A Study of Planetary Theory in the Great Expansion System(Dayan li大衍历,727 CE):The Case of Mars

The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different planets had important astrological significance.Thus,planetary theory is an important part of Chinese mathematical astronomy.The Great Expansion System,which was compiled by Yixing一行of the Tang唐dynasty(618–907 CE),provided many innovations in planetary theory.Based on the extant Treatises on Mathematical Harmonics and Astronomy(Lüli zhi律历志)in Chinese official histories,the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet.It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet,which was the basis for calculating the true position of the planet.In addition,Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China.The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems.Mars is taken as a case study to investigate the planetary theory in the Great Expansion System,including the astronomical constants related to Mars,two important astronomical tables,namely the table of the equation of center and the table of the phase motion of Mars in one synodic period,and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center.Two questions are addressed.First,how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars?Second,how did Yixing calculate the true position of Mars on any given day?The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.