The Calculation of Shoushi Li When the Sun Transited Zodiacal Signs Improved by Xing Yunlu

Astronomy and Astrophysics – Astronomy

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History And Philosophy Of Astronomy, Ephemerides, Sun: General

Scientific paper

The book Gujin likao was written by Xing Yunlu, an ancient astronomer in the latter Ming dynasty. In this paper, base on our previous recovery for both calendars of Shoushi Li and Datong Li, we investigate the Xing's practical calculations for the times and locations when the sun transited zodiacal signs, then check and compare his results with our calculations after accepted Xing's parameters and the methods. First, when using the improving Shoushi methods claimed by Xing, we obtain,in the year of Wanli Jihai (1599), the standard error of the time between our calculations and Xing's results when the sun transit each of the zodiacs is 5.93 Ke (=85.39 min), but when ignore the biggest error derived by Zodiacs Xu, the error will decrease to 1.38 Ke (=19.87 min), and at the same time the standard deviation of solar longitude at middle-night just before transit is 0.06 Du (=0.059 °). The second,when employing our recovering methods of Datong Li and comparing with Xing's calculation, we ascertain that in the same year the standard error of the time when the sun transit each of the zodiacs is 1.09 Ke (=15.70 min), and the standard error of solar longitude at middle-night just before transit is 0.005 Du (=0.049 °). So we are sure we have recovered the work declared by Xing. And in fact Xing do not improve the method of Shoushi Li but provide the new values of the tropical year-length, the data of Zhoutian Fen (the degrees of the whole ecliptic or celestial equator), and the range of each zodiac. At the same time, the bigger deviations between both calendars derived by Xing just caused by his new parameters, and this probably leads to Xing approving Shoushi Li and despising Datong Li.

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