The Real New Moon Algorithms In Calendars Of The Song Dynasty And Their Accuracy Analyzed

The real new moon is an extremely important concept in Chinese calendars. The real new moon algorithm is the direct foundation in ancient ephemeris arranging. Simultaneously,its calculation would have direct influence on the accuracy of the solar and lunar eclipses.In this paper,the real new moon algorithm in calendars of the Song Dynasty and its analysis can be compared and analyzed in the way of math formulistic and computer programmed,and then the sources of error would be analyzed and obtained.The main results the paper has obtained are as follows:1) With the algorithm theoretical model of the real new moon in the ancient time of China,the computation process of the real new moon is reconstructed and expressed with the modern mathematical formula.2) Applications have been prepared in accordance with the real new moon algorithm formulated.The calculation process of the new moon in calendars including "Jiyuan Li" is prepared into software,which not only can calculate the time of the real new moon of any given date,but also can clearly visualize the middle results such as the mean new moon,the name of the real new moon and the rectified number of sun and moon..3) The paper calculates all the real new moon moments using the methods of the 8 calendars including "Jiyuan Li".Comparing these calculations with modern values,we estimate the error of these calendars.The calendars' accuracy in calculating real new moon of the Song Dynasty is about 34 minutes at the overall level and the largest error is 2.3140 hours.The highest accuracy is "Chengtian Li" to 0.3708 hours and the lowest is "Tongyuan Li" to 0.7054 hours.On the practicality of the calendar,"Chengtian Li" is the worst,while "Kaixi Li" is the best,which accuracy changes over time by less than 1 minute per year.Based on this,it concludes that low accuracy in the real moon calculations was the reason that the calendar was frequently changed in the Song Dynasty.4) According to analyzing error cycle,the error of mean new moon,the error of rectified number of sun and moon and a comprehensive analysis of various errors, the main factors and the error characteristics impacting the real new moon will be found.The error of the new moon demonstrates the cyclical nature of characteristics and the error of the mean new moon can be calculated.The largest error of rectified number of sun and moon appears only when the sun and the moon run near perigee at the same time.The rectified number of moon is the largest factor among the many effects to the real new moon.The error of constant on anomalistic moon and error of the mean new moon play the most important role in declining in accuracy of the real new moon.The intercept of the error fitting straight line or each calendar represents error of the mean new moon actually and the slope reflects the increased accumulated trend of the error of synodic moon and anomalistic moon.