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The Real New Moon Algorithms in Calendars of the Song Dynasty and Their Accuracy Analyzed

Author: ZuoYanHui
Tutor: QuAnJing
School: Northwestern University
Course: History of Science and Technology
Keywords: New Moon Central difference Era calendar Accuracy Error
CLC: P194.3
Type: Master's thesis
Year: 2009
Downloads: 69
Quote: 1
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Abstract


New Moon is an extremely important concept in the ancient Chinese calendar . The New Moon algorithms the ancient calendar spectrum prepared directly based on the same time , the accuracy of its projections directly affect the accuracy of eclipses . In this paper, a mathematics the formulaic and computer program means of comparative analysis of the algorithm and accuracy of the Song Dynasty calendar New Moon , and then analyzes the sources of error given Schomburg . The main work is as follows : 1 ) start from the the ancient Chinese fixed Schomburg algorithm model clearly combed the Song calendar New Moon algorithms , using modern mathematical formula expressed . 2 ) According to the New Moon formulaic algorithm to write applications. New Moon \visual expression . 3) calculate the era calendar 8 calendar line during New Moon moment , compared with the true value of the New Moon , drawn at each new moon projected error . Song Dynasty calendar projections given the overall level of new moon in about 34 minutes , the maximum error of 2.3140 hours . The most accurate \On the practicality of the calendar , the worst \To arrive at the calendar reduced accuracy is an important reason of the Song frequent calendar reform . 4) through the analysis of the error cycle , Schomburg error , the sun to correct a number of errors and the moon to correct the number of errors and comprehensive analysis of various error to find the impact of the main factors and characteristics given Schomburg error . The New Moon errors will show some cyclical characteristics , which can be calculated by the Schomburg error . The sun and the moon to correct the number of errors most value appears only in the sun and the moon at the same time running to near perigee . Moon error corrections role in many of the New Moon errors , near point constant error by the Schomburg error the New Moon accuracy dropped . Ministries calendar of error in fitting a straight line , the intercept of the line on behalf of the actual by the Schomburg error , slope reflects the anomalistic month , synodic month cumulative increasing trend of constant error value .

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CLC: > Astronomy,Earth Sciences > Astronomy > Time,calendar > Calendar > Ancient calendars
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