Research On The Planetary Theory Of Four Astronomical Systems In The Early Song Dynasty

The planetary theory is an important part of the traditional Chinese astronomical system,and the calculation accuracy of the apparent positions of the planets is one of the important criteria for checking the quality of the astronomical system.Reverence for Heaven System is the official calendar system that has been used for the longest time in the Song Dynasty.The planetary theory in this astronomical system has pushed ancient Chinese planetary theory to a whole new level.Before Reverence for Heaven System,Response to Heaven System,Response to Heaven System and Matching Heaven System are the transitional stage astronomical system for the planetary theory to mature.The study of the planetary theory in the four astronomical systems of the early Song Dynasty will help to clarify the development process of the traditional Chinese planetary theory.The specific work of this paper is as follows:1.Interpretation and collation of the astronomical constants of the four astronomical systems in the early Song Dynasty,analyzing the precision of the astronomical constants of these four astronomical systems,the research shows that the precision of the five planets conjunction period and the perihelion precession value of the four astronomical systems in the early Song Dynasty are based on Supernal Epoch System and Matching Heaven System.Excellent,before the Northern Song Dynasty Era Epoch System,the algorithm of the five planets perihelion ecliptic was the same as that of Great Expansion System,only the Extending Enlightenment System was different,but Response to Heaven System and Extending Enlightenment System belonged to the same system,and the other three astronomical systems influenced by Great Expansion System.2.Interpret the structure and astronomical meaning of the movements of five planets within a synodic period of the four astronomical systems in the early Song Dynasty,and discuss the development of these four calendar movements of five planets within a synodic periods.The movements of five planets within a synodic period of Venus in Supernal Epoch System is the same as that in Great Expansion System,and Mercury is the same as Veneration for Heaven System.Reverence for Heaven System first created the "Chuxinglv" in the movements of five planets within a synodic period,Matching Heaven System Jupiter,Mars movements of five planets within a synodic period is improved on the basis of Great Expansion System,the division is more fine,The "Chuxinglv" and the the movements within a synodic period watch of Reverence for Heaven System are often used by later astronomical system.3.The expansion and contraction difference is the key to calculating the apparent position of the planet.This paper interprets the structure of the four astronomical systems in the early Song Dynasty,and gives a new collation principle for the Yingsuoli of the four astronomical systems in combination with the previous work.Response to Heaven System,Supernal Epoch System and Matching Heaven System are all influenced by Reverence for the Arcana System.The design and structure of Reverence for Heaven System have their own style.Reverence for Heaven System is the standard template.4.Combining the original literature,discuss the five planets of the four astronomical systems in the early Song Dynasty,give the calculation ideas and calculation examples of the four astronomical systems,and discuss the inheritance and innovation relationship between the four astronomical systems.The movements of five planets within a synodic period accuracy and the Yingsuoli accuracy are the breakthrough points,and the specific reasons that affect the apparent position accuracy of the planet are analyzed.Studies have shown that planetary theory in the early Song Dynasty,Response to Heaven System and Supernal Epoch System did not make much progress.They were roughly borrowed from Great Expansion System,and Matching Heaven System compared the use of calendar system calculation terms.This method was adopted by Matching Heaven System,which paved the way for the maturity of ancient Chinese planetary theory.Reverence for Heaven System was the first to create a fixed-combination algorithm,which has been followed by later generations.5.Using python language to simulate the algorithm of the four astronomical systems and five stars in the early Song Dynasty,and discuss the calculation accuracy of the apparent positions of the planets in the early 30 years of the promulgation of the four astronomical systems in the early Song Dynasty.The research results show that the maximum absolute errors of the ecliptic longitudes of Mars,Jupiter,Saturn,Mercury and Venus in Response to Heaven System are: 7.635°,3.431°,2.765°,20.4954°,10.578°;The maximum absolute value errors of Jupiter,Saturn,Mercury and Venus are: 6.9825°,4.349°,3.2897°,19.3519°,9.08°;Mars,Jupiter,Saturn,Mercury and Venus have the largest ecliptic longitudes The absolute value errors in Matching Heaven System are: 6.2483°,3.485°,2.708°,17.99°,8.91°;the maximum absolute value errors of the ecliptic longitudes of Mars,Jupiter,Saturn,Mercury and Venus in Reverence for Heaven System are: 7.465°,4.572°,2.364°,15.877°,7.866°.