Wuxing jiyao 五星紀要

Wuxing jiyao 五星紀要 "Essential records on the Five Planets" is a brief book on astronomy written during the early Qing period by Mei Wending 梅文鼎 (1633-1721). It is included in the series Mei Hu'an Xiansheng lisuan quanshu 梅勿庵先生曆算全書.

The book is written in a question-and-answer format and consists of 21 chapters discussing the annual orbits of the Five Planets, the counterclockwise motion of the three outer planets around the Sun, a diagram of the Five Planets with the Sun in the centre (the heliocentric model), the Five Planets with the Earth the centre (the geocentric model), the epicycle differing from the annual orbit, the parallel motion of the Five Planets, direct and retrograde motion of angular separation, the two uses of parallel motion and the necessity of taking the true celestial degrees as the standard, the epicycles of Venus and Mercury, diagrams of the epicycle's cross lines and intersection angles, the cross lines of the epicycles, the nature of the epicycle, the calculation of the epicycles' intersection angles, the method for calculating the apparent latitude of Venus, the variation of the maximum latitude due to height and depth, the variation in the radius of the ecliptics, the variation in the epicycle radius and its effect on the actual latitude, the calculation of apparent latitude using two different height methods, the north-south directional changes in the forward and backward latitude of Venus, the technique of adding and subtracting the forward and backward latitude of Venus, and the variation of the latitude of the Five Planets due to height and depth.

The book presents a geocentric model of the universe, placing the Earth at the centre while considering the Sun, Moon, and the five major planets as orbiting around it. Each celestial body occupies its celestial sphere. Additionally, there is a celestial sphere for the fixed stars and an imagined "prime movement sphere" (zongdong tian 宗動天), making a total of nine celestial spheres beyond Earth, namely the prime movement sphere, the fixed-star sphere (hengxing bentian 恒星本天), and the spheres of Saturn, Jupiter, Mars (the "three upper planets", shang san xing 上三星), the Sun, Venus, Mercury (the "two lower planets", xia er xing 下二星), and the Moon (from outermost to innermost). The Five Planets follow their orbits around Earth, but they also have their rotational motion cycles, called "annual wheels" (suilun 歲輪). Although Mei Wending was familiar with Tycho Brahe's (1546-1601) works, Mei's interpretation of this planetary model did not align with Brahe's teachings. Mei held that if considering the degrees of motion of the planets on their annual wheels, they also formed a circular pattern with the Sun at the centre. This suggests that Mei Wending did not truly endorse a heliocentric model. Instead, he remained firmly within the Ptolemaic geocentric tradition, differing only in minor technical aspects.