中国古代的日食时差算法

因月亮视差引起的对日食食甚时刻的修正值,即定朔时刻与日食食甚时刻之差,中国古代称为时差.本文讨论了中国古代时差算法的沿革及其算法模型,并与理论算法作了比较,分析了其精度误差.从理论上来说,时差算法是关于太阳的时角和黄经的二元函数,但是中国古代的时差算法只考虑了时角因素,而完全没有考虑到太阳的黄经变化对时差的影响,因此中国古代的时差算法是一个不完全的算法.本文的讨论结果表明,中国古代的时差算法虽然是一个有缺陷的算法,但其结果和理论结果还是比较接近,特别是和二至时的理论结果相比,误差只达到2min左右.

Shicha Algorithm in Ancient China

Shicha means the correction to the time of the middle solar eclipse caused by lunar parallax, namely the time difference between the time of syzygy and the middle eclipse. This paper discusses the history and model of Shicha algorithm in ancient China and compares it with theoretical algorithm, analyzes the error of Shicha algorithm. Theoretically, the algorithm of Shicha is a function including two independent variables, one is the longitude of the sun and the other hour angle. The algorithm of Shicha in ancient China is an incomplete algorithm because it only considers the latter factor and neglects the former. This paper shows that although the algorithm of Shicha in ancient China is an incomplete algorithm, the result is still near to the theoretical result, especially in equinox and solstice, this error is only about two minutes.