The Ancient Chinese Calendar Shoushi Li Still Usable for Predicting Solar Eclipses in the Year 2012

In 1280 A.D.in the Yuan dynasty (from 1279 A.D. to 1367 A.D.) the Chinese ancient calendar Shoushi Li (or Shou-shih li) was made by Guo Shoujing (or Kuo Shou-ching) and his colleagues. The calender has a high precision. It is the last calendar designed by ancient indigenous Chinese scientists. The Shoushi Li is thus one of the most famous calendars in the ancient China, and was recorded in the Lizhi (ancient calendar book of China) of the Yuanshi (annals of the Yuan dynasty). There are seven important calculation parts in the Shoushi Li, including solar positions, syzygies, corrections of solar motion and lunar motion, eclipses, and so on. The locations of the five planets are also in the list. Almost every part has a corresponding section in a modern astronomical ephemerides. The period of its usage (from 1281 A.D. to 1644 A.D.) is the longest among calendars in the ancient China. It was also a new calendar system at the time, in the sense that it dropped the traditional method of carrying out calculations from an epoch of the distant past. The essential constants of calculation were obtained from meticulous observations. Currently this calendar can still predict the solar eclipse to occur in May 21, 2012 and the local circumstance in Beijing. The error for the time of the middle of eclipse is 4min and the error of magnitude of the maximal eclipse is 0.04. This paper also provides the results from the Shoushi li for local circumstance and accuracy during the year 1990 to the year 2050 in Beijing. The standard deviation of the time errors is 103.04min and that of magnitides at the maximal eclipses is no less than 0.33. After investigating 186 solar eclipses from the year 1280 to the year 2050, the overall accuracy of the Shoushi Li can be deirved. Considering missed and erroneous records of solar eclipeses the standard deviations of the two aspects should not be better than 50.65min and 0.19, respectively. We have extended the calendar algorithms in steps by using a computer, and we find that the errors of the Shoushi Li increases with time after issueing. This calendar has not been in use for 450 years, but in some cases it is still of high accuracy, and the solar eclipse in 2012 is an example.