Title

A study on the Method for Determining the Time Of the Solstices in Ancient China It’s Precision

Author

Rong-bin Wang

Genre

Article  

Pages

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Key words

ancient Chinese calendars, Shoushi calendar, winter solstice

Abstract

      Zu.Chongzhi（A.D. 429-500）, a celebrated mathematician and astronomer in Southern ＆Northern Dynasties, invented a relatively strict mathematical method for determining the time of the solstices first in the history of astronomy in ancient China. The method was based on two hypothetical conditions: 1) the change of the solar shade length is symmetrical with the solstices as its symmetric center. 2) the change of the solar shade length in a day ins uniform. This study analyses the mathematical fundamentals of the method and it is showed in this paper that the main errors of Zu’s formula are due to the solar shade length’s error and the formula’s hypothetical conditions. It is also showed that the errors of the hypothetical conditions are very small and the method was reliable in the years of the method was used. It is found that the error of Zu’s formula decreases as the time between the date of the set of solar shades and the winter solstice increases

    The data analysis to the solstices of the Shoushi calendar shows that the writer of the calendar possibly adopted the principle of counting fractions over 1/2 as 1 and disregarding the rest on the basis of average value. This study also discusses why the errors of summer solstices are much greater than those of the winter solstices in the Shoushi calendar, and points out that the method for determining the time of solstices is only practical for the winter solstice, the summer solstice is subordinately determined by the winter solstice and the length of tropical year in ancient Chinese calendars. The authors of the Shoushi calendar invented new instruments for measuring the solar shade used an advanced data handling method so that they made a great contribution to improve the precision of the winter solstices but not to the formula of the calculation.