A Study on the Calculation of the Longitude of the Starting Point of Planetary Yingsuo Li and its Precession Value in Ancient China

The Tang dynasty astronomer Yixing (一行) was the first to use planetary biancha (变差, change difference) to describe the procession of the starting point of planetary yingsuo li (盈缩历 the table of planetary expansion-contraction difference) relative to the winter solstice point every year in the Great Expansion System (Dayan li 大衍历). From then on, some systems followed the practice of the Great Expansion System and directly gave the value of the planetary biancha. For those systems that did not directly give this value, it can be calculated according to related algorithms in the systems. In this paper, we comprehensively examine the values of planetary biancha in the Great Expansion System and similar systems. For those systems that did not directly give the value of planetary biancha, we reconstruct the formula of the precession of the planetary starting point of planetary yingsuo li and summarize its rules. The discussion in this paper shows that the starting point of planetary yingsuo li is not planetary perihelion. However, since the error of the longitude of the starting point of planetary yingsuo li and the longitude of planetary perihelion is relatively small, thus for the outer planets, the starting point of planetary yingsuo li can be viewed as planetary perihelion. Accordingly, planetary biancha and the precession of the starting point of planetary yingsuo li is not the precession of planetary perihelion. Since there is no obvious rule to follow in the planetary biancha and the precession of starting point of planetary yingsuo li, it is speculated that the ancient Chinese astronomers may have mastered the ability to measure the planetary perihelion, and planetary biancha and the precession value of the starting point of planetary yingsuo li should be a value adjusted by the astronomers using the high epoch accumulated years (shangyuan jinian, 上元积年) after they determined the starting point of planetary yingsuo li.