The calculation of planetary motions constituted a major part of ancient Chinese mathematical astronomy. The “calendar”, which was essentially a mathematical astronomical system, and included methods for the calculation of the planetary motions. Mars, was the most difficult planet to predict its movements, hence its Chinese name yinghuo (literally: puzzling luminary). The first existent calendar, the Three Concordance System, gives detailed descriptions of syzygies of the five planets. For Mars the syzygy is divided into six phases: Direct motion immediately after appearance before dawn, First Station, Retrogradation, Second Station, Second Direct Motion, and Invisible Direct Motion. As time went on, later astronomical systems gave more and more sophisticated descriptions of the Martian motion. This paper will

investigate the descriptions about Martian motion in ancient Chinese mathematical astronomy from 1st century BC to 6th century AD, focusing on five calendars: the Three Concordance (Santong) Calendar (7 BC), the Quarter-Day (Sifen) Calendar (85 AD), the Happy Epoch (Yuanjia) Calendar (443 AD), the Great Brightness (Daming) Calendar (463 AD), and the Imperial Principle (Huangji) Calendar (604 AD). We will see improvements on the computation of Martian motion as the Chinese made progress in the understanding of the planetary motions. In particular, the unevenness of solar and planetary motions was taken into consideration in the Imperial Principle Calendar.

The Chinese approached the planetary calculation with numerical methods, which contrasts interestingly with the Greek geometrical methods.