Wuxing xingdu jie 五星行度解

Wuxing xingdu jie 五星行度解 "Explanation of the motions of the Five Planets" is a book on astronomy written during the Qing period 清 (1644-1911) by Wang Xichan 王錫闡 (1628-1682), who is also the author of the Xiao'an xinfa 曉庵新法.

This book of 1 juan examines models of the structure of the universe and the specific movements of the planets. The Chongzhen lishu 崇禎曆書 adopted Tycho Brahe's (1546-1601) system as its cosmological framework. However, as Brahe passed away before he could fully develop his theory of planetary motion, his system contains numerous inconsistencies and contradictions. Wang Xichan authored this book with the intention of refining and improving the theory of planetary motion within the Tychonic system.

Wang asserts that each planetary sphere is a physical entity, a notion that may have been influenced by the European theory of the twelve celestial spheres introduced by early Jesuit missionaries. In Western thought, the term celestial sphere refers to all heavenly bodies above moving in accordance with their respective orbits. In contrast, Wang's interpretation implies that while the five planets move along the periphery of their spheres, the Sun, which occupies the centre, does not itself move within them—an idea that is also incorrect.

Wang holds that among the five planets, Saturn, Jupiter, and Mars all rotate counterclockwise and are carried eastward by the Sun's sphere. Venus and Mercury, however, rotate clockwise within their respective spheres. Each follows its own motion while also moving one degree per day with the sun's sphere. However, since the spheres of Venus and Mercury are small and do not encompass the earth, their parallel motion aligns with that of the sun. This again differs from the Tychonic system.

Wang's book offers a detailed analysis of the three outer planets - Jupiter, Mars, and Saturn. Wang Xichan includes two diagrams to illustrate their orbital trajectories and movement patterns. He then examines the inner planets, Venus and Mercury, again supplementing his explanations with two diagrams for clarity. Following this, Wang discusses methods for determining the distances of the planets from earth. Finally, he presents a comprehensive assessment of all five planets, drawing four key conclusions regarding their motions. His theses are: when the centre of a planetary sphere moves within the sun's orbital path, the radius of this path decreases; when it moves outside, the radius increases. When the sun is at its highest position, the radius of its path is larger; when the sun is at its lowest, the radius is smaller. By using radius ratios, one can ascertain the distances of celestial spheres from earth and thus calculate the sizes of planetary bodies. The ecliptic circle represents the sun's celestial sphere, and the sun should reside at its centre. However, it is slightly displaced toward the Primum Mobile. The true centre of the sun's sphere is occupied by the earth.

Wang Xichan further asserts that the five planets should ideally reside at the centre of their respective celestial spheres, but instead, they are slightly displaced toward the periphery. Meanwhile, the sun occupies the centre of the planetary spheres. Additionally, the earth is not precisely at the centre of the sun's celestial sphere, nor is the sun exactly at the centre of the planetary spheres. Instead, both occupy the centre of their respective orbital paths, which move in cyclic motions (with the centre of the sun's sphere orbiting around the centre of the Earth's sphere), resulting in variations such as elongation and contraction in planetary distances.

At the end of the book, Wang provides numerical data for the daily motions of the five planets, with 95.21467429 minutes per day for Saturn, 90.25125719 minutes per day for Jupiter, 46.15757990 minutes per day for Mars, 61.65089339 minutes per day for Venus, and 3°10.66990430 per day for Mercury.

However, due to the extreme simplicity of his observational instruments - he did not have even a telescope - his measurements were significantly limited in accuracy. As a result, he was unable to establish a completely new or more refined cosmological model. While his book provides modifications and corrections to the Tychonic system and new formulas for calculating the apparent longitudes of the five planets, these innovations, though seemingly novel, remain fundamentally inaccurate because they were based purely on theoretical conjecture rather than empirical verification.

The text is included in the series Shoushange congshu 守山閣叢書 and Congshu jicheng chubian 叢書集成初編.