中国古代的月食食限及食分计算法

ANCIENT CHINA'S ALGORITHMS OF THE LUNAR ECLIPTIC LIMIT AND THE DEGREE OF LUNAR OBSCURATION

中国古代曾先后以望时日、月分别距黄白交点的度距及日、月间的度距等三种不同的天文量来表述月食食限,并提出了不可能发生月偏食、必定发生月偏食、不可能发生月全食、必定发生月全食等四种食限概念和具体数值,它们都曾达到很高的精度。中国古代先后有过五种不同形式的月食食分计算法,它们都与现代食分的定义相吻合,并虑及日、月与远、近地点的相对位置不同,以及月亮视差因月亮在黄道南北而异等因素,对月食食分计算的影响。

The lunar ecliptic limit had been indicated in ancient China by three astronomical dimensions: the distance between the sun (or the moon) and the node of the ecliptic and the lunar orbit at full moon; and the distance between the sun and the moon at full moon. The lunar ecliptic limit was distinguished into four different kinds: the limit in which a partial eclipse probably occurred; the limit of the partial eclipse; the limit in which a total eclipse probably occurred; and the limit of the total eclipse. These four kinds of values varied in different dynasties, but some excellent results were obtained. There were five different forms of algorithms for the degree of lunar obscuration in ancient China, which corresponded with the current definition of lunar obscuration and took into consideration the different relative positions between the sun (or the moon) and the apogee or the perigee, and the impact of such factors as the lunar parallax in the degree of lunar obscuration.