch of the distant past. The basic constants were obtained by meticulous observations and then used in calculations. In this paper, the calculation methods of planetary locations in Shoushi Li are inves- tigated and recovered by studying the official texts of Yuanshi. （1） The locations of the ephemeris of Jupiter in 1299 are derived and our recovering method is affirmed by compar- ing with other studies. （2） The calculated accuracies of celestial longitudes of the five-planet from 1280 to 1650 are obtained. For Jupiter, Mars, Saturn, Venus and Mercury, the average values of absolute errors are 0.49° , 1.91° , 0.70° , 2.82° and 5.01° . Jupiter and Saturn have comparatively higher accuracies. （3） Zhoulu, Lilu, Dulu, Heying and Liying are used for planetary calculations in Shoushi Li. Their accurate values, instead of those adopted in Shoushi Li, are derived and calculated by modern astronomical methods and then inputted into Shoushi models. It is found that the accuracies of planetary locations are not improved. The errors of Jupiter and Saturn are 1.83° and 1.21°. But the errors of Mercury, Venus and Mars ascend to 30.04° , 54.86° and 10.82° , respectively. It is indicated that the accuracies can not be increased by revising some of the important parameters based on modern science.