中国古代太阳中天观测及二至点测算精度

The Accuracy of the Sun's Meridian Observation and the Solstices Survey and Calculation in Ancient China

研究了元代《授时历议》所保存的天象观测和推步资料,得出:(1)在AD 1277-1280年 间所作的98次太阳中天观测的时刻及地平高度的绝对值平均误差分别为2.64 min和6.78'。(2) 6部古历--《大衍历》、《宣明历》、《纪元历》、《统天历》、《重修大明历》和《授时历》推 步BC 522年前的3个冬至时刻的误差范围为0.97-3.51 d;而AD 435-1280年间的45个冬至 时刻的绝对值平均误差则分别为9.35、10.42、5.54、2.97、5.68、3.36 h。(3)古代确定的AD 442- 1280年问的16个二至时刻的绝对值平均误差为199.59 min,其中元代的误差为27.89 min。

This paper investigates the Sun's meridian observation and the solstices survey and calculation, which recorded in Shoushi Liyi in the 13th century, an ancient treatise for reviewing Shoushi calendar in Yuan dynasty of China. It is derived that (1) from 1277 to 1280 and after 98 meridian observations of the Sun, the absolute value of average error of the time is 2.64 min and for altitude is 6.78';(2) to all the six ancient calendars of the Dayan, Xuanming, Jiyuan, Tongtian, Chongxiu Daming and Shoushi, the errors when three winter solstices reckoned before BC 522 are within 0.97 to 3.51 d and to other 45 data calculated from the period of AD 435 to 1280, the absolute value of mean error of the six calendars are 9.35, 10.42, 5.54, 2.97, 5.68, 3.36 h; (3) the absolute value of mean error of 16 ancient solstices times within AD 422 to 1280 is 199.59 min and in Yuan dynasty the result is just 27.89 min.