Chinese · System c. 1st century BCE – early 1st century CE; Hanshu compiled c. 58–111 CE

Santong li: the Five Steps

Hanshu 漢書 ch. 21 'Lü li zhi' 律曆志; Santong li 三統曆 planetary section, Wubu 五步

Liu Xin's Santong li system, preserved in the Hanshu, gives each of the five planets a 'Five Steps' entry: its synodic cycle as a sequence of phases with day counts and daily rates, including explicit stations (留) and retrograde phases (逆). Jupiter, for example, stations and turns after 25 days, retrogrades 1/7 degree a day for 84 days, then stations again for about 24 days. It is the earliest fully preserved Chinese numerical model of planetary stations and retrogradation.

Author: Liu Xin
Date: System c. 1st century BCE – early 1st century CE; Hanshu compiled c. 58–111 CE
Original language: Classical Chinese
Key term: 留 liu; 逆 ni; 旋 xuan (station (始留 'begins stationing', 復留 'stations again'); retrograde; 'turns', i.e. reverses)
Kind: Mathematical astronomy
Planets: Mercury, Venus, Mars, Jupiter, Saturn

On the shelf · Asia, Islam and medieval Europe · 11−1800 → 2026

−1800−1500−1000−5001500100015002026

Span · System c. 1st century BCE – early 1st century CE; Hanshu compiled c. 58–111 CESame shelfThis source’s span

Editions

2 editions.

Year	Edition	©
1962	Ban Gu, Hanshu, Zhonghua shuju edition (1962), juan 21.	?
1969	Sivin, Nathan. 'Cosmos and Computation in Early Chinese Mathematical Astronomy.' T'oung Pao 55 (1969): 1–73.	©

? unclear · © in copyright

Read it

No digitised copy known.

No digitised copy known. The editions above are the way in.

References

Hanshu 漢書, juan 21, Chinese Wikisource

Also on the Asia, Islam and medieval Europe shelf

Date	Source	Planets	Kind
c. 100–90 BCE	Shiji, Treatise on the Celestial OfficesSima QianAstrological	Ma Ju	Astrological
compiled c. 58–111 CE	Hanshu, Treatise on Celestial PatternsBan GuAstrological	Ve Ma	Astrological
499 CE	ĀryabhaṭīyaĀryabhaṭaMath. astronomy	Me Ve Ma Ju Sa	Math. astronomy
c. 6th century CE	Bṛhat Saṃhitā, ch. 6: the course of MarsVarāhamihiraAstrological	Ma	Astrological
c. 900 CE (observations 877–918)	al-Zīj al-Ṣābiʾal-BattānīMath. astronomy	Me Ve Ma Ju Sa	Math. astronomy
c. 1025–1028 CE	Doubts concerning PtolemyIbn al-HaythamTheory / model	General	Theory / model