中国古代历法中合朔时的太阳位置

The Sun’s Position at the Time of the New Moon in Ancient Chinese Calendars

分析了古代历法中推求合朔和朔日夜半时的太阳位置算法。这些历法可以分为三类,分别按日月为平运动,考虑了月亮的不均匀运动和考虑了日、月的不均匀运动来计算太阳位置。合朔等时刻的太阳位置在《皇极历》之前推求的一直是赤道位置,自此部历法开始推求的是黄道位置,这是一个重要的进步。古代历法日月运动不均匀的改正主要是考虑了由椭圆运动引起的中心差。在探讨太阳运动的不均匀改正时,主要讨论了《皇极历》、《大衍历》和《会元历》,宋代的《会元历》不论在总体上或细节上都大大超过了《皇极历》和《大衍历》。

The algorithms for the sun＇s positions at the time of the new moon and at the midnight of the new-moon day in ancient Chinese calendars are analyzed, which can be classified under three types, of which the motions of the sun and moon were treated as uniform for the first type, the non-uniform motion of the moon was taken into consideration for the second type, and the non-uniform motions of the sun and moon were taken into account for the third type. The calculated positions of the sun at the time of the new moon and at other times were denoted in the equator system before Huangji CaUendar. However the positions were denoted in the ecliptic system since Huangfi Callendar, which is a great advance. The equation of the center caused by the elliptic motion was mainly taken into consideration in correcting for the non-uniform motions of the sun and moon in ancient Chinese calendars. As for the correction for the non-uniform motion of the sun, Huangfi Callendar, Dayan Callendar and Huiyuan Callendar are mainly discussed in this paper, and the results show that Huiyuan Callendar of the Song dynasty exceeds the other two calendars greatly as a whole or in the details.