摘要
研究《历象考成后编》中求解刻卜勒方程以计算日月中心差的方法的来源及其精度,同时对书中日月理论的总体精度进行分析,发现:书中用于太阳和月亮中心差计算的方法分别是薄利奥和卡西尼方法的简化版本。前一种方法用于太阳中心差计算时可以把最大误差控制在1角秒之内,而后一种方法用于月亮中心差计算的最大误差也不会超过11角秒。尽管从现代观点来看这两种方法并不是当时的最佳选择,但是,相对于书中日月理论的总体精度水平而言,该书编者的选择还是相当明智的。由于书中吸收了自刻卜勒到牛顿时代西方日月理论发展中诸如此类的重要成果,清代日月位置计算的精度实现了一次飞跃:与《历象考成》中的理论相比,该书日行理论的精度提高了10倍以上,月行理论在月黄经的计算方面精度提高了4倍以上,在黄纬计算方面精度则提高了将近10倍,从而为清代交食预报精度的提高奠定了直接的基础。
This paper discusses the Western sources of the methods employed in the Lixiang Kaocheng Houbian (Later Edition of the Established System of Calendrical Astronomy) to resolve the Kepler Equation in calculating the solar and lunar equations of center. Meanwhile, it also analyzes the precision of these methods and the overall accuracy of the lunisolar theory of the book in positional calculations. The methods, as applied to the equation of center of the sun and the moon respectively, are found to be simplified versions of the procedures of I. Boulliau and J. Cassini. While the former can be correct to within 1 arcsecond in calculating the equation of solar center, the latter displays an error not exceeding 11 arcseconds as used to calculate the equation of lunar center. The Jesuit authors' selection of these two methods turns out to be very reasonable with respect to the overall precision level of the lunisolar theory of the book, although it was not the best choice of the time as seen from the present point of view. Since the book appropriated the most important European achievements from the time of Kepler to thet of Newton like the two methods, the positional astronomy of the sun and moon thus witnessed a very remarkable advancement in the Qing dynasty: as compared with the theory of the old Lixiang Kaocheng, the precision of the positional calculation of the sun enhanced more than ten times, whereas the lunar theory became over four times more accurate in the longitudinal calculation and nearly ten times more accurate in the latitudinal calculation, thus laying a sound foundation for improvement in the predictive calculation of solar and lunar eclipses.
出处
《中国科技史料》
CSCD
2003年第2期132-146,共15页
China Historical Materials of Science and Technology
基金
国家自然科学基金项目"中国古代历法的计算机模拟与综合研究"(项目编号:10173012)
关键词
《历象考成后编》
中心差
日月理论
刻卜勒方程
计算
Lixiang Kaocheng Houbian, theory of the sun and moon, equation of center, Kepler equation, I. Kgler
