Overview

Calendars are used to measure time for practical business purposes and to record historical events. They are also used to determine days of festivities or natural events (such as solar eclipses) and to prognosticate auspicious or inauspicious days. Across cultures, calendars are based on astronomical phenomena, including the movement of the Moon, the "movement" of the Sun, and the positions of planets and starry constellations. The traditional Chinese calendar is a combination of a solar calendar (based on the “position” of the Sun and the resultant seasonal phenomena) and a lunar calendar (following the lunar phases).

The "peasant calendar" (nongli 農曆), also known as the "old calendar" (jiuli 舊曆) or the "Chinese calendar" (Zhongli 中曆), is the traditional calendar used in China before the official adoption of the Western calendar in 1912. It remains widely used among the public, especially in Hong Kong, Taiwan, and Chinese overseas communities, primarily for traditional holidays and festivities and for determining auspicious days and hours.

The peasant calendar divides the year into 24 so-called Solar Terms (ershisi jieqi 二十四節氣), whose names indicate agricultural activities and natural phenology, such as Daxue 大雪 "Heavy snow", Shuangjiang 霜降 "Hoar frost descends", or Jingzhe 驚蟄 "Excited insects". This traditional calendar is allegedly in use since the Xia period 夏 (17th-15th cent. BCE), and therefore also called the "Xia calendar" (Xiali 夏曆).

The oldest records on the Chinese calendar are to be found in the text Xia xiaozheng 夏小正. Because the Moon is central to its calculation, it is also known as the "Yin, i.e. Moon or lunar, calendar" (yinli 陰曆). The months are strictly aligned with the new moon, and it is therefore necessary to insert an intercalary month (runyue 閏月) from time to time to reconcile the lunar and solar calendars. A year with an intercalary month is called runnian 閏年. The "peasant calendar" is thus, in fact, a lunisolar calendar (modern term yinyangli 陰陽曆), not a purely lunar calendar.

The first month is called zhēngyuè (!) 正月, but the other months are numbered, such as eryue 二月 "second month", sanyue 三月 "third month", and so on. Each month begins at midnight on the day when the lunar path (baijing 白經) and the solar path (huangjing 黃經) coincide. This day is called the "first day" (chuyi 初一). Days are counted as chu'er 初二 (the second day), chusan 初三 (the third day), and so on, but from the tenth day onwards, the syllable chu is dropped and the word ri "day" is added instead, such as shiri 十日 "the tenth", shiyiri 十一日 "the eleventh", etc. There are "long months" (dayue 大月) of 30 days, and "small or short months" (xiaoyue 小月) of 29 days, arranged over the year so that the average length of a month is 29.53059 days. This results in a lunar year of 354 to 355 days, requiring a leap of about 10 to 12 days relative to the solar year.

An intercalary month therefore has to be inserted alternately every two or three years, producing an average (called runzhou 閏周 "intercalary cycle") of seven intercalary months (called zhangrun 章閏"full set of intercalary months") over a period of 19 years (zhangsui 章歲 "full set of years"; in Western astronomy called the Metonic year). This is because 19 years are very close in length to 235 lunar months, as already observed in the Four-Parts Calendar (sifen li 四分曆) from 85 CE. The time of year at which an intercalary month is inserted depends on the 24 Solar Terms and the general conditions expected at that time. Unlike the Western calendar, where the intercalary day is always February 29th, the Chinese lunar calendars know intercalary months throughout the year (except for months during which the so-called "middle" zhongqi 中氣 Solar Terms occur: yushui 雨水, chunfen 春分, guyu 穀雨, xiaoman 小滿, xiazhi 夏至, dashu 大暑, chushu 處暑, qiufen 秋分, shuangjiang 霜降, xiaoxue 小雪, dongzhi 冬至, and dahan 大寒), for instance, the "intercalary (month after the) third month" (run sanyue 閏三月).

The ancient "intercalary cycle" method remained imperfect, and was therefore refined by Zhao Fei 趙{非+欠}, who lived in the small empire of Northern Liang 北涼 (398-439) during the Sixteen States period 十六國 (300~430). He defined the intercalary cycle as 221 intercalary months in 600 years. Zu Chongzhi 祖沖之 (429-500) of the Liu-Song period 劉宋 (420-479) used a relationship of 144 intercalary months in 391 years, which is more accurate than Zhao Fei’s method. Li Chunfeng's 李淳風 (602-670) Linde Calendar 麟德曆 from the Linde reign-period 麟德 (664-665) of the Tang era 唐 (618-907) was the last calendar in which the intercalary cycle had to be recalculated.

The beginning of the first month of the traditional peasant calendar starts at the winter solstice, when the day is shortest and the night longest (December 21 according to the Western Calendar). The New Year's Day (yuandan 元旦) of the traditional Chinese calendar was (and is) the day of the second new moon after the winter solstice. During the Xia period, the beginning of the year fell on the first day of the first month (zhengyue chuyi 正月初一); during the Shang period 商 (17th-11th cent. BCE), on the first day of the twelfth month of the Xia calendar; during the Zhou period 周 (11th cent.-221 BCE), on the first day of the eleventh month of the Xia calendar; and during the Qin 秦 (221-206 BCE) and the early Han 漢 (206 BCE-220 CE) periods, on the first day of the tenth month. As a result of the calendar reform (the introduction of the Taichu Calendar 太初曆) under Emperor Wu 漢武帝 (r. 141-87 BCE) of the Han dynasty, the beginning of the calendric year was shifted back to the first day of the first month of the Xia calendar, a practice that remains to this day.

Modules of the Chinese calendar

Chronology

Time is measured in several ways. In addition to the units familiar in the Western calendar (seasons, months, weeks and hours), the traditional Chinese calendar also uses several other concepts, namely the 24 Solar Terms (ershisi jieqi 二十四節氣), the sexagenarian cycle (ganzhi 干支; a combination of the ten signs or characters called Celestial Stems and the twelve signs known as Terrestrial Branches), and the Jupiter year.

Dynasties

In Western historiography, history is conventionally divided into the three ages of Antiquity (ca. 600 BCE–600 CE), the Middle Ages (ca. 600–1500), and the Modern Age. Marxist theoreticians divided history into the age of the slaveholding society (corresponding to Antiquity), the age of feudalism (ca. 600-1750), and the age of capitalism. This socio-economic approach is also important in the People's Republic of China, where Marxist theoreticians have had, and still have, difficulty applying this model to Chinese history. They see the end of the age of feudalism (fengjian shehui 封建社會) in the Xinhai Revolution 辛亥革命 of 1911 and the period of capitalism from 1912 to the "liberation" (jiefang 解放) of 1949. A similar tripartite timeline, such as the Antiquity – Middle Age – Modern Age model, which implies a kind of intellectual and scientific progress, does not exist in traditional Chinese historiography. Modern sinologists see the Chinese age of Antiquity (the "Golden Age" that served as a model for later times) as the period from 1200 BCE to ca. 300 CE, that of the Middle Ages (the "Dark Age" of equestrian warriors) from 300-900 CE, and the Modern Age (with a great progress in technology and fundamental changes in the social structure) as beginning with the Song dynasty, or alternatively, with the First Opium War (1839-1842).

Instead of a tripartite model of progress, Chinese history was traditionally divided into repetitive dynastic cycles, in which a ruling family or dynasty experienced a rise and victory over a predecessor (often due to military strength, but also moral superiority, and therefore being selected as "sons of Heaven", see Heaven), an apogee of cultural, economic and military (seen in territorial expansion) success, and a downfall due to corruption among the officialdom and depravity of the ruling house.

The concept of the dynastic cycle focuses on the political history of the dynasty itself and neglects factual changes in the power structure, the administrative system, society, the economy, and the material and intellectual culture. Chinese history, therefore, seems to be an everlasting "revolution" (in the astronomical sense) of the ups and downs of ruling families, some of which were able to unify the entire territory of China and others of which failed to do so, resulting in the division of China into several empires or states. Still today, biographies of persons begin with an indication of the dynasty under which he or she lived.

While the Egyptian dynasties are numbered, the Chinese dynasties are named. Most of these names derive from a territory over which a dynastic founder ruled before becoming emperor. The name of the Han dynasty 漢 (206 BCE-220 CE), for instance, derives from the name of a river in the region Hanzhong 漢中, over which Liu Bang 劉邦 (Han Gaozu 漢高祖, r. 206-195 BCE), the dynastic founder, was made king. Similarly, the Wei dynasty 魏 (220-265) takes its name from the kingdom of Wei, over which Cao Cao 曹操, the father of the dynasty's first emperor (Cao Pi 曹丕, i.e., Emperor Wen 魏文帝, r. 220-226), had ruled. The names of the dynasties (chao 朝, literally "the place to be faced", i.e., the court) are at the same time the names of their empires (guo 國). The Han dynasty (Han chao 漢朝) ruled over the Han empire, and the Tang dynasty 唐 (618-907) over the Tang empire. Throughout history, therefore, "China" was known by many different names, changing with the accession of a new dynasty. The Japanese even continued to refer to China as "Tang" (Tō) after the dynasty's downfall. The last three imperial dynasties adopted mottos as their names, namely Yuan 元 (1279-1368) "the (new) Origin", Ming 明 (1368-1644) "the Brilliant", and Qing 清 (1644-1911) "the Pure".

There are not a few cases in which new emperors chose a name for their dynasty that had already been used. To distinguish these dynasties and their empires, historians used suffixes (such as geographical terms, time words, or family names), such as the Southern Qi 南齊 (479-502) and the Northern Qi 北齊 (550-577), the Liu-Song 劉宋 (420-479) and the (Great) Song 宋 (960-1279), the Cao-Wei 曹魏 and the Later 後魏 or Northern Wei 北魏 (386-534). These suffixes are also used to distinguish distinctive phases in a dynasty's life cycle, such as Western Zhou 西周 (11th cent.-770 BCE) and Eastern Zhou 東周 (770-221 BCE), Western 西漢 or Former Han 前漢 (206 BCE-8 CE) and Eastern 東漢 or Later Han 後漢 (25-220 CE), Western 西晉 (265-316) and Eastern Jin 東晉 (317-420), Northern Song 北宋 (960-1126) and Southern Song 南宋 (1127-1279). In all these cases, the dynasty had been forced to relocate its capital as a consequence of a drastic political event (an invasion by "barbarians" or the refounding of the dynasty following internal turmoil).

Unlike in Europe, where dynasties are named after ruling families (Tudor, Bourbon, Hapsburg), the name of the dynasty is not identical to the family name of the ruling house (the family Liu 劉 constituted the Han dynasty, the family Li 李 the Tang, and the rulers of the Song dynasty had the family name Zhao 趙). The only exception is the short-lived Chen dynasty 陳 (557-589), whose founder had the family name Chen, but the name of the dynasty was chosen because its founder, Chen Baxian 陳霸先 (Emperor Wu 陳武帝, r. 557-559), had been king of Chen before adopting the title of emperor. The names of the dynasties are also used to designate the time during which they ruled. The Han ruled during the Han period (Han dai 漢代), and the Qing during the Qing period (Qing dai 清代).

This method is problematic during periods when several dynasties shared "China" among themselves. During the Three Empires period 三國 (220-280), for instance, the three dynasties Wei, Shu 蜀 (221-263) and Wu 吳 (222-280) ruled simultaneously over different parts of "China". It is therefore not appropriate to speak of the Wu period or the Shu period. Historians disputed which of the three dynasties was the rightful successor to the Han, and ultimately chose the Wei dynasty. The Three Empires period can, therefore, be identified with the Wei period, but the Wei dynasty ended before the last of the Three Empires, Wu, was conquered by the Wei's successor, the Jin dynasty. Similar instances of parallel ruling houses include the Southern and Northern dynasties period 南北朝 (300~600, with a group of dynasties following each other in the south, and several realms in the north that ruled over different parts of northern China), the Five Dynasties period 五代 (907-960, with five dynasties ruling consecutively over the north and the Ten States 十國 (902~979) ruling over various parts of southern China), and the Song period. The Song period is actually an exception from the former cases because the Song ruled only over central and southern China, while the north was occupied by the Liao empire 遼 (907-1125), and then the Jin empire 金 (1115-1234), and the northwest by the Western Xia empire 西夏 (1038-1227). There is no overarching term for this period of time, such as "Southern and Northern Dynasties".

Reign-Periods

Because there is no fixed year in Chinese history to which the calendar is tied (such as the birth year of Jesus Christ, Mohammed's escape from Medinah, or the "creation of the world"), the actual ordinal year of an emperor's reign (the reign-period or era) or that of his reign mottos (nianhao 年號) was used to indicate a year. Before and in the first decades of the Han period 漢 (206 BCE-220 CE), there were still no reign mottos. Years were therefore indicated by the length of a ruler's reign, such as Jingwang shisan nian 敬王十三年 "thirteenth year of King Jing's (the king of Zhou, r. 520-476 BCE) reign" or Wendi san nian 文帝三年 "third year of Emperor Wen's 漢文帝 (r. 180-157 BCE) reign".

It is important to note that the first year of a reign or reign-period was not the year in which the emperor acceded to the throne, but the next, after the first New Year had passed. This was an expression of filial piety towards the late king or emperor. King Jing of the Zhou dynasty, for instance, acceded to the throne in 520 BCE, but his first year of reign (Jingwang yuannian 敬王元年) was 519 BCE. The first year of a reign or reign-period (the period under a certain motto) is called yuannian 元年, while the others are regularly counted (ernian 二年, sannian 三年 etc.).

The first introduction of a new reign era was inaugurated in 163 BCE under Emperor Wen, who declared this year as Houyuan yuannian 後元元年 "First year of the later Origin", a kind of "new or second start". His successor, Emperor Jing 漢景帝 (r. 157-141 BCE), inaugurated two new reigns, Zhongyuan 中元 "Middle Origin" (this name might have been given retrospectively) in 149 BCE, and Houyuan 後元 "Later Origin" in 143 BCE. His son, Emperor Wu 漢武帝 (r. 141-87 BCE), was the first to choose a motto for the first full year of his reign, namely Jianyuan 建元 "Establishment of a (new) origin", in 140 BCE. Six years later, he changed the reign motto to Yuanguang 元光 "Brilliance of the origin", which lasted for another six years. Emperor Wu's reign mottos were also the first to have a meaningful slogan. During his whole reign from 141 to 87 BCE, he used eleven reign mottos. From then on, all emperors used reign mottos, and even usurpers or counter-emperors proclaimed a reign under new auspices. Liu Yu 劉豫 (1073-1146), the illegal Emperor of Qi 齊, for instance, chose the motto Fuchang 阜昌 "Brilliance of Qufu 曲阜" (1130-1137; Qufu was the home town of Confucius that was located in Liu Yu's small empire), and the usurper Li Zicheng 李自成 (1606-1645), who proclaimed himself Emperor of Dashun 大順 (r. 1644-1645), chose the motto Yongchang 永昌 "Everlasting brightness" (1644-1645). President Yuan Shikai 袁世凱 (1859-1916) declared himself emperor on January 1, 1916 (he was forced to resign on April 24) and chose the reign motto Hongxian 洪憲 "All-Embracing Constitution".

Most reign mottos are two syllables or words long, but during the Song period 宋 (960-1279), some four-syllable mottos were chosen, such as Taiping xingguo 太平興國 "Flourishing of the State under the Great Peace" (976-983), Dazhong xiangfu 大中祥符 "Auspicious Omen of the Great Centre" (1008-1016) or Jianzhong jingguo 建中靖國 "Pacified State Established in the Middle" (1101). Some mottos were fashionable at certain times, such as those with the words chun 淳 "pure" and you 祐 "heavenly assistance", which were almost exclusively used by the Song dynasty.

To make identification by a reign motto easier, the mottos were rarely used more than once throughout Chinese history. There are, however, some exceptions, like the motto Yong'an 永安 "Everlasting Peace", which was used by the Wu dynasty 吳 (258-263), the Jin dynasty 晉 (304), the statelet of Northern Liang 北涼 (401-411), the Northern Wei dynasty 北魏 (528-529) and the Western Xia 西夏 (1098-1100).

There are two basic problems with this method. The first is that, if a ruler was not recognised as the legal sovereign, or during periods of political division, several mottos (and therefore different calendars with different years) were used simultaneously. During the Eastern Zhou period 東周 (770-221 BCE), not only did the legitimate king of Zhou rule by his own calendar, but each regional ruler also counted the length of his own rule as an instrument of measuring years. This makes it very difficult to identify a year during that period and easily leads to errors. One example might highlight this complexity.

The Western year 477 BCE was the ...

Similar, though less extreme, cases occurred during the Three Empires period 三國 (220-280), the Southern and Northern Dynasties 南北朝 (300~600), the Five Dynasties period 五代 (907-960), and the Song 宋 (960-1279), Liao 遼 (907-1125) and Jin 金 (1115-1234) dynasties.

Most emperors before the Ming period 明 (1368-1644) changed their reign mottos several times during their reigns, and the year count began anew. The change of a reign motto is indicated by the word gaiyuan 改元 "change to a new first year". Such a change could occur during the course of a year and was sometimes carried out midway through a year, not necessarily at the beginning of a new calendar year. Empress Wu Zetian 武則天 (r. 684-690) was most notorious for this practice because reign mottos, expressing a style of rule or an auspicious omen supporting the reign, played an important role in her legitimisation. Yet other rulers, too, engaged in this practice. On the day eryue yimao 二月乙未 ([30th day of the] second month, with the cyclical signs yi and mao) of the sixth year of the Xianqing reign-period 顯慶 (i.e., April 4, 661 CE), Emperor Gaozong 唐高宗 (r. 649-683) of the Tang dynasty changed the reign motto to Longshuo 龍朔, and the first year of this reign began on sanyue bingshen 三月丙申 ([1st day of the] third month, with the cyclical signs bing and shen), with the new moon. During his more than thirty-year-long reign, he changed his motto no less than fourteen times, and Empress Wu Zetian, who was the de facto emperor for slightly less than five years, proclaimed four reign mottos, on average, one for each year. The opposite paradigm was Emperor Xuanzong 唐玄宗 (r. 711-755), who ruled even longer, but proclaimed only three reign mottos, of which the longest, Kaiyuan 開元 (713-741), lasted for 29 years.

From the Ming period onwards, there were very few occasions on which the an emperor changed his reign motto. Emperor Yingzong 明英宗 (r. 1435-1449) of the Ming chose a new motto when he returned to the throne in 1456; and Huang Taiji, the khan of the Jurchens, who had two mottos, the second of which was chosen in 1636 when he renamed his dynasty from (Later) Jin 後金 to Qing 清 (1644-1911). During the Ming and Qing periods, each emperor had, in practice, only one reign motto. For this reason, the emperors of these two dynasties are usually not called by their posthumous title (like Wendi 文帝 or Wudi 武帝) or their temple name (like Taizong 太宗 or Taizu 太祖), but by their reign motto (e.g., the Wanli Emperor 萬曆帝 or the Guangxu Emperor 光緒帝). Among these, the Jiajing Emperor 嘉靖帝 (r. 1521-1566) ruled for 45 years, the Wanli Emperor for 48 years, the Kangxi Emperor 康熙帝 (r. 1661-1722) for 61 years, and the Qianlong Emperor 乾隆帝 (r. 1735-1796) for 60 years. In Western literature, era names are often misapplied to emperors, such as "Emperor Kangxi". Reign-periods are sometimes abbreviated and joined to expressions signifying two or three reign-periods, like Kang-Yong-Qian 康雍乾 for the reign-periods Kangxi, Yongzheng 雍正 (1723-1735), and Qianlong, or Dao-Xian 道咸 for the decades of the reign-periods Daoguang 道光 (1821-1850) and Xianfeng 咸豐 (1851-1861).

A particular problem with chronology is that a sovereign’s first reign motto was chosen only for the new year after accession to the throne, as an expression of piety towards the predecessor. This means that Kaiyuan yuannian 開元元年 (year 713 CE) was the first year with the reign motto Kaiyuan "Opening the Origin", but it was already the second calendric year in which Emperor Xuanzong 唐玄宗 (r. 712-755) of the Tang ruled. For the Qing period, this means that the Kangxi reign-period lasted from 18 Feb 1662 to 4 Feb 1723, but the Kangxi Emperor ruled from 5 Feb 1661 to 20 Dec 1722.

To make things even more complex, the Chinese New Year begins according to the lunar calendar, which is somewhat later than the Western calendar. The four- to eight-week difference at the start of the year must be accounted for when converting traditional Chinese years to Western years. It is therefore not quite correct to say that the year Yongzheng yimao 雍正乙卯 was 1735 (the 13th year of the Yongzheng reign-period, with the cyclical signs yi and mao). The year yimao (and the 13th year with the reign motto Yongzheng) ran from 24 Jan 1735 to 11 Feb 1736, while the Yongzheng Emperor had already died on 8 Oct 1735, and his son took over official functions on October 16, the first day of the ninth lunar month. For convenience, the small overlap between the Western and Chinese calendars is often neglected when indicating years only, even though this can lead to date errors.

The practice of counting years by reign mottos was also used in Vietnam and is still in use in Japan (the only East Asian country where an emperor still rules). The reign motto of the retired Japanese emperor Akihito 明仁 (r. 1989-2019) was Heisei 平成 "Outbalanced Completion", and Bảo Đại 保大 "Protection of Grandness" (1926-1945) was the reign motto of the last emperor of Vietnam (while his personal name was Nguyễn Phúc Thiển 阮福晪). The Manchu rulers of the Qing dynasty had their reign mottos proclaimed in three languages - Chinese, Manchu, and Mongolian, with roughly corresponding meanings, such as the Chinese motto Kangxi 康熙 "Peaceful relaxation", while the Manchu counterpart was Elhe taifin and the Mongolian one Engke amuɣulang.

After the foundation of the Republic in late 1911, policymakers decided to designate 1912 as the First Year of the Republic (Minguo yuannian 民國元年). With this decision, the traditional Chinese method of counting years was retained, while the official luni-solar calendar was replaced by the Western calendar, at least in public. The Republican government in Taiwan has retained the "reign-motto" system for counting the age of the Republic.

Chinese coins are inscribed with reign mottos, rather than showing idealised portraits of rulers, as in the West. A common inscription on a widely circulated coin, for instance, was Kaiyuan tongbao 開元通寶 "Circulating wealth from the Kaiyuan reign-period (713-741)". As the Qing rulers only had one single reign motto, Qing-period coin inscriptions directly refer to the ruler, such as Daoguang tongbao 道光通寶 to the Daoguang reign-period (1821-1850).

Years and the ganzhi 干支 cycle

In the Chinese calendar, the start of each period is tied to the new moon (shuo 朔). Each month in the lunar calendar thus begins with a new moon (black and invisible), just as the year begins when Yin (inactive, hidden, dark) prevails in nature. The problem for ancient astronomers was that the Moon's velocity along its path around the Earth is not constant (like all celestial bodies, the Moon follows an elliptical path on which it moves faster in parts of its orbit closer to the Earth), and therefore the length of time between one new moon and the next is not exactly the same. A long-term average of this length is called the "lunar month" (shuowangyue 朔望月) or "levelled month" (pingshuo 平朔), and the calculation method is called "fixing (the date of the) new moon" (dingshuo 定朔).

Each year bears a designation comprising two cyclical signs, namely the 10 Celestial Stems (shi tiangan 十天干) of the Ten-Years Cycle and the 12 Terrestrial Branches (shi'er dizhi 十二地支), which together form a cycle of 60 (ganzhi 干支 cycle; only the first half of all possible combinations is used). In popular belief, each year represents one of twelve animals, and the character of that animal is ascribed to all persons born in that year. This "zodiac" (which has nothing to do with starry constellations like in the West) is connected to the twelve Terrestrial Branches, which are always in the second position of the cyclical combination. This means that all years with the cyclical combinations jiazi 甲子, bingzi 丙子, wuzi 戊子, gengzi 庚子, and renzi 壬子 are "years of the rat". There are many online tools that indicate which year corresponds to which animal. In translations, the animal cycle is usually preferred over the ganzhi combination because it is easier for Westerners to comprehend than a detailed explanation of the clumsy combination of the two Stems and Branches cycles.

The Ten Stems are also commonly used to count, for instance, chapters or volumes of a book, or items in a list (up to ten). During the Xia 夏 (17th - 15th cent. BCE) and the Shang periods, the temple names of kings included a number of the Ten Stems, such as Tai Kang 太康 (or Tai Geng 太庚) and Kong Jia 孔甲 of the Xia and, in a much more regular way, Shang Jia 上甲, Bao Yi 報乙, Bao Ding 報丁 and Bao Bing 報丙 of the Shang. The rules of this pattern remain insufficiently explained.

When combined with a reign motto, years are often indicated by the cyclical combination (a method called ganzhi jinian fa 干支紀年法), such as Daoguang renchen 道光壬辰 "the year with the cyclical combination renchen 壬辰 during the Daoguang reign-period (1821-1850)", i.e., 1832, or dingchou nian 丁丑年 or dingchou sui 丁丑歲 "during the year with the cyclical combination dingchou". The latter example can be determined only exactly if the statement's historical context is known, because cyclical combinations repeat every sixty years. The year dingchou might refer to 1877, 1937 or 1997, etc. The cyclical designations are also used for important historical events, such as the Reform Movement of 1898 (wuxu bianfa 戊戌變法 "constitutional change during the wuxu year") or the Revolution of 1911 (xinhai geming 辛亥革命 "Revolution of the xinhai year").

Aside from the animal-based cyclical combinations, Chinese literature employs several alternative designations for years that are partly astronomical, partly colloquial, and partly poetic. The astronomical designations for the twelve Terrestrial Branches are derived from the names of the stations of the planet Jupiter (suixing 歲星) in its twelve-year cycle around the Sun. For each year of the Jupiter cycle, there are designations that probably originate in Indian astronomy. According to this method (called suixing jinian fa 歲星紀年法), the year with the cyclical combination jiayin 甲寅, for instance, is called efeng shetige 閼逢攝提格.

Historically, three points in time marked the start of the calendrical year, known as san zheng 三正 "three first-months". These were the New Year of the Xia Calendar (Xiazheng 夏正), that of the Yin or Shang Calendar (Yinzheng 殷正), and that of the Zhou Calendar (Zhouzheng 周正). The beginnings of the year were defined as the time when the star Antares (dahuoxing 大火星, modern name Xinxiu er 心宿二) was visible at dawn. During the Xia period, this was the beginning of the third astronomical month (yin 寅); during the Shang period, the fourth; and during the Zhou period, the fifth month. The first month of the Xia calendar therefore corresponded to the twelfth month of the Yin/Shang calendar and to the eleventh month of the Zhou calendar. The successive changes in the beginning of the year under these three dynasties were called the "Three Connected (calendars)" (santong li 三統曆). The historians Wang Tao 王韜 (1828-1897), Zhu Wenxin 朱文鑫 (1883-1939) and Shinzō Shinjō 新城新藏 (1873-1938) found that the theory of these three changes was developed only during the Spring and Autumn or the Warring States period, and that the use of these three calendars cannot be proved by historical evidence. Qian Caocong 錢寶琮 (1892-1974) believed that these were regional calendars used by the peoples of the Xia, Shang, and Zhou, rather than official calendars of the three successive dynasties.

Months

Months in the calendar are normally numbered, except for the first month of the year, which is called zhēngyuè (!) 正月. The other months are given regular numbers, such as eryue 二月 "second month", sanyue 三月 "third month", and so son. Intercalary months (runyue 閏月) occur in nine out of a cycle of seventeen years. They bridge the gap between the lunar calendar and the solar calendar, which advances over time.

The Chinese lunar calendar includes intercalary months throughout the year, except in months that contain so-called zhongqi 中氣 Solar Terms occur: yushui 雨水, chunfen 春分, guyu 穀雨, xiaoman 小滿, xiazhi 夏至, dashu 大暑, chushu 處暑, qiufen 秋分, shuangjiang 霜降, xiaoxue 小雪, dongzhi 冬至, and dahan 大寒. The names of the intercalary months depend on the preceding month; for instance, the "intercalary (month after the) third month" (run sanyue 閏三月). The sequence of the months is therefore sanyue 三月, run sanyue 閏三月, siyue 四月. There are short months with 29 days and long months with 30 days.

It is important to note that the months of the luni-solar calendar (whose year begins between late January and late February) do not align with the astronomical months, whose cycle begins in December. The names of these months follow the cycle of the twelve Terrestrial Branches. Furthermore, there are colloquial and poetic names for each of the twelve months (see dizhi 地支).

According to the beliefs of correlative thinking, each month is associated with a cardinal direction, a type of wind, a musical pitch-pipe, and one of 28 starry constellations (ershiba xiu [!] 二十八宿), with which the planet Jupiter culminates over the course of the year.

All three calendrical months of one season are given designations that are also used in the field of family relationships, namely mengchun 孟春 "oldest month of spring", zhongchun 仲春 "middle month of spring", and jichun 季春 "smallest month of spring", and so on.

Early texts, such as the Xia xiaozheng 夏小正 "Small calendar of the Xia" (today a chapter of the semi-Classic Da Dai Liji 大戴禮記) or Yueling 月令 "Proceedings of Government in the different months" (today a chapter of the Classic Liji 禮記), describe astronomical phenomena, the phenology of nature, and the farmers' work each month of the year. In the first month, for example, the star Ju 鞠 appears. At the beginning of dusk, the constellation Shen 參 culminates. The tail of the Northern Dipper points downwards. At that time, a favourable wind blows. Thunder is necessary in the first month. The husbandman goes out as soon as the snow begins to melt. The frost fades, and people remove the remaining dirt. The hibernating animals wake up; the wild goose appears in the northern villages; the pheasant cries excitedly; the fish appear and break the ice; in the gardens, leeks sprout; the voles come out; the otters offer fish; and the eagles behave like turtledoves. The willows push, the plums, apricots and peaches begin to flower, nodules cover the herb gao 縞, and the chicks breed and feed (transl. according to Grynpas). In the last month of spring, the Sun is in the constellation Wei 胃, the constellation culminating at dusk being Qixing 七星, and that culminating at dawn Qianniu 牽牛. Rainbows begin to appear. This month, the influences of life and growth are fully developed, and the warm, genial airs diffuse themselves. The rains of the season will be falling, and the waters beneath will be swelling. The Elaeococca begins to flower. Moles are transformed into quails. Duckweed begins to grow. The crooked shoots are all put forth, and the buds are unfolded (transl. Legge).

The important ancient history book Chunqiu 春秋 "Spring and Autumn Annals", is so named because its entries list the seasons, months, and days. This method was so impressive that it gave its name to an entire age, the Spring and Autumn period 春秋 (770-5th cent. BCE).

Because the months of the traditional Chinese lunisolar calendar do not align with Western months, one should pay close attention when translating traditional Chinese dates. The month Xianfeng san nian liu yue 咸豐三年六月 is NOT (!) June 1853, but spands from 6 Jul to 4 Aug. A correct translation would thus be: "sixth month of the third year of the Xianfeng reign-period".

Weeks and Days

In the modern calendar, months are divided into three ten-day weeks (xun 旬). The first week is called shangxun 上旬, the second or middle zhongxun 中旬, and the last xiaxun 下旬. Traditionally, however, these weeks were not directly tied to the lunar months but were sub-units of the sexagenary cycle of 60 days, with six weeks constituting one cycle. The days of the weeks were therefore counted using the ten Celestial Stems (jia 甲, yi 乙, bing 丙, ... gui 癸). The weeks run through the year, independently of the beginning of months and the solar year. Unlike Western calendric weeks, which are not tied to the beginning of a year, they overlap the boundaries of months and the beginning of a new year. For example, the traditional Chinese year in 2009 began on 26 Jan on the day with the cyclical combination xinwei 辛未; the year 2010 began on 14 Feb with the combination yiwei 乙未; and 2011 on 3 Feb with the combination jichou 己丑.

The term xun 旬 is also used to denote a decade of life, for instance, qi xun 七旬 "seven decades (of life)".

The Western seven-day week was introduced in China in 1912, although it was known there long before under the name qiyao 七曜 "seven illuminators". This concept reached China during the Tang period 唐 (618-907) through Buddhist transmission. The Chinese names for the days of the seven-day week changed over time. The earliest reference to the qiyao days appears in Fan Ning's 范甯 (c. 339-401) commentary on the Classic Guliangzhuan 穀梁傳. The oldest detailed description of the idea behind the seven-day week and of their names in foreign languages, is found in the Buddhist calendric treatise Xiuyao lijing 宿曜曆經 (Tripitaka no. 1299, full title Wenshushili Pusa ji zhuxian suo shuo jixiong shiri shan'e xiuyao jing 文殊師利菩薩及諸仙所說吉凶時日善惡宿曜經, translated from Sanskrit by the monk Bukong 不空 [Amoghavajra], 705-774).

Each day was associated with one "star" or its deity, similar to the Western week (Wednesday as the day of Wotan, or Italian martedì as the day of God Mars). These were the Sun, the Moon, and the five visible planets: Mars, Mercury, Jupiter, Venus, and Saturn. In Chinese translation, the names of the five planets were replaced by the five "elements" associated with them (see Five Agents), namely Fire for Mars, Water for Mercury, Wood for Jupiter, Metal for Venus, and Earth for Saturn, so Sunday was riyaori 日曜日 "Sun-day", Monday yueyaori 月曜日 "Moon-day", Tuesday huoyaori 火曜日 "fire-day", etc. This system is still in use in Japan and Korea (nichiyōbi, getsuyōbi, kayōbi, etc. in Japanese, and ilyoil, wolyoil, hwayoil, etc. in Korean). In more recent times (early 20th century), the term yaori 曜日 became obsolete and was replaced by a system centred on Sunday, the day of the Lord, while the other days were counted by numbers. There are two terms for "day" in this system, namely xingqi 星期 (an ancient name for the qixi festival 七夕 on the 7th day of the 7th lunar month) and libai 禮拜 "ritual prayer". The latter term clearly shows Christian influence. Sunday is xingqi tian 星期天 or libai tian 禮拜天 (in the People's Republic rather qingqi ri 星期日), Monday xingqi yi 星期一 or libai yi 禮拜一, etc. A rarely seen system of counting days calls Sunday zhuri 主日 "Day of the Lord", Monday zhanli er 瞻禮二 "Ritual observation two" (because, according to Catholic day counting, Sunday is the first day of the week), etc. It is also used in Vietnam, where Monday is called chủ nhật 主日, Monday ngày thứ hai "day number two" (Vietnamese words), etc. This system leads to some confusion because Saturday is called zhanli qi 瞻禮七 "Ritual observation seven" (as the last day of the week), while the secular system calls it xingqi liu 星期六 "star-period six" and the Protestant system libai liu 禮拜六 "Ritual prayer six".

In some printed calendars, the term zhou 週 "cycle" is used to mean "week", and the days are called: zhouri 週日 (Sunday), zhouyi 週一 (Monday), etc.

An example of a traditional date looks either like Xuantong san nian ba yue shijiu ri 宣統三年八月十九日 "Nineteenth day of the eighth lunar month of the third year of the Xuantong reign-period" (i.e., 10 Oct 1911), or bayue guichou 八月癸丑 "eight month, day with the cyclical combination guichou".

Hours

The traditional Chinese day was divided into twelve hours ("double-hours" from the Western perspective, in Chinese shi 時 or shichen 時辰). These hours do not begin at midnight; midnight falls exactly in the middle of the midnight hour, the "hour of the rat". The popular names of the twelve hours are those of twelve animals that are also used for the twelve-year cycle. In more scholarly terms, the hours are named after the twelve Terrestrial Branches. The expression mao shi 卯時 means the time between 5 and 7 AM, or "the hour of the rabbit". The word mao also means "early morning", as in the expression dianmao 點卯 "morning muster of officials". The animal designations are preferred by Westerners when referring to Chinese time, but are rarely used in Chinese. Two of the Terrestrial Branches are still known in modern time designations, namely zi 子 in ziye 子夜 "midnight", and wu 午 in the terms shangwu 上午 "before noon", zhongwu 中午 "high noon", xiawu 下午 "afternoon" and wufan 午飯 "lunch", etc. Quite famous is also the exterior gate of the imperial palace, the Wumen 午門, which was located to the south (the symbolic direction of midday).

In ancient times, the hours were announced publicly from the drum tower (gulou 鼓樓) in each larger city. Bell towers (zhonglou 鐘樓) served to announce the morning, as well as the death of an emperor or a hostile attack.

The Twenty-Four Solar Terms (jieqi 節氣)

The 24 Solar Terms (ershisi jieqi 二十四節氣) are periods during which certain phenological events occur, particularly the arrival of seasons, the growth and withering of plants, peaks in temperature and precipitation, and cycles in the life of insects and other animals. The term jieqi literally means "nodes of energy" and refers to the growing and declining energy (qi 氣) of Yin and Yang throughout the year. The year begins at the point where Yin (the less energetic) prevails and Yang (the more energetic) just begins to rise again. This point can be either around the winter solstice (dongzhi 冬至 "winter has arrived") or when spring visibly begins. Because of this ambiguous definition, the beginning of the year was not always defined in the same way in earlier times. Some authors translate jieqi as "mini-seasons", each lasting two weeks. They are related to the solar year because it is the Sun that influences the "energy" on Earth, not the Moon, whose appearance and movement determine the calendar.

There are two different types of jieqi, namely the twelve proper jieqi, and the twelve zhongqi 中氣 "middle energies". They alternate with each other. These designations might have originated during the Warring States period 戰國 (5th cent.-221 BCE) and are first mentioned in full in the chapter Tianwen xun 天文訓 "On the patterns of Heaven" of the book Huainanzi 淮南子.

The Solar Terms were originally examined with the help of a gnomon (guibiao 圭表), whose shadow determined the hour of the day (by the position of the shadow in the segment of a circle), but also, by the changing length of the shadow over the months, the process of the year. This is easiest at those points of time when the shadow is shortest (xiazhi 夏至 "summer has arrived") and longest (dongzhi 冬至 "winter has arrived"). The time between those occurrences was divided into twelve parts, with eleven additional points of time that marked the start of "mini-season". Each of these twelve segments was passed two times a year. The beginning point of the season dongzhi was seen as the beginning of the solar year (the point when the Yang energy was lowest), and the point xiazhi (the Yang energy being strongest) as the midpoint of it. During the Solar Terms chunfen 春分 and qiufen 秋分, the vernal and autumnal equinoxes occur. The term qingming 清明 is also known as the time of the Qingming Festival or Tomb-Sweeping Festival (qingmingjie 清明節). It might be well to recall the fact that the Solar Terms are part of the lunar year and therefore begin with the Chinese New Year.

This gnomon method is called "balancing the energy (terms)" (pingqi 平氣). Each of the twelve months of the year includes one jieqi point and one zhongqi point (marking the beginning of a term), for instance, the solar term lichun 立春 as the jieqi and the term yushui 雨水 as the zhongqi. In some cases, a month may include only one of the Solar Terms because the Solar Terms follow the solar year, while the months in the shorter lunar year may include only one. With the introduction of the Taichu Calendar 太初曆 during the mid-Former Han period 前漢 (206 BCE-8 CE), the rule was established that a jieqi term might occur in the second half of a month and the first half of the following, and a zhongqi term only within the time limits of one month. Should there, in any case, be a month without a zhongqi term, that month was then made an intercalary month of the preceding month.

A reform of this method was carried out during the Sui period 隋 (581-618). The astronomer Zhang Zixin 張子信 (mid-6th century) realised that the "velocity of the Sun" varied throughout the year (because the Earth moves on a slightly elliptical orbit and is faster when it is closer to the Sun). In 604, therefore, Liu Chuo 劉焯 (544-610) created the Huangji Calendar 皇極曆, in which the Sun’s course along the "Yellow Path" (the ecliptic of the Sun) is divided into 24 segments of equal size. Each solar term begins when the Sun enters the particular segment. This new method was called "fixation of energy (terms)" (dingqi 定氣). Both methods continued to be used, the old one for the calendar in daily use, the new one for scholarly calculation. Only during the Qing period 清 (1644-1911) was the old pingqi method finally abolished.

The Jupiter Cycle

In ancient times, astronomers observed that the planet Jupiter (modern name muxing 木星) appeared to "revolve" around the Earth over a period (the sidereal period) of roughly twelve years. It was therefore called the "year-star" (suixing 歲星) and used to fix the calendar. Jupiter's path around the Earth was divided into twelve segments or "paces" (shi'er ci 十二次), making it possible to name an individual year according to Jupiter's position against the starry sky. Ancient histories of the Spring and Autumn period, for instance, record the year when "the Year-Star was in Leo" (sui zai chunhuo 歲在鶉火). With the help of such statements, historical events can be dated more precisely. In the history book Guoyu 國語, the astronomer Ling Zhou Jiu 伶州鳩 (6th cent.) says that the conquest of the Shang by King Wu of Zhou occurred in the Jupiter year Dunhuo 鶉火 (1057 BCE). The Jupiter positions are also called the "twelve regions" (shi'er fenye 十二分野). These celestial regions are identified with regions of China (fenye 分野).

Except for the twelve segments of the Jupiter years, Chinese astronomers divided the celestial globe into twelve "double-hour" segments, each named after one of the twelve Terrestrial Branches. The direction of the sequence was opposite to that of the Jupiter segments that follow the direction from west to east. It was believed that there was a Counter-Jupiter, or "Grand Jupiter" (taisui 太歲), an imaginary celestial body whose movements were used to count the double-hours. Similar to Jupiter, the Counter-Jupiter revolved once around the Earth every twelve years, but in the opposite direction, yet in a fixed relation to Jupiter, so that the position of the imaginary Counter-Jupiter can always be known once that of the real planet is analysed.

The twelve stations of the Jupiter were probably derived from the four symbols of the cardinal directions (sigong 四宮 "four palaces" or sixiang 四象 "four appearances", i.e., the Black Turtle 玄武 for the North, the White Tiger 白虎 for the West, the Vermillion Bird 朱雀 for the South and the Green Dragon 青龍 for the East) that are each divided into three sub-regions. Unfortunately this geometrical division is not congruent with the areas of the ascension of the Jupiter. In the chapter on music and astronomy (Lüli zhi 律曆志) in the official dynastic history Hanshu 漢書, the twelve stations of the Jupiter correspond with the twenty-four Solar Terms, the jieqi marking the beginning of the station, and the zhongqi term being located within the time-frame of the Jupiter station.

From the late Ming period 明 (1368-1644) onwards, under the influence of European astronomy introduced to China by the Jesuits, the designations of the twelve Jupiter stations were also used to refer to the twelve zodiacal signs (shi'er gong 十二宮) of the solar ecliptic, yet the corresponding areas are not exactly congruent. Capricornus (mojie gong 魔羯宮), for instance, corresponds to the Xingji area (xingji gong 星紀宮), but the beginning (entering point) of this area is identical to the dongzhi 冬至 solar term.

The "Jupiter year" is in fact only 11.86 solar years long, and therefore lapses into the solar year. Its use (called suixing jinian 歲星紀年 "recording years by the Jupiter year") was in practice abolished with the introduction of the Sifen Calendar 四分曆 in the Later Han period.

History of Chinese Astronomy

Chinese astronomers had already developed calendars in times immemorial. The oldest written traces of the calendar appear in the oracle bone inscriptions of the Shang period 商 (17th-11th cent. BCE). The calendar had reached full maturity by the Warring States period 戰國 (5th cent.-221 BCE). The literature on astronomical matters is vast, ranking only third after writings on agriculture and medicine. Astronomy was, from the beginning, connected to both mathematics and astrology. The latter falls between philosophy and mathematics and can thus be called a kind of pseudoscience. Much data are preserved in ancient writings on solar eclipses (rishi 日食), lunar eclipses (yueshi 月食), lunar occultations (yue yanxing 月掩星), halos (yun 暈), sunspots (modern term taiyang heizi 太阳黑子), meteors (liuxing 流星), comets (huixing 彗星) and novae (xinxing 新星).

Compared with the Western calendar, the Chinese system of calculating and recording time has many idiosyncratic features that must be explained. The difficulty of astronomy made it necessary for ancient kings to employ a "Grand Scribe" (taishi 太史), an astronomer, astrologer, and recorder of historical events. In most official dynastic histories, a chapter on the calendar is included (Lizhi 曆志 or Lüli zhi 律曆志). The duty of the astronomer and his bureau was to calculate the beginning of the year, the twelve months, intercalary months, the twenty-four Solar Terms, the occurrence of lunar and solar eclipses, and the movements and positions of the five planets. This set of data is called the "calendric standard" (lifa 曆法). Chinese astronomy was primarily concerned with calculating calendar data, particularly the movements of the Moon and the Sun, because these two celestial bodies were significant to the Chinese luni-solar calendar.

Another important field of Chinese astronomy was the observation of celestial phenomena. The treatises in the official dynastic histories are called Tianwen zhi 天文志 "On the patterns of Heaven". The most important instrument for these observation was the armillary sphere (hunyi 渾儀). While the ancient Greeks focused on the ecliptic of the Sun (huangdao 黄道 "yellow path"), Chinese astronomers were interested in the celestial equator (chidao 赤道). It was divided into 360 degrees (du 度). During the Yuan period 元 (1279-1368), the Shoushi Calendar 授時曆 was introduced, which can be seen as the most perfect development of the Chinese calendar before the Jesuits brought Western astronomical science to China.

Mythology

According to mythology, the oldest Chinese astronomer was Xi He 羲和, an official of the mythological emperor Yao 堯. As a cultural hero, Xi He created the calendar and handed it over to mankind. In the chapter Yaodian 堯典 of the Classic Shangshu 尚書 "Book of Documents", it is also said that Xi Zhong 羲仲 lived in the Yanggu Valley 暘谷 of Mt. Yuyi 嵎夷, where he offered sacrifices to the Sun and brought agriculture into accord with the seasons. This spot is believed to have been near modern Juxian 莒縣, Shandong, where, in the 1960s, Neolithic pottery bearing a sun symbol was found. It is interpreted as an ancient "character" for 旦 "dawn", the rising Sun. Three other persons were sent to the other cardinal directions: Xi Shu 羲叔 to Nanjiao 南交 in the South, He Zhong 和仲 to Meigu 昧谷 in the West, and He Shu 和叔 to Youdu 幽都 in the Northeast. These persons determined the seasons by observing different stars that appear on the southern sky at dusk (huanghun 黃昏). It is also said what activities the peasants undergo during these periods of the year:

The names mentioned for the four seasons in this text are Zhongchun 仲春 "mid-spring", Zhongxia 仲夏, Zhongqiu 仲秋 and Zhongdong 仲冬. Later, these names were used to designate the middle month of each season (the middle month of Spring, etc.).
The chapter Yaodian continues to explain that the year is 366 days long, with four seasons (siji 四季), and that intercalary months (runyue 閏月) were used to bring the lunar calendar into accord with the solar calendar.

Xia, Shang, and Western Zhou periods

The oldest known calendar is the so-called Xia xiaozheng 夏小正 "Small Correctness of the Xia" (zheng meaning the "correct" beginning of the year). It was supposedly created during the Xia period 夏 (21st-17th cent. BCE) and has been transmitted as a chapter of the book Da Dai Liji 大戴禮記. In this calendar, all months are characterised by certain marks, except the second, eleventh and twelfth months. The calendar not only notes which starry constellation was to be observed at dusk in the southern sky (the hunzhong xing 昏中星 "evening star"), but also which constellations were to be seen at dawn in this place (the danzhong xing 旦中星 "morning star"). It also records in which direction the handle of the Northern Dipper (Beidou 北斗, Ursa Maior) was pointing.

Another trace of Xia-period astronomy appears in the posthumous names of the last kings of the Xia dynasty, such as Kong Jia 孔甲, Yin Jia 胤甲 or Lü Gui 履癸, which include some of the Ten Celestial Stems. These must therefore already have been used as "numbers" at that time. The oracle bone inscriptions from the Shang period show that the Ten Celestial Stems and twelve Terrestrial Branches were used to designate days in the sexagenary cycle. A long list of these designations appears on an oracle bone from the reign of King Wu Yi 武乙 (probably r. 1129-1095 BCE).

The months were designated by common numbers, except the first, which is called zhengyue 正月. The length of the months varied. Large months (dayue 大月) had a length of 30 days, and small months (xiaoyue 小月) had a length of 29 days. The intercalary month – used to bring the solar calendar (365 days) into accord with the lunar year (360 days) – was placed at the end of the year, and not, as in later times, in the midst of other months. Numerous eclipses and novae are mentioned in the oracle bone inscriptions. The use of Solar Terms (jieqi 節氣) is also attested.

Lunar phases (yuexiang 月相) play an important role in the bronze vessel inscriptions and in the texts of the Shangshu and the Yizhoushu 逸周書. Many texts begin with a date, such as wei shiyue you yiyue dinghai 唯十月又一月丁亥 "In the eleventh month, on the day with the cyclical combination dinghai". The word shuo 朔 for the new moon is not mentioned in this type of text, but all other phases of the Moon are, namely chuji 初吉 (the first day after the new moon to the 7th or 8th day), ji shengba 既生霸 (or ji shengpo 既生魄, from the 8th or 9th day to the 14th or 15th day of the month), ji wang 既望 "full moon" (from the 15th or 16th day to the 22nd or 23rd day of the month), and ji siba 既死霸 (or ji sipo 既死魄, from the 23rd day of the month to the next new moon). Astronomical phenomena are also mentioned in the Classic Shijing 詩經 "Book of Songs", for instance, that "in the seventh month, the Fire Star passes the meridian" (qi yue liu huo 七月流火; Binfeng 豳風, song Qiyue 七月), "the Three Stars are seen from the door" (san xing zai hu 三星在戶; Tangfeng 唐風, song Choumou 綢繆), "the Moon is in the Hyades" (yue li yu Bi 月離于畢; Xiaoya 小雅, ode Jianjian zhi shi 漸漸之石), the "Golden Star" (jinxing 金星, i.e., Venus), the Milky Way (yinhe 銀河), a solar eclipse (perhaps 776 or 735 BCE), and the use of gnomons.

Spring and Autumn and Warring States periods

Astronomical knowledge of the Eastern Zhou period is reflected in the chapter Yueling 月令 "Proceedings of government in the different months" of the Classic Liji 禮記. This text uses the twenty-eight starry constellations (ershiba xiu 二十八宿) to measure time. It explains which constellation is positioned in the southern sky at dawn at the beginning of each month, and where the Sun sets. A typical notation is, for instance: Mengchun zhi yue, ri zai ying Shi, hun 孟春之月，日在營室，昏參中，旦尾中。其日甲乙。 "In the first month of spring, the Sun is in Shi, the star culminating at dusk being Shen, and that culminating at dawn Wei. Its days are jia and yi" (transl. Legge).

The history books Chunqiu 春秋 and Zuozhuan 左傳 contain rich information about the calendar. They mention 37 solar eclipses, 32 of which can be identified with historical eclipses. The year 687 BCE (7th year of Duke Zhuang of Lu 魯莊公, summer, 4th month, day xinmao) records: ye, hengxing bu jian, yezhong, xingyun ru yu 夜，恆星不見，夜中，星隕如雨 "at night, the regular stars were not visible. At midnight, there was a fall of stars like rain." (transl. Legge). This is the oldest record of a meteorite shower in the constellation Lyra. The year 613 (autumn, 7th month) records: You xing bei ru yu Beidou 有星孛入于北斗 "there was a comet, which entered the Northern Bushel". This might be the earliest mention of Halley's Comet.

Around 600 BCE, astronomers began using gnomons to measure the length of the day and the year’s turning points, the winter and summer solstices. The winter solstice was called rinanzhi 日南至 "southern arrival of the Sun", and not, as later, dongzhi 冬至 "arrival of the winter". This was the starting point of the year, and the first month was called Chun wang zhengyue 春王正月 "Spring, right month of the King". The winter solstice is mentioned twice in the Zuozhuan, separated by 133 years. Moreover, 48 intercalary months are recorded (with only one record missing). This exactly corresponds to a relation of seven intercalary months in 19 years. To align the lunar year with the solar year, the calendar consisted of 365¼ days and was therefore called Sifen li 四分曆 "Quarter Calendar". The six old calendars (gu liu li 古六曆: the Calendar of the Yellow Emperor 黃帝曆, the Calendar of Zhuan Xu 顓頊曆, the Xia Calendar 夏曆, the Yin Calendar 殷曆 of the Shang dynasty, the royal Zhou Calendar 周曆, and the ducal Calendar of Lu 魯曆) – called so because they predated the calendar reform under Emperor Wu 漢武帝 (r. 141-87 BCE) of the Han dynasty 漢 (206 BCE-220 CE) – were "quarter calendars". These calendars did not differ in their calculation method, but were named after mythological emperors, dynasties, or (in the case of Lu) that of the regional states where it was used.

The various regional states of the Warring States period had their own astronomers, some of whom are known by name. In the state of Qi 齊, the astronomer Gan Gong 甘公 or Gan De 甘德 wrote the book Tianwen xinzhang 天文星占, and in the state of Wei 魏, master Shi Shen 石申 had authored the book Tianwen 天文. Both books dealt largely with astrology, but also contained important information about the movements of planets and the constellations. Fragments or ideas from these two texts are preserved in the book Shishi xingjing 石氏星經, which is now known as Gan-Shi xingjing 甘石星經.

It was common for historians to name a year according to the length of the sovereign’s rule. The problem of the Warring States period was that, except for the king of Zhou, each regional ruler (zhuhou 諸侯) claimed to be a more or less independent sovereign and used his own calendar. To circumvent this confusion, it was necessary to create a year designation independent of worldly rulers. The result was the introduction of the Jupiter calendar (suixing jinian fa 歲星紀年法), which provided a way to name years by the position of the planet Jupiter along the path of its "revolution around the Earth". The Jupiter position was used for the "absolute" year designations until the Han period, when the Stem-and-Branch cycle (ganzhi jinian fa 干支紀年法) began to prevail for the designation of years.

The many "masters and philosophers" of the age began contemplating the shape and construction of the universe. The book Zhuangzi 莊子 (ch. Tianyun 天運) and the ballad Tianwen 天問 in the collection Chuci 楚辭 include many questions in this vein. The sky was seen as a "large cover" with a round shape, while the Earth was believed to be "square like a chessboard" (tian yuan ru zhanggai, di fang ru qiju 天圓如張蓋，地方如棋局). This was the "Canopy-Heaven Model" (gaitian shuo 蓋天說). It was later revised to a projection in which Heaven was a hat-like cover over a round plate, the Earth (tian si gai li, di fa fu pan 天似蓋笠，地法覆槃). The book Laozi 老子 (Daodejing 道德經) touches on the question of the creation of the universe, but only the Han-period book Huainanzi 淮南子 (chapter Tianwen xun 天文訓) gives a clear account of the conception that in the beginning there was a chaos (hundun 混沌), which then separated into the light and pure matter that ascended to the sky, and the heavy and muddy parts that constituted the Earth. The sky represented the active energy (yangqi 陽氣), and the Earth the inactive potential (yinqi 陰氣). Together, they produced the "ten thousand creatures" (wanwu 萬物). The Huainanzi is also the first book in which astronomical knowledge was precisely laid down and in which the mathematical relations of the musical pitch-pipes, weights and measures are explained.

In the final phase of the Warring States period, the twenty-four Solar Terms became increasingly important because they were directly related to agricultural activities, and thus to the economic output and financial revenue of the contending states. These terms are also described in the book Huainanzi. At that time, the most important constituents of the calendar were the Solar Terms, as determinants of the solar year, and the new moon intervals, as elements of the lunar year. Thus, the luni-solar calendar of traditional China had come into being.

Han period

After the kingdom of Qin conquered the various regional states and created the Qin Empire, the Zhuan Xu calendar was adopted as the empire-wide calendar. In this calendar, the tenth month (roughly corresponding to Western November and December) marked the beginning of the year, and intercalary months were added at the end of the year. The calendar’s beginning (the epoch, liyuan 曆元) was inaugurated in the year with the cyclical combination jiayin 甲寅, on the day jiayin 甲寅 of the first month (zhengyue 正月), during the solar term Lichun 立春, on a new moon day, and when the five planets were seen in the east.

The Han dynasty initially adopted the Qin calendar, but Emperor Wu initiated a calendar reform and, in 104 BCE, ordered the astronomers Deng Ping 鄧平 and Luoxia Hong 落下閎 (156-87) to supervise it. That same year (the 7th of the reign-period Yuanfeng 元封) was renamed the 1st of the reign-period Taichu 太初. The new calendar was therefore called the Taichu Calendar (Taichu li 太初曆). It is the oldest Chinese calendar whose data are fully recorded. The calculation method of this calendar was less precise than that of the Sifen Calendar, particularly in aligning the lunar and solar years (or tropical year), but it had some decisive advantages over the older calendars:

The beginning of the year was fixed as the first month zhengyue 正月 (corresponding to Western January and February), rather than the tenth month. This restored a direct link between the beginning of the year and the seasonal phenomena (the beginning of spring as the beginning of the year, as the month begins after a new moon). The intercalary month was flexibly placed at the end of a month that included a zhongqi solar term, rather than at the end of the year. The synodic periods of the planets were measured with high accuracy — for example, Mercury's synodic period was determined to be 115.87 days, only 0.01 day shorter than the modern value of 115.88 days. A 135-month eclipse cycle was used. Within this cycle, the Sun passes through the lunar nodes (huang-bai jiaodian 黃白交點) 23 times, with two such passages constituting one eclipse year. That is, 1 eclipse year = 346.66 days, which is less than 0.04 days longer than the modern value of 346.62 days.

The Taichu Calendar was in use for 188 years before it was replaced in 85 CE by the Sifen Calendar. At that time, the tropical year and the times of the new moon no longer aligned with the calculated data. The scholar Jia Kui 賈逵 (30-101 CE) therefore advocated a different calculation method, invented by Fu An 傅安, which was not based on days but on the Sun and Moon's movement along the ecliptic and the positions of the 28 constellations. As a consequence, the beginning of the dongzhi 冬至 winter term was moved from its position in the constellation Qianniu 牵牛 to 21 ¼ degrees in the constellation Dou 斗. Jia Kui had probably observed the phenomenon of the precession (suicha 歲差) of the Earth's axis, which results in the precession of the equinoxes along the ecliptic. He had also become aware of the Moon's varying velocity in its orbit, which is higher when it is closer to Earth (at perigee). He therefore suggested the "method of the nine ways" (jiudaoshu 九道術) or nine segments of the orbit, an attempt to model the Moon's motion using nine lunar paths — an approach linked to the Five Agents theory. These changes by Jia Kui were based on the ancient Sifen Calendar.

In the very late years of the Han period, Liu Hong 劉洪 created the Qianxiang Calendar 乾象曆, in which he reduced the fractional part of the length of the tropical year to less than ¼ and calculated the solar year as 365.2462 days. The Qianxiang Calendar was the first calendar to correctly determine the angle between the ecliptic and the celestial equator and to calculate the beginning of a lunar month (dingshuo 定朔) exactly, taking into account the Moon's changing velocity. It therefore used a sidereal month rather than a synodic month. He also determined the angle between the ecliptic and the celestial equator, as well as the Moon's daily motion in degrees during one anomalistic month, greatly advancing the calculations of new moons, full moons, and solar and lunar eclipses.

The most famous astronomer of the Eastern Han period was Zhang Heng 張衡 (78-139), who not only invented the so-called earthquake detector of the Lord of the Wind (Hou Feng didong yi 后風地動儀) but also developed an armillary sphere driven by a water clock (loushui zhuan huntian yi 漏水轉渾天儀). This instrument was an advancement of Geng Shouchang's 耿壽昌 (mid-1st cent. BCE) celestial globe (hunxiang 渾象). Somewhat earlier than Zhang Heng, Xi Meng 郗萌 wrote a text called Xuanyeshuo 宣夜說, in which he explained that the sky could not be like a hard-shelled egg but must be boundless and filled with ether (qi 氣), on which the celestial bodies floated. Zhang Heng later explained that the sky was "round like a pill" and the Earth "round like the yolk of an egg" (tian yuan ru danwan, di ru luan zhong huang 天圓如彈丸，地如卵中黃).

In 1973, an important document of Han-period astronomy was discovered in Tomb No. 3 at the Mawangdui 馬王堆 site in Changsha 長沙, Hunan. Written on silk, an illustrated text of 8,000 characters discusses divination methods for the Five Planets (Wuxingzhan 五星占). It records the positions of the planets over a 70-year period and, in 29 illustrations, the shapes of comets and their tails. The treatise on the Five Agents (Wuxing zhi 五行志) in the history Hanshu 漢書 provides a detailed description of a lunar eclipse in 89 BCE, and of sunspots observed in the year 28 BCE. This is the earliest mention of this astronomical phenomenon. The Chinese were always interested in extraordinary phenomena in the sky because they were interpreted as auspicious or inauspicious influences on the course of political life. Because of the overlap between astrology and astronomy, Chinese sources are extremely rich in reports of celestial appearances and anomalies.

The Treatise on Astronomy (Tianwen zhi 天文志) in the Hanshu records a "guest star" (kexing 客星; perhaps a nova) in the constellation Fang 房 (approx. Scorpio) in the sixth lunar month of 134 BCE. This was the very same new star observed by the Greek astronomer Hipparchos of Nicaea (d. 120 BCE), although Hipparchus left no records of its timing or position.

Period of Division

During the Three Empires period, Yang Wei 楊偉 discovered that the intersection of the ecliptic with the Moon's orbital plane (huangbai jiaodian 黄白交点) had shifted over time. In his Jingchu calendar 景初曆 from 237 CE, he described this phenomenon and explained that the beginning of an eclipse was no longer confined to the point of intersection but could occur anywhere within the eclipse area (shixian 食限). He also developed methods for calculating the magnitude of solar and lunar eclipses (shifen 食分) and the position angle of first contact (chukui fangwei jiao 初虧方位角). These discoveries greatly improved the accuracy of eclipse predictions. His colleague Chen Zhuo 陳卓 (c. 230-c. 320) in the empire of Wu 吳 compiled a synopsis of star data from earlier times, including those of Master Shi 石氏, Master Gan 甘氏 and Wu Xian 巫咸. This synopsis, with a star chart, described 283 constellations (xingguan 星官 "star offices") and provided exact data on 1,464 individual stars. It remained in use until the late Ming period, when Western knowledge supported Chinese astronomers. Ge Heng 葛衡 invented an astronomical device called the astrolabe (huntianxiang 渾天象). In this tool, a flat disc or small sphere was placed at the centre of the armillary sphere to represent the Earth. As the celestial sphere (hunxiang 渾象) rotated around its axis, the Earth remained stationary at the centre. This design provided a more vivid and intuitive representation of the huntian theory of a celestial sphere.

In the statelet of Later Qin 後秦 (384-417), Jiang Ji 姜岌 developed a new method for determining the Sun's position using lunar eclipses. The results were recorded in his Sanji jiazi yuanli 三紀甲子元曆 Calendar from 384. He was the first scholar to suggest that the red colour of dusk and dawn was the cause of the Sun's rays passing through a thicker layer of air.

Zhao Fei 趙{匪欠}, who lived in the state of Northern Liang 北涼 (398-439), made progress on intercalary years and explained that in a 19-year period there must be 7 intercalary months (the Metonic cycle), or, in other terms, 221 intercalary months over a span of 600 years. He published the Yuanshi Calendar 元始曆 in 412.

Yu Xi 虞喜 (281-356) of the Eastern Jin dynasty discovered the phenomenon of precession (suicha 歲差). During the Southern Dynasties period, Zu Chongzhi 祖沖之 (429-500) incorporated it into calendrical calculations. He distinguished between the sidereal year (hengxing nian 恒星年) and the tropical year (huigui nian 回歸年), marking a significant advance. Zu Chongzhi also determined the length of one draconic month (jiaodian yue 交點月; the time between two successive passages of the Moon through the same node) as 27.21223 days—differing from the modern value by only one ten-thousandth.

Before Zu Chongzhi, He Chengtian 何承天 (370-447), based on long-term observations, used the "day-adjustment method" (tiaori fa 調日法) to calculate a more precise value for the synodic month (shuowang yue 朔望月; the time between two new moons), marking a methodological improvement. The day-adjustment method uses the excess fraction approximation (strong rate, guosheng fenshu jinsi zhi 過剩分數近似值 or qianglü 強率) and the deficient fraction approximation (weak rate, buzu fenshu jinsi zhi 不足分數近似值 or ruolü 弱率) of a number to derive a more accurate fractional approximation.

Zu Geng 祖暅 (456-536), the son of Zu Chongzhi, discovered that the "Node Star" (niuxing 紐星), which earlier generations had regarded as the North Star (beiji xing 北極星), had already deviated from the celestial pole by more than one degree. This proved that the celestial north pole is constantly shifting and that the pole star changes over time.

Zhang Zixin 張子信 of the Northern Qi dynasty 北齊 (550–577 CE) discovered that the Sun and planets do not move uniformly. He also found that when the Moon is at the southern or northern ecliptic during conjunction, it determines whether a solar eclipse occurs, whereas lunar eclipses do not show this phenomenon.

Sui and Tang periods

After the Sui dynasty 隋 (581–618 CE) reunified China, the first calendar used was Zhang Bin's 張賓 basic Kaihuang Calendar 開皇曆 (584). However, the Kaihuang Calendar was crude and simplistic. Following intense debates, it was replaced in 597 by the calendar of Zhang Zhouxuan 張胄玄. This calendar was later revised in 608 and became known as the Daye Calendar 大業曆. The Daye Calendar incorporated Zhang Zixin's discovery of the irregular motion of the planets and utilised the method of summing an arithmetic progression to compile a table of planetary positions for conjunction cycles. This method further enhanced the calculation of planetary motions.

During the implementation of the Daye Calendar, Liu Zhuo 劉焯 (544-610) completed the Huangji Calendar 皇極曆. He applied equal-interval second-order difference interpolation to model the irregular motions of the Sun and Moon, a method that became a distinctive feature of Chinese astronomy. Liu Zhuo also proposed a large-scale geodetic survey to disprove the traditional claim that "the Sun's shadow differs by only one inch over a thousand li (half-miles)" (ri ying qian li cha yi cun 日影千里差一寸). This claim had already been questioned earlier by He Chengtian 何承天. However, the Huangji Calendar was never adopted.

The powerful and stable Tang dynasty (618–907 CE) created favourable conditions for significant advances in astronomy. In 633, Li Chunfeng 李淳風 (602-670) developed the Huntian Ecliptic Armillary Instrument (huntian huangdao yi 渾天黃道儀), elevating the Chinese armillary sphere to a highly complex level. Between the existing mechanism of six fixed rings (liuhe yi 六合儀) and the movable-ring system (siyou yi 四游儀), he added a new component, the Three Celestial Rings Instrument (sanchen yi 三辰儀). This consisted of three interlocking rings representing the lunar path (the white path ring, baidao huan 白道環), the ecliptic (ecliptic ring, huangdao huan 黃道環), and the celestial equator (equatorial ring, chidao huan 赤道環). With this configuration, astronomers could directly read three sets of celestial coordinates—equatorial, ecliptic, and lunar—from the instrument during observations.

Building on the Huangji Calendar, Li Chunfeng developed the Linde Calendar 麟德曆, which was officially adopted in the second year of the Linde reign (665) under Emperor Gaozong 唐高宗. The Linde Calendar used the "fixed-new-moon method" (ding shuo fa 定朔法) to compile the daily calendar chart (riyong lipu 日用曆譜). This meant that not only were the irregular motions of the Sun and Moon considered when calculating solar and lunar eclipses, but they were also incorporated into the calendar’s construction. This approach had originally been proposed by He Chengtian, but entrenched traditional views meant it took more than two centuries of struggle before it was finally accepted. The Linde Calendar also abolished the concept of the intercalary cycle (run zhou 閏周) and instead relied entirely on observation and statistical methods to determine accurate values for the tropical year and the synodic month.

Among the Dunhuang manuscripts preserved in the British Museum in London is a star chart (Dunhuang Star Chart, Dunhuang xingtu 敦煌星圖) that may also be associated with Li Chunfeng. This is suggested by the presence at the beginning of the chart of 48 sections of miscellaneous meteorological divinations (qixiang zazhan 氣象雜占), each comprising an illustration above and explanatory text below.

In 725, the monk Yixing 一行 (683-727) and Liang Lingzan 梁令瓚 (b. 690) improved Zhang Heng's water-driven armillary sphere from the Han period. They housed the sphere in a wooden cabinet, with half exposed and the other half concealed. On the cabinet's surface stood two wooden figurines on either side of the sphere—one struck a drum every quarter of an hour, while the other rang a bell every two hours—automatically and precisely on time. This can be considered the earliest known self-striking clock. It was named the Kaiyuan Water-Powered Celestial Globe with Overhead View Diagram (Kaiyuan shuiyun huntian fushi tu 開元水運渾天俯視圖). Before this invention, they also built an ecliptic armillary instrument with sliding rings (huangdao youyi 黃道游儀), based on Li Chunfeng's Huntian Ecliptic Instrument. They modified the Three Celestial Rings by perforating the equatorial ring, allowing the ecliptic ring to slide along it and enabling adjustments for precession. Using this instrument, Yixing observed the positions of over 150 stars and found that the positions of fixed stars listed in earlier star charts, star catalogues, and armillary spheres had shifted significantly. Yixing did not provide an explanation for this phenomenon, which is primarily caused by precession.

At the same time, Yixing also instructed senior astronomers Yuan Tai 元太 and Nangong Shuo 南宮說, among others, to go to 11 different locations to measure the altitude of the North Pole (i.e., the elevation angle of the celestial pole) and the length of the shadow cast by an eight-chi 尺-high gnomon at solar noon during the spring and autumn equinoxes, as well as the summer and winter solstices. At four locations in what is today the province of Henan, namely Huaxian 滑縣, Kaifeng 開封, Fugou 扶溝, and Shangcai 上蔡, Nangong Shuo not only measured the lengths of shadows and the altitudes of the North Pole but also physically quantified the distances between these four places. The results showed that the distance from Huaxian to Shangcai was 526.9 li, yet the difference in the length of the gnomon's shadow at the summer solstice was already 2.1 cun 寸. This empirical data completely disproved the long-held traditional belief that the Sun's shadow changed by only one cun per thousand li.

Moreover, by comparing Nangong Shuo's data with those from other locations, Yixing further discovered that the relationship between shadow difference and north-south distance was not proportional. As a result, he shifted to using differences in the North Pole's altitude—which effectively correspond to geographic latitude—to calculate distance. He concluded that a one-degree difference in the North Pole's altitude corresponded to 351.27 li (approximately 129.22 kilometres). Although this value contained significant errors, it represented the first meridian arc measurement (ziwu xianshi ce 子午線實測) in world history.

More importantly, Yixing critically challenged the methodological errors in earlier attempts to calculate the size of the heavens. He questioned whether the universe was as limited as traditionally believed, thereby effectively halting efforts to compute the dimensions of the cosmos. His ideas also profoundly influenced Liu Zongyuan 柳宗元 (773-819). In correspondence with Liu Yuxi 劉禹錫 (772-842), Liu Zongyuan discussed Yixing's work and advanced the idea of an infinite universe. He argued that the universe has neither boundaries nor a centre (see Tiandui 天對).

Based on large-scale observations, Yixing completed the first draft of the Dayan Calendar 大衍曆 in 727. After his death, it was finalised the following year by his successors. The Dayan Calendar employed the fixed solar term method (dingqi fa 定氣法) to compile a solar motion table, dividing the Sun's path over one tropical year into 24 equal segments by celestial longitude, each marking a solar term (jieqi). However, because the time between two consecutive Solar Terms varies due to the Sun's uneven motion, Yixing invented the unequal-interval second-order difference interpolation method（budeng jianju erci cha neicha fa 不等間距二次差內插法) to address this issue. To calculate the irregular motions of the planets, the Dayan Calendar used tables with sine-like properties and an interpolation formula involving third-order differences for approximation. The Dayan Calendar organised all its computational elements into seven major sections, including one called buzhong shuo 步中朔 ("new moons within the step calculations"), which became a model for future calendrical systems.

Among the calendars of the late Tang and Five Dynasties periods (907–960 CE), two are especially noteworthy: the Xuanming Calendar 宣明曆, officially adopted in 822, and the Futian Calendar 符天曆, which circulated among the populace during the Jianzhong reign-period 建中 (780–783 CE). Xu Ang's 徐昂 Xuanming Calendar introduced three correction factors for solar eclipse calculations: time difference (shicha 時差), solar term difference (qicha 氣差), and quarter-hour difference (kecha 刻差), thereby improving the precision of corrections for the Moon's daily parallax. Cao Shiwei's 曹士蔿 Futian Calendar abolished the use of accumulated years from the epoch origin (shangyuan jinian 上元積年) and instead used 10,000 as the denominator for the fractional parts of astronomical data. These two innovations greatly simplified calendrical calculations, which is why the Futian Calendar gained popularity among the common people. However, it was dismissed by the ruling elite as a "minor (i.e., unreliable) calendar" (xiao li 小曆) and was never officially adopted.

The Tiaoyuan Calendar 調元曆, promulgated in the 4th year of the Later Jin's Tianfu reign (939), abandoned the use of accumulated years. It was in use for five years (939–943) and later adopted by the Liao dynasty 遼 (907-1125) for 48 years (947–994). The innovations of these two calendars were fully implemented only in the Yuan dynasty's 元 (1276-1368) Shoushi Calendar 授時曆 in 1280.

Song, Yuan and Ming periods

The appearances of supernovae in the years 1006 and especially 1054 (the first year of the Zhihe reign under Emperor Renzong of the Song Dynasty) have become highly valued sources of information in modern astronomical research. At the location where the 1054 supernova appeared, the Crab Nebula (Xiezhuang xingyun 蟹狀星雲) remains. It is one of the most fascinating objects of study in contemporary astronomy.

During this period, five measurements of star positions were recorded: the first in the 3rd year of the Dazhong Xiangfu (1010), the second during the Jingyou era (1034–1038 AD), the third during the Huangyou era (1049–1053 AD), the fourth during the Yuanfeng era (1078–1085 AD), and the fifth during the Chongning era (1102–1106). Of these, the Yuanfeng observations were compiled into a star chart, which was engraved on a stone stele for preservation. This is the famous Suzhou Astronomical Stone Carving (Suzhou shike tianwen tu 蘇州石刻天文圖).

Observational results from the Yuanfeng era were also preserved in the form of star charts in the book Xin yixiang fayao 新儀象法要, written by Su Song 蘇頌. This work served as the instruction manual for the Water-Powered Armillary Sphere and Celestial Globe (shuiyun yixiang tai 水運儀象臺), constructed in 1092. The text describes over 150 mechanical components and includes more than 60 illustrations, making it an excellent resource for the study of ancient scientific instruments.

After completing the Water-Driven Armillary Sphere and Celestial Globe, Su Song and Han Gonglian 韓公廉 went on to construct another instrument, an armillary sphere (huntian xiang 渾天象). Its celestial globe was larger than a person, allowing individuals to enter its interior and observe from within. Small holes were drilled into the sphere's surface at the positions of the stars, so that when viewed from inside, the points of light resembled stars in the sky. Today, this type of instrument is also referred to as an "imitation celestial sphere" (jiatian xiang 假天儀) and is considered a forerunner of the modern planetarium.

Shen Kuo 沈括 (1031-1094), famous for his book Mengxi bitan 夢溪筆談 and a contemporary of Su Song, also made significant contributions to astronomy. In 1074, while constructing an armillary sphere, he omitted the ecliptic ring and instead used calculations to determine the Moon's ecliptic coordinates. This marked the beginning of a shift in Chinese armillary design from complexity to simplification. Shen Kuo also narrowed the aperture at the lower end of the sighting tube to limit the observer's eye movement, thereby reducing aiming errors. Additionally, he corrected the alignment of the sphere's polar axis by observing the position of the North Star. He improved the clepsydra (louhu 漏壺; water clock) and conducted theoretical research on the variation of water flow rates across different seasons. He raised the issue of the discrepancy between the true or apparent solar day (zhen taiyang ri 真太陽日) and the mean solar day (ping taiyang ri 平太陽日).

More importantly, Shen Kuo proposed an innovative calendar reform. He proposed the Twelve-Qi Calendar (Shi'er qi li 十二氣歷), stating: "Take the first day of the Beginning of Spring (Lichun) as the first day of early spring, the Waking of Insects (Jingzhe) as the first day of mid-spring, with long months having 31 days and short months having 30; each year ends evenly, and there will never be a leap month." This was essentially a solar calendar. However, due to traditional customs, it was never adopted.

During the more than 300-year Song period, 18 calendars were used. Among them, two of the most innovative were the Jiyuan Calendar 紀元歷 (1107) by Yao Shunfu 姚舜輔 and the Tongtian Calendar 統天歷 (1199) by Yang Zhongfu 楊忠輔. The Jiyuan Calendar was the first to use observations of Venus to determine the Sun’s position. The Tongtian Calendar determined the length of the tropical year as 365.2425 days — exactly the same as the average year in the current Gregorian calendar, though it was introduced 383 years before the Gregorian reform of 1582. The Tongtian Calendar also proposed that the length of the tropical year changes over time, with values in ancient times being longer than they are today.

In 1276, after Yuan forces captured the Southern Song capital Lin'an 臨安 (present-day Hangzhou), Kublai Khan gathered personnel from the astronomical bureaus of both the Jin and Song dynasties in Dadu 大都 (present-day Beijing). Alongside newly selected talents, they formed a professional astronomical team. Under the leadership of Wang Xun 王恂 (1235-1281) and Guo Shoujing 郭守敬 (1231-1316), this team engaged in instrument-making, astronomical measurements, and the compilation of a new calendar. In just five years, from 1276 to 1280, they achieved remarkable accomplishments, elevating ancient Chinese astronomy to a new peak.

First, a variety of new instruments were created, including the "simple device" (jianyi 簡儀), the zenith instrument (yangyi 仰儀), a "height instrument" (gaobiao 高表), a "shadow tool" (jingfu 景符), a "correct directional instrument" (zhengfang’an 正方案 True), and an "exquisite instrument" (linglongyi 玲瓏儀), all of which were innovative. The "simple instrument" was a revolutionary reform of the armillary sphere, and its design and manufacturing technology led the world for over 300 years, only rivalled by the instrument invented by the famous astronomer Tycho Brahe in 1598.

The "simple instrument" used pinhole imaging to project the Sun's image onto a hemispherical surface, enabling direct reading of its celestial coordinates. The "height instrument" was a scaled-up version of the traditional 8-foot instrument, increasing its size to four zhang (approximately 12 metres, see weights and measures). This enhancement reduced measurement error to one-fifth of its previous value. The "shadow tool" was an auxiliary instrument for the "height instrument", utilising pinhole imaging to eliminate the blurriness at the end of the instrument's shadow, thereby improving observational accuracy (as seen at the Dengfeng Observatory 登封觀星臺). The "correct directional instrument" consisted of 19 concentric circles drawn on a four-foot square wooden board, with a rod placed at the centre. When the shadow of the rod fell on a specific circle, the position was recorded. By connecting two points on the same circle from morning to evening, the midpoint of the line joining them and the centre of the circle would indicate true south. If the board were stood on its side, it could also measure the height of the North Star above the horizon. This instrument was portable, making it suitable for fieldwork. The "exquisite instrument", similar to the armillary sphere created by Su Song and Han Gonglian, was an astronomical performance instrument that allowed people to enter and view its workings.

After 1281, Guo Shoujing continued inventing new instruments, the most prominent of which was the Lantern Water Clock in the Hall of Great Brilliance (Daming Dian denglou 大明殿燈漏). This mechanical timekeeper, shaped like a lantern ball, was driven by hydraulics and featured animal models that moved at set intervals, similar to the mechanical automata that adorned European clocks.

Second, an unprecedented scale of observational work was conducted. Observation stations were established at 27 locations across the country to measure local geographic latitudes. These stations were positioned at 10-degree intervals, ranging from the South China Sea at 15°N to the Bohai Sea 渤海 at 65°N. The stations recorded the length of shadows at the summer solstice and the duration of day and night on that day.

Third, a series of astronomical data were directly measured, and older data were checked and refined, with the most precise data selected. For example, the value for the tropical year was taken from the Tongtian Calendar of the Southern Song (1199), while the values for the synodic month, perigee month, and nodal month were taken from the revised Daming Calendar (1181) by Zhao Zhiwei 趙知微 (12th cent.) of the Jin empire 金 (1115-1234), as well as the Xizheng Gengwu Yuan Calendar 西征庚午元曆, created by Yelü Chucai 耶律楚材 (1190-1244) in the early phase of the Mongolian empire in China. The measurement of the distances between the 28 lunar mansions had an average error of less than 5°, a precision twice that of the Song period. The newly measured obliquity of the ecliptic had an error of just over 1°.

Fourth, based on extensive observations and research, the Shoushi Calendar 授時曆 was created in 1280 and implemented the following year. It used triple interpolation to calculate the Sun's daily apparent motion along the ecliptic and the Moon's daily motion around the Earth. It employed a technique similar to spherical trigonometry, known as the arc-chord method, to determine the Sun's ecliptic longitude, right ascension and declination, the obliquity of the ecliptic, and the distance between the lunar node and the intersection of the celestial equator. These two methods hold significant importance in the history of astronomy and mathematics.

The Shoushi Calendar was used continuously from the Yuan period until the Ming Dynasty fell in 1644. During the Ming period, it was renamed the Datong Calendar 大統曆, but the changes were minor. The only difference was that the times for sunrise and sunset in Beijing were replaced with those observed in Nanjing, the imperial capital in the early Ming period. The calendar's epoch (liyuan) was set to 1384, and the method for accounting for century-long variations in the length of the tropical year was omitted. Apart from these changes, the calendar remained essentially unchanged.

In addition to official Shoushi Calendar, the Islamic Calendar (Huili 回曆) also circulated among China's minority groups, having been introduced from Arab countries. In 1267, the Central Asian astronomer Jamāl ad-Dīn from Bukhara (Ch. Zhamaluding 札馬魯丁, and variants) presented the Wannian Calendar 萬年曆, which Kublai Khan officially adopted. In the same year, Jamāl ad-Dīn was tasked with manufacturing seven astronomical instruments in the Arab style, including a Ptolemaic-type armillary sphere, a large ruler, a globe, and a star chart. In 1271, the Directorate of Islamic Astronomy (huihui sitianjian 回回司天監) was established in Shangdu 上都 (present-day Zhenglan Banner 正蓝旗, Inner Mongolia), and an Islamic almanac (huihuili 回回曆) was issued.

After the fall of the Yuan in 1368, the Directorate's staff were relocated to Nanjing, and a section of Islamic Astronomy was established within the Directorate of Astronomy (qintianjian 欽天監). There, they continued calculating celestial phenomena, issuing calendrical books, and comparing the Datong Calendar with the Islamic Calendar, while also translating several astronomical texts from Farsi and Arabic. In 1382, the government ordered Wu Bozong 吳伯宗 (1334-1384), Li Chong 李翀, Haidar 海達爾, Adawuding 阿答兀丁, Mashayihei 馬沙亦黑 (fl. 1379), and Muhammand (Mahama 馬哈麻) to translate from Persian the astronomical-astrological treatise Kitāb al-Mudḫal fī ṣināʿat aḥkām al-nuğūm (as Huihui tianwen shu 回回天文書 or Tianwen baoshu 天文寶書) by Kūšyār ibn Labbān (also known as Kūšyār Gīlānī or Kūšyār Daylami; Ch. Kuoshiya'er 闊識牙耳; 971-1029). The book introduced the division of stars into six classes, marking the first appearance of the concept of star magnitude in China. It listed the star magnitudes (xingdeng 星等) and ecliptic longitudes (huangjing 黃經) of 12 constellations, comprising a total of 30 stars.

From 1470 to 1477, Bei Lin 貝琳 (d. 1490) compiled and published the Qizheng tuibu 七政推步, originally translated during the Yuan period. This work served as a systematic introduction to Arabic astronomy, including a star catalogue listing the ecliptic longitudes, latitudes, and magnitudes of 277 stars. It marked the first translation between Chinese and foreign star names. The calendar portion of the Qizheng tuibu was later summarised and incorporated into the Astronomical Treatise (Lizhi 曆志) of the dynastic history Mingshi 明史, becoming an integral part of Chinese ancient astronomy, which remains in use by several ethnic groups to this day.

The advent of Western astronomy in the late Ming period

Aside from the translation of Arab or Persian books on astronomy, nautical astronomy (qianxing shu 牽星術) was tested, for instance, during the voyages of Zheng He 鄭和 (1371-1433) between 1405 and 1432. In 1572 and 1604, Chinese astronomers observed supernovae. However, there were few innovations in the 16th century. Although two calendar reform movements in 1595 and 1610, were ultimately unsuccessful, the idea of calendar reform attracted significant attention.

At this time, European Jesuit missionaries began arriving in China. Recognising China's interest in acquiring new knowledge, they adopted an academic approach to their missionary work. One of the earliest missionaries to come to China, the Italian Matteo Ricci (Ch. Li Madou 利瑪竇; 1552-1610; arrived in 1583), repeatedly reported back to Europe on Chinese interest in astronomy. Influenced by him and at his request, many of the Jesuits who came to China afterwards had some knowledge of astronomy, with some even receiving specialised training. The European astronomical knowledge they introduced was well received by progressive Chinese intellectuals of the time, who translated books and disseminated advanced Western astronomical knowledge.

Among the early publications introducing European astronomical knowledge were: Hungai tongxian tushuo 渾蓋通憲圖說 "Illustrated explanation of the armillary sphere and the celestial globe" (1607, with star charts), Jianpingyi shuo 簡平儀說 "Explanation of the simplified astrolabe" (1611), Biaodushuo 表度說 "Explanation of the sundial" (1614), Tianwenlüe 天問略 "A brief inquiry into astronomy" (1615), and Yuanjingshuo 遠鏡說 "Explanation of the telescope" (1626). Most of these works focused on European astronomical instruments. In the Tianwenlüe, the Ptolemaic geocentric model with its twelve celestial spheres was presented, along with some of Galileo's discoveries made through telescopic observation. Except for the Hungai tongxian tushuo, written by Li Zhizao 李之藻 (1565-1630), the other books were written by Jesuit missionaries with the assistance of Chinese scholars.

In addition to translating and introducing European astronomical knowledge, Chinese scholars also learned European astronomical calculation methods from the Jesuits. As a result, in 1610, Xu Guangqi 徐光啟 (1562–1633) used Western methods to predict a solar eclipse on the new moon of the 11th lunar month (December 15). Observations confirmed that his prediction was relatively accurate, highlighting Western techniques. Later, during a solar eclipse on the first day of the 5th lunar month of the 2nd year of the Chongzhen reign-period 崇禎 (June 21, 1629), the official predictions from the Directorate of Astronomy were significantly incorrect. This prompted the Ming government to initiate a calendar reform. Xu Guangqi was ordered to establish a Calendar Bureau (liju 曆局) of about one hundred people inside the Xuanwu Gate 宣武門 of Beijing. Jesuit missionaries such as Johann Schreck (Deng Yuhan 鄧玉函; 1576-1630), Giacomo Rho (Luo Yagu 羅雅谷; 1593-1638), and Johann Adam Schall von Bell (Tang Ruowang 湯若望; 1591-1666) were invited to participate in the compilation and translation work. After five years of effort, the work was completed and titled the "Treatise of the Chongzhen Calendar" Chongzhen lishu 崇禎曆書. The most notable differences between this work and the traditional Chinese astronomical system were the adoption of Tycho Brahe's (1546-1601) cosmological model and geometric calculation methods; the introduction of the Earth and the concepts of geographic latitude and longitude; the application of spherical trigonometry; and the use of European standard units of measurement, such as dividing the circle into 360 degrees, the day into 96 quarter-hours (ke 刻) or 24 hours, and using base-60 subdivisions for both degrees and hours.

However, the Chongzhen lishu, completed in 1634, was never officially promulgated. In 1644, after the Qing army entered Beijing, Schall von Bell, deciding to serve the new dynasty, revised and condensed the work, renaming it the "Treatise on the New Western Calendar" (Xiyang xinfa lishu 西洋新法曆書) and presenting it to the Qing government. The Qing appointed him Director of Astronomy (qintianjian jianzheng 欽天監監正) and ordered the use of the "New Western Method" (Xiyang xinfa 西洋新法) to compile the civil calendar for the coming year, which was named the Shixian Calendar 時憲曆.

From that point on, except during the years 1664 to 1668, when Schall von Bell was imprisoned on accusations by Yang Guangxian 楊光先 (1597-1669), the Qing government continuously employed European missionaries to lead the Directorate of Astronomy until 1826. At times, two or even three missionaries were appointed at once.

Between 1669 and 1673, the Directorate of Astronomy, under the supervision of Ferdinand Verbiest (Nan Huairen 南懷仁; 1623-1688), constructed six large-scale Tycho-style astronomical instruments, which are still preserved at the Ancient Observatory in Beijing. Verbiest also compiled a manual describing them, titled Lingtai yixiang zhi 靈臺儀象志 "Illustrated treatise on instruments of the Spirit Platform".

In 1722, following revisions to the New Western Calendar, the book Lixiang kaocheng 曆象考成 "Comprehensive compilation of astronomical phenomena" was completed. In 1742, a supplement, Lixiang kaocheng houbian 曆象考成後編, was added. This was the first time Kepler's (1571-1630) first and second laws of planetary motion were applied in China; however, in this version, the Earth was incorrectly placed at the focus of the ellipse rather than the Sun. In 1752, a work titled Yixiang kaocheng 儀象考成 "Comprehensive treatise on instruments and phenomena" was compiled, which included a star catalogue listing 3,083 stars. During the Daoguang reign-period 道光 (1821-1850), after the departure of the missionaries, Chinese astronomers remeasured the stars listed in that catalogue. In 1844, they completed a supplement titled Lixiang kaocheng xubian 儀象考成續編, which expanded the star catalogue to 3,240 stars.

In addition to commissioning the Directorate of Astronomy to compile astronomical works, the Qing government organised two large-scale national surveying projects during the reigns of Emperors Kangxi and Qianlong. The first, carried out from 1708 to 1718, measured the latitudes and longitudes of more than 630 locations across China, establishing a geographic coordinate network centred on Beijing. Measurements were standardised using the Ministry of Works' (gongbu 工部) construction "foot" (yingzaochi 營造尺), defining 1 li (c. 0.5 km) as 1,800 chi and setting 200 li equal to one degree of the Earth's meridian. This method of linking units of length to the arc of one degree of the Earth's meridian was a groundbreaking innovation in global science—predating the French National Assembly's decision to define the metre as one ten-millionth of the Earth's meridian arc by about 80 years. During this survey, it was found that the arc length per degree between 38° and 39° latitude was shorter than that between 41° and 47°, with a difference of 258 chi over just 6 degrees. Even within the 41° to 47° range, the arc lengths per degree varied. This was the first time in the world that data indicating the Earth's shape as an oblate spheroid was obtained through direct ground-based measurements.

During the Qing period, a group of private astronomers approached their studies with great seriousness. Among the most renowned were Xue Fengzuo 薛鳳祚 (1600-1670), Wang Xichan 王錫闡 (1628-1682), and Mei Wending 梅文鼎 (1633-1721). Xue Fengzuo, building on translations of Western astronomical texts, authored over ten works, including the Lixue huitong 歷學會通. Beyond introducing general theories, he described in detail methods for calculating celestial motions. A distinguishing feature of his work was his use of logarithms. To simplify calculations, he replaced the base-60 system with a decimal (base-10) system and even created new mathematical tables, including trigonometric function tables. Wang Xichan was often paired with him in the phrase "South Wang, North Xue" (nan Wang bei Xue 南王北薛), though Wang's accomplishments were considered greater. His works include Xiao'an xinfa 曉庵新法 and Wuxing xingdu jie 五星行度解. In the former, he proposed a method for calculating Venus transits and improved calculations for solar and lunar eclipses. In the latter, he derived a set of formulas for determining planetary positions, achieving greater accuracy than earlier methods. Mei Wending was also a prolific writer (see his Lisuan quanshu 曆算全書) and made important contributions to the popularisation of astronomy. In his research on planetary motion, along with Jiang Yong 江永 (1681-1762) and others, he developed early ideas about gravity.

After Mei Wending, more scholars advanced astronomy through textual scholarship. They applied contemporary astronomical knowledge to exegetical studies, textual collation, authenticity analysis, and the reconstruction of lost material from the classics and historical records. As a result, many confusing or problematic sources were clarified and organised. Notable contributions include: Li Rui 李銳 studied Han-period calendars such as the Santong Calendar 三統曆, the Sifen Calendar 四分曆, and the Qianxiang Calendar 乾象曆; Gu Guanguang 顧觀光 researched the ancient "Six Calendars" and the trigonometrical book Zhoubi suanjing 周髀算經. In addition, Ruan Yuan 阮元 compiled biographies of astronomers, Chourenzhuan 疇人傳, and Wang Yuezhen 汪曰禎 authored a compendium of calendar methods throughout the ages, Lidai changshu jiyao 歷代長術輯要. These works served as valuable reference tools for the study of the history of Chinese astronomy.

The modern era from the late 19th century on

The Copernican theory was formally introduced to China by the French Jesuit Michel Benoist (Ch. Jiang Youren 蔣友仁; 1715-1774), who arrived in 1744. In 1760, he presented the Complete Map of the World (Kunyu tushuo 坤輿全圖). The Copernican theory was formally introduced to China by the French Jesuit Michel Benoist (Ch. Jiang Youren 蔣友仁; 1715-1774), who arrived in 1744. In 1760, he presented the Complete Map of the World Outlines of Astronomy (1849) by British astronomer John Herschel (1792-1871), by Li Shanlan 李善蘭 and the British missionary Alexander Wylie (1815-1887), that the Chinese public truly came to understand the significance of Copernicus's theory and the nature of modern astronomy. The book provides a detailed description of the structure and motion of the solar system, as well as content on stellar systems. Li Shanlan wrote a highly combative preface for this Chinese translation, in which he criticised the various fallacies opposing the Copernican theory centred on the motion of the Earth around the Sun in an elliptical orbit.

However, the imperial Directorate of Astronomy had no interest in embracing new ideas or adopting new technologies. Therefore, when modern astronomical knowledge (such as Kant's and Laplace's nebular hypothesis) first reached China, it primarily served as an ideological weapon for reform movements and modernisation, but it did not significantly influence actual astronomical research.

The first modern astronomical institutions in China were established by imperialist powers. In 1873, France established the Xujiahui Observatory (Xujiahui Tianwentai 徐家彙天文臺) in Shanghai, and in 1900 another observatory was established on Sheshan 佘山. In 1894, Japan invaded Taiwan and set up a meteorological station in Taipei. In 1900, Germany established a meteorological observatory in Qingdao 青島, Shandong. These institutions primarily provided intelligence for naval operations along the Chinese coast. The imperialists also looted the few astronomical instruments China possessed. After the Eight-Nation Alliance (baguo lianjun 八國聯軍) invaded Beijing in 1900, French and German troops took all the instruments of the Directorate of Astronomy. The instruments taken by the French were returned after three years, but those seized by the Germans were not returned to China until after World War I. After such a calamity, the Qing government's astronomical institutions were left on the brink of collapse.

After the 1911 Revolution (Xinhai geming 辛亥革命), China adopted the globally used Gregorian calendar from 1912 but continued to use the Republic of China era years (Minguo jinian 民國紀年; 1912 as the First Year of the Republic, Minguo yuannian 民國元年). The Beiyang Government renamed the imperial Directorate of Astronomy to the Central Observatory (Zhongyang Guanxiangtai 中央觀象臺). The Central Observatory's work was limited to compiling the calendar and publishing the Guangxiang suishu 觀象歲書 (Astronomical Yearbook).

Following the May Fourth Movement (wusi yundong 五四運動) of 1919, as scientific and democratic ideals rose, the Chinese astronomical community became increasingly active. On October 30, 1922, the Chinese Astronomical Society (Zhongguo tianwen xuehui 中國天文學會) was officially established in Beijing, electing Gao Lu 高魯 (1877-1947) as president and Qin Fen 秦汾 (1882-1973) as vice president. The Society began publishing the Chinese Astronomical Society Bulletin (Zhongguo tianwen xuehui huibao 中國天文學會會報) in 1924. It was renamed The Universe (Yuzhou 宇宙) in 1930 and continued publication until 1949.

In 1924, the Chinese government took over the meteorological observatory in Qingdao, renaming it the Qingdao Observatory (Qingdao Guanxiangtai 青島觀象臺). In 1926, the Mathematics Department (Shuxue Xi 數學系) of Sun Yat-sen University (Zhongshan Daxue 中山大學) in Guangzhou expanded into a Department of Mathematics and Astronomy (Suan-tian Xi 數天系), and in 1929 an observatory was established. In 1947, an Astronomy Department (Tianwen Xi 天文系) was formed. In 1928, the Astronomical Research Institute (Tianwen Yanjiusuo 天文研究所) was founded in the capital, Nanjing, and in 1934 the Purple Mountain Observatory (Zijinshan Tianwentai 紫金山天文臺) was completed. After the completion of this observatory, the Central Observatory in Beijing was converted into an Astronomy Exhibition Hall (Tianwen Chenlieguan 天文陳列館).

After the Sino-Japanese War began in 1937, the Purple Mountain Observatory was relocated to Kunming 昆明, Yunnan, in 1938, and an observation station (guancezhan 觀測站) was established on Phoenix Mountain (Fenghuangshan 鳳凰山). During the eight years of the War of Resistance against Japan, these astronomical institutions were severely damaged. After the war, they did not recover quickly.