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Monday, January 13, 2020

Chinese calendar

From Wikipedia, the free encyclopedia
 
See caption
2017 Chinese calendar
 
Page of a Chinese calendar
 
The traditional China calendar (officially known as the Agricultural Calendar [農曆; 农历; Nónglì; 'farming calendar']), or Former Calendar (舊曆; 旧历; Jiùlì), Traditional Calendar (老曆; 老历; Lǎolì) or Lunar Calendar (陰曆; 阴历; Yīnlì; 'yin calendar'), is a lunisolar calendar which reckons years, months and days according to astronomical phenomena. It is defined by GB/T 33661-2017, "Calculation and promulgation of the Chinese calendar", issued by the Standardisation Administration of China on 12 May 2017. 

Although modern-day China uses the Gregorian calendar, the traditional Chinese calendar governs holidays—such as the Lantern Festival—in both China and in overseas Chinese communities. It also gives the traditional Chinese nomenclature of dates within a year, which people use for selecting auspicious days for weddings, funerals, moving, or starting a business. 

Like Chinese characters, variants of this calendar are used in different parts of the Chinese cultural sphere. Korea, Vietnam, and the Ryukyu Islands adopted the calendar, and it evolved into Korean, Vietnamese, and Ryukyuan calendars. The main difference from the traditional Chinese calendar is the use of different meridians, which leads to some astronomical events—and calendar events based on them—falling on different dates. The traditional Japanese calendar also derived from the Chinese calendar (based on a Japanese meridian), but its official use in Japan was abolished in 1873 as part of reforms after the Meiji Restoration. Calendars in Mongolia and Tibet have absorbed elements of the traditional Chinese calendar, but are not direct descendants of it.

Days begin and end at midnight, and months begin on the day of the new moon. Years begin on the second (or third) new moon after the winter solstice. Solar terms govern the beginning and end of each month. Written versions in ancient China included stems and branches of the year and the names of each month, including leap months as needed. Characters indicated whether a month was long (, 30 days) or short (, 29 days); stem branches for the first, eleventh, and 21st days, and the date, stem branch and time of the solar terms. 

History


Solar calendars

See caption
Five-phase and four-quarter calendars
 
The traditional Chinese calendar was developed between 771 and 476 BC, during the Spring and Autumn period of the Eastern Zhou dynasty. Before the Zhou dynasty, solar calendars were used.

One version of the solar calendar is the five-elements calendar (五行曆; 五行历), which derives from the Wu Xing. A 365-day year was divided into five phases of 73 days, with each phase corresponding to a Day 1 Wu Xing element. A phase began with a governing-element day (行御), followed by six 12-day weeks. Each phase consisted of two three-week months, making each year ten months long. Years began on a jiǎzǐ (甲子) day (and a 72-day wood phase), followed by a bǐngzǐ day (丙子) and a 72-day fire phase; a wùzǐ (戊子) day and a 72-day earth phase; a gēngzǐ (庚子) day and a 72-day metal phase, and a rénzǐ day (壬子) followed by a water phase. Other days were tracked using the Yellow River Map (He Tu). 

Another version is a four-quarters calendar (四時八節曆; 四时八节历; 'four sections, eight seasons calendar', or 四分曆; 四分历). Weeks were ten days long, with one month consisting of three weeks. A year had 12 months, with a ten-day week intercalated in summer as needed to keep up with the tropical year. The 10 Heavenly Stems and 12 Earthly Branches were used to mark days.

A third version is the balanced calendar (調曆; 调历). A year was 365.25 days, and a month was 29.5 days. After every 16th month, a half-month was intercalated. According to oracle bone records, the Shang dynasty calendar (c. 1600 – c. 1046 BC) was a balanced calendar with 12 to 14 months in a year; the month after the winter solstice was Zhēngyuè.

Lunisolar calendars

The first lunisolar calendar was the Zhou calendar (周曆; 周历), introduced under the Zhou dynasty. This calendar set the beginning of the year at the day of the new moon before the winter solstice. It also set the shàngyuán as the winter solstice of a dīngsì year, making the year it was introduced around 2,758,130.

Several competing lunisolar calendars were also introduced, especially by states fighting Zhou control during the Warring States period. The state of Lu issued its own Lu calendar(魯曆; 鲁历). Jin issued the Xia calendar (夏曆; 夏历) in AD 102, with a year beginning on the day of the new moon nearest the March equinox. Qin issued the Zhuanxu calendar (顓頊曆; 颛顼历), with a year beginning on the day of the new moon nearest the winter solstice. Song's Yin calendar (殷曆; 殷历) began its year on the day of the new moon after the winter solstice.

These calendars are known as the six ancient calendars (古六曆; 古六历), or quarter-remainder calendars, (四分曆; 四分历; sìfēnlì), since all calculate a year as ​365 14 days long. Months begin on the day of the new moon, and a year has 12 or 13 months. Intercalary months (a 13th month) are added to the end of the year. The Qiang and Dai calendars are modern versions of the Zhuanxu calendar, used by mountain peoples. 

Qin and early Han dynasties

After Qin Shi Huang unified China under the Qin dynasty in 221 BC, the Qin calendar (秦曆; 秦历) was introduced. It followed most of the rules governing the Zhuanxu calendar, but the month order was that of the Xia calendar; the year began with month 10 and ended with month 9, analogous to a Gregorian calendar beginning in October and ending in September. The intercalary month, known as the second Jiǔyuè (後九月; 后九月; 'later Jiǔyuè'), was placed at the end of the year. The Qin calendar was used into the Han dynasty. 

Han-Ming dynasties and Taichu calendar

Emperor Wu of Han r. 141 – 87 BC introduced reforms halfway through his reign. His Taichu Calendar (太初曆; 太初历; 'grand beginning calendar') defined a solar year as ​365 3851539 days, and the lunar month was ​29 4381 days. This calendar introduced the 24 solar terms, dividing the year into 24 equal parts. Solar terms were paired, with the 12 combined periods known as climate terms. The first solar term of the period was known as a pre-climate, and the second was a mid-climate. Months were named for the mid-climate to which they were closest, and a month without a mid-climate was an intercalary month. 

The Taichu calendar established a framework for traditional calendars, with later calendars adding to the basic formula. The Dàmíng Calendar (大明曆; 大明历; 'brightest calendar'), created in the Liang dynasty by Zu Chongzhi, introduced the equinoxes. The use of a syzygy to determine the lunar month was first described in the Tang dynasty Wùyín Yuán Calendar (戊寅元曆; 戊寅元历; 'earth tiger epoch calendar'). The Yuan dynasty Shòushí calendar (授時曆; 授时历; 'teaching time calendar') used spherical trigonometry to find the length of the tropical year. The calendar had a 365.2425-day year, identical to the Gregorian calendar.

Modern calendars

Although the Chinese calendar lost its place as the country's official calendar at the beginning of the 20th century,[10] its use has continued. The Republic of China adopted UTC+08:00 in 1928, but changed to a single time zone; some calendars followed the last calendar of the Qing dynasty, published in 1908. This caused confusion about the date of the 1978 Mid-Autumn Festival, and those areas then switched to the UTC+8-based calendar.

Shíxiàn calendar

During the late Ming dynasty, Xu Guangqi and his colleagues worked out a new calendar based on Western astronomical arithmetic; however, the new calendar was not released before the end of the dynasty. In the early Qing dynasty, Johann Adam Schall von Bell submitted the calendar to the Shunzhi Emperor. The Qing government issued it as the Shíxiàn (seasonal) calendar.

In this calendar, the solar terms are 15° each along the ecliptic and it can be used as a solar calendar. However, the length of the climate term near perihelion is less than 30 days and there may be two mid-climate terms. The Shíxiàn calendar changed the mid-climate-term rule to "decides the month in sequence, except the intercalary month."[This quote needs a citation] The present traditional calendar follows the Shíxiàn calendar, except:
  1. The baseline is Chinese Standard Time, rather than Beijing local time.
  2. Astronomical data is used, rather than mathematical calculations.

Proposals

To optimize the Chinese calendar, astronomers have proposed a number of changes. Gao Pingzi (高平子; 1888–1970), a Chinese astronomer who co-founded the Purple Mountain Observatory, proposed that month numbers be calculated before the new moon and solar terms be rounded to the day. Since the intercalary month is determined by the first month without a mid-climate and the mid-climate time varies by time zone, countries which adopted the calendar but calculate with their own time could vary from the time in China.

Outlying areas

Calendars of ethnic groups in the mountains and plateaus of southwestern China and the grasslands of northern China are based on their phenology and algorithms of traditional calendars of different periods, particularly the Tang and pre-Qin dynasties.

Structure


Elements

Elements of the traditional Chinese calendar are:
  • Day, from one midnight to the next
  • Month, the time from one new moon to the next. These synodic months are about ​29 1732 days long.
  • Date, when a day occurs in the month. Days are numbered in sequence from 1 to 29 (or 30).
  • Year, the time of one revolution of the earth around the sun. It is measured from the first day of spring (lunisolar year) or the winter solstice (solar year). A year is about ​365 31128 days.
  • Zodiac, ​112 year, or 30° on the ecliptic. A zodiac is about ​30 716 days.
  • Solar term, ​124 year, or 15° on the ecliptic. A solar term is about ​15 732 days.
  • Calendar month, when a month occurs within a year. Some months may be repeated.
  • Calendar year, when it is agreed that one year ends and another begins. The year begins on the first day of spring, defined as the second (sometimes third) new moon after the winter solstice. A calendar year is 353–355 or 383–385 days long.
The Chinese calendar is lunisolar, similar to the Hindu and Hebrew calendars.

Features

The movements of the sun, moon, Mercury, Venus, Mars, Jupiter and Saturn (known as the seven luminaries) are the references for calendar calculations.
  • The distance between Mercury and the sun is less than 30° (the sun's height at chénshí:辰時, 8:00 to 10:00 am), so Mercury was sometimes called the "chen star" (); it is more commonly known as the "water star" (水星).
  • Venus appears at dawn and dusk, and is known as the "bright star" (啟明; 启明) or "long star" (長庚; 长庚).
  • Mars looks like fire and occurs irregularly, and is known as the "fire star" (熒惑; 荧惑 or 火星). Mars is the punisher in Chinese mythology. When Mars is near Antares (心宿二), it is a bad omen and can forecast the death of an emperor or removal of a chancellor (荧惑).
  • The period of Jupiter's revolution is 11.86 years, so Jupiter is called the "age star" (歲星; 岁星); 30° of Jupiter's revolution is about a year on earth.
  • The period of Saturn's revolution is about 28 years. Saturn, known as the "guard star" (鎮星), guards one of the 28 mansions every year.
The Big Dipper is the celestial compass, and its handle's direction determines the season and month. The stars are divided into Three Enclosures and 28 Mansions according to their location in the sky relative to Ursa Minor, at the centre. Each mansion is named with a character describing the shape of its principal asterism. The Three Enclosures are Purple Forbidden, (紫微), Supreme Palace (太微), and Heavenly Market. (天市) The eastern mansions are , , , , , , . Southern mansions are , , , , , , . Western mansions are , , , , , , . Northern mansions are , , , , , , . The moon moves through about one lunar mansion per day, so the 28 mansions were also used to count days. In the Tang dynasty, Yuan Tiangang (袁天罡) matched the 28 mansions, seven luminaries and yearly animal signs to yield combinations such as "horn-wood-flood dragon" (). 

Codes

Several coding systems are used to avoid ambiguity. The Heavenly Stems is a decimal system. The Earthly Branches, a duodecimal system, mark dual hours (shí, ; or shíchen (時辰; 时辰)) and climatic terms. The 12 characters progress from the first day with the same branch as the month (first Yín day () of Zhēngyuè; first Mǎo day () of Èryuè), and count the days of the month.

The stem-branches is a sexagesimal system. The Heavenly Stems and Earthly Branches make up 60 stem-branches. The stem-branches mark days and years. The five elements of the Wu Xing are assigned to each of the stems, branches and stem-branches. 

Day

See caption
Explanatory chart for traditional Chinese time
China has used the Western hour-minute-second system to divide the day since the Qing dynasty. Several era-dependent systems had been in use; systems using multiples of twelve and ten were popular, since they could be easily counted and aligned with the Heavenly Stems and Earthly Branches.

Week

As early as the Bronze-Age Xia dynasty, days were grouped into nine- or ten-day weeks known as xún (). Months consisted of three xún. The first 10 days were the early xún (上旬), the middle 10 the mid xún (中旬), and the last nine (or 10) days were the late xún (下旬). Japan adopted this pattern, with 10-day-weeks known as jun (). In Korea, they were known as sun (,).

The structure of xún led to public holidays every five or ten days. During the Han dynasty, officials were legally required to rest every five days (twice a xún, or 5–6 times a month). The name of these breaks became huan (; , "wash").

Grouping days into sets of ten is still used today in referring to specific natural events. "Three Fu" (三伏), a 29–30-day period which is the hottest of the year, reflects its three-xún length. After the winter solstice, nine sets of nine days were counted to calculate the end of winter.

The seven-day week was adopted from the Hellenistic system by the 4th century CE, although its source is unclear. It was again transmitted to China in the 8th century by Manichaeans via Kangju (a Central Asian kingdom near Samarkand), and is the most-used system in modern China. 

Month

Months are defined by the time between new moons, which averages approximately ​29 1732 days. There is no specified length of any particular Chinese month, so the first month could have 29 days (short month, 小月) in some years and 30 days (long month, 大月) in other years.

A 12-month-year using this system has 354 days, which would drift significantly from the tropical year. To fix this, traditional Chinese years have a 13-month year approximately once every three years. The 13-month version has the same alternation of long and short months, but adds a 30-day leap month (閏月; rùnyuè) at the end of the year. Years with 12 months are called common years, and 13-month years are known as long years. 

Although most of the above rules were used until the Tang dynasty, different eras used different systems to keep lunar and solar years aligned. The synodic month of the Taichu calendar was ​29 4381 days long. The 7th-century, Tang-dynasty Wùyín Yuán Calendar was the first to determine month length by synodic month instead of the cycling method. Since then, month lengths have primarily been determined by observation and prediction. 

The days of the month are always written with two characters and numbered beginning with 1. Days one to 10 are written with the day's numeral, preceded by the character Chū (); Chūyī (初一) is the first day of the month, and Chūshí () the 10th. Days 11 to 20 are written as regular Chinese numerals; Shíwǔ (十五) is the 15th day of the month, and Èrshí (二十) the 20th. Days 21 to 29 are written with the character Niàn (廿) before the characters one through nine; Niànsān (廿三), for example, is the 23rd day of the month. Day 30 (as applicable) is written as the numeral Sānshí (三十). 

History books use days of the month numbered with the 60 stem-branches:
天聖元年....二月...., 奉安太祖、太宗御容于南京鴻慶宮.
Tiānshèng 1st year....Èryuè....Dīngsì, the emperor's funeral was at his temple, and the imperial portrait was installed in Nanjing's Hongqing Palace.

Because astronomical observation determines month length, dates on the calendar correspond to moon phases. The first day of each month is the new moon. On the seventh or eighth day of each month, the first-quarter moon is visible in the afternoon and early evening. In the 15th or 16th day of each month, the full moon is visible all night. On the 22nd or 23rd day of each month, the last-quarter moon is visible late at night and in the morning. 

Since the beginning of the month is determined by the new moon occurs, other countries using this calendar use their own time standards to calculate it; this results in deviations. The first new moon in 1968 was at 16:29 UTC on January 29. Since North Vietnam used UTC+07:00 to calculate their Vietnamese calendar and South Vietnam used UTC+08:00 (Beijing time) to calculate theirs, North Vietnam began the Tết holiday at 29 January at 23:29 and South Vietnam began it on 30 January at 00:15. The time difference allowed asynchronous attacks in the Tet Offensive.

Names of months

Lunar months were originally named according to natural phenomena. Current naming conventions use numbers as the month names. Every month is also associated with one of the twelve Earthly Branches.

Month number Starts on Gregorian date Phenological name Earthly Branch name Modern name
1 between 21 January – 20 February 陬月; zōuyuè; 'corner month'. square of Pegasus month 寅月; yínyuè; 'tiger month' 正月; zhēngyuè; 'first month'
2 between 20 February – 21 March 杏月; xìngyuè; 'apricot month' 卯月; mǎoyuè; 'rabbit month' 二月; èryuè; 'second month'
3 between 21 March – 20 April 桃月; táoyuè; 'peach month' 辰月; chényuè; 'dragon month' 三月; sānyuè; 'third month'
4 between 20 April – 21 May 梅月; méiyuè; 'plum flower month' 巳月; sìyuè; 'snake month' 四月; sìyuè; 'fourth month'
5 between 21 May – 21 June 榴月; liúyuè; 'pomegranate month' 午月; wǔyuè; 'horse month' 五月; wǔyuè; 'fifth month'
6 between 21 June – 23 July 荷月; héyuè; 'lotus month' 未月; wèiyuè; 'goat month' 六月; liùyuè; 'sixth month'
7 between 23 July – 23 August 蘭月; 兰月; lányuè; 'orchid month' 申月; shēnyuè; 'monkey month' 七月; qīyuè; 'seventh month'
8 between 23 August – 23 September 桂月; guìyuè; 'osmanthus month' 酉月; yǒuyuè; 'rooster month' 八月; bāyuè; 'eighth month'
9 between 23 September – 23 October 菊月; júyuè; 'chrysanthemum month' 戌月; xūyuè; 'dog month' 九月; jiǔyuè; 'ninth month'
10 between 23 October – 22 November 露月; lùyuè; 'dew month' 亥月; hàiyuè; 'pig month' 十月; shíyuè; 'tenth month'
11 between 22 November – 22 December 冬月; dōngyuè; 'winter month'; 葭月; jiāyuè; 'reed month' 子月; zǐyuè; 'rat month' 十一月; shíyīyuè; 'eleventh month'
12 between 22 December – 21 January 冰月; bīngyuè; 'ice month' 丑月; chǒuyuè; 'ox month' 臘月; 腊月; làyuè; 'end-of-year month'

Chinese lunar date conventions

Though the numbered month names are often used for the corresponding month number in the Gregorian calendar, it is important to realize that the numbered month names are not interchangeable with the Gregorian months when talking about lunar dates.
One may even find out the heavenly stem and earthly branch corresponding to a particular day in the month, and those corresponding to its month, and those to its year, in order to determine the Four Pillars of Destiny associated with it, for which the Tung Shing, also referred to as the Chinese Almanac of the year, or the Huangli, and containing the essential information concerning Chinese astrology, is the most convenient publication to consult. Days rotate through a sexagenary cycle marked by a coordination between heavenly stems and earthly branchs, hence the referral to the Four Pillars of Destiny as, "Bazi", or "Birth Time Eight Characters", with each pillar consisting of a character for its corresponding heavenly stem, and another for its earthly branch. Since Huangli days are sexagenaric, their order is quite independent from their numeric order in each month, and from their numeric order within a week (referred to as True Animals with relation to the Chinese zodiac). Therefore, it does require painstaking calculation for one to arrive at the Four Pillars of Destiny of a particular given date, which rarely outpace the convenience of simply consulting the Huangli by looking up its Gregorian date.

Solar term

The solar year (; ; Suì), the time between winter solstices, is divided into 24 solar terms known as jié qì. Each term is a 15° portion of the ecliptic. These solar terms mark both Western and Chinese seasons as well as equinoxes, solstices, and other Chinese events. The even solar terms (marked with "Z") are considered the major terms, while the odd solar terms (marked with "J") are deemed minor. The solar terms qīng míng (清明) on April 5 and dōng zhì (冬至) on December 22 are both celebrated events in China.

24 Jié Qì
Number Name Chinese Marker Event Date
J1 Lì chūn 立春 Beginning of spring February 4
Z1 Yǔ shuĭ 雨水 Rain water February 19
J2 Jīng zhé 惊蛰 Waking of insects March 6
Z2 Chūn fēn 春分 March equinox March 21
J3 Qīng míng 清明 Pure brightness April 5
Z3 Gŭ yŭ 谷雨 Grain rain April 20
J4 Lì xià 立夏 Beginning of summer May 6
Z4 Xiǎo mǎn 小满 Grain full May 21
J5 Máng zhòng 芒种 Grain in ear June 6
Z5 Xià zhì 夏至 June solstice June 22
J6 Xiǎo shǔ 小暑 Slight heat July 7
Z6 Dà shǔ 大暑 Great heat July 23
J7 Lì qiū 立秋 Beginning of autumn August 8
Z7 Chǔ shǔ 处署 Limit of heat August 23
J8 Bái lù 白露 White dew September 8
Z8 Qiū fēn 秋分 September equinox September 23
J9 Hán lù 寒露 Cold dew October 8
Z9 Shuāng jiàng 霜降 Descent of frost October 24
J10 Lì dōng 立冬 Beginning of winter November 8
Z10 Xiăo xuě 小雪 Slight snow November 22
J11 Dà xuě 大雪 Great snow December 7
Z11 Dōng zhì 冬至 December solstice December 22
J12 Xiăo hán 小寒 Slight cold January 6
Z12 Dà hán 大寒 Great cold January 20

Solar year

The calendar solar year, known as the suì, (岁) begins at the December solstice and proceeds through the 24 solar terms. Due to the fact that the speed of the Sun's apparent motion in the elliptical is variable, the time between major solar terms is not fixed. This variation in time between major solar terms results in different solar year lengths. There are generally 11 or 12 complete months, plus two incomplete months around the winter solstice, in a solar year. The complete months are numbered from 0 to 10, and the incomplete months are considered the 11th month. If there are 12 complete months in the solar year, it is known as a leap solar year, or leap suì.
 
Due to the inconsistencies in the length of the solar year, different versions of the traditional calendar might have different average solar year lengths. For example, one solar year of the 1st century BC Tàichū calendar is ​365 3851539 (365.25016) days. A solar year of the 13th-century Shòushí calendar is ​365 97400 (365.2425) days, identical to the Gregorian calendar. The additional .00766 day from the Tàichū calendar leads to a one-day shift every 130.5 years.

Pairs of solar terms are climate terms, or solar months. The first solar term is "pre-climate" (節氣; 节气; Jiéqì), and the second is "mid-climate" (中氣; 中气; Zhōngqì).

The first month without a mid-climate is the leap, or intercalary, month. In other words, the first month that doesn't include a major solar term is the leap month. Leap months are numbered with rùn , the character for "intercalary", plus the name of the month they follow. In 2017, the intercalary month after month six was called Rùn Liùyuè, or "intercalary sixth month" (六月) and written as 6i or 6+. The next intercalary month (in 2020, after month four) will be called Rùn Sìyuè (四月) and written 4i or 4+

Lunisolar year

The lunisolar year begins with the first spring month, Zhēngyuè (正月; 'capital month'), and ends with the last winter month, Làyuè (臘月; 腊月; 'sacrificial month'). All other months are named for their number in the month order. If a leap month falls after month 11—as it will in 2033—the 11th month will be Shíèryuè (十二月; 'twelfth month'), and the leap month will be Làyuè.

Years were traditionally numbered by the reign in ancient China, but this was abolished after the founding of the People's Republic of China in 1949. For example, the year from 8 February 2016 to 27 January 2017 was a Bǐngshēn year (丙申) of 12 months or 354 days.

During the Tang Dynasty, the Earthly Branches were used to mark the months from December 761 to May 762. Over this period, the year began with the winter solstice.

Age reckoning

In China, a person's official age is based on the Gregorian calendar; for traditional use, age is based on the Chinese sui calendar. At birth, a child is considered the first year of lifetime using ordinal number (instead of "zero" using cardinal number); after each Chinese New Year, one year is added to their traditional age. Because of the potential for confusion, infant ages are often given in months instead of years. 

After the Gregorian calendar's introduction in China, the Chinese traditional age was referred to as the "nominal age" (虛歲; 虚岁; xūsuì; 'incomplete age') and the Gregorian age was known as the "real age" (實歲; 实岁; shísùi; 'whole age'). 

Year-numbering systems

 
Eras
In ancient China, years were numbered from a new emperor's assumption of the throne or an existing emperor's announcement of a new era name. The first recorded reign title was Jiànyuán (建元; 'founding era'), from 140 BC; the last reign title was Xuāntǒng (宣統; 宣统; 'announcing unification'), from 1908 AD. The era system was abolished in 1912, after which the current or Republican era was used.

Stem-branches
The 60 stem-branches have been used to mark the date since the Shang Dynasty (1600-1046 BC). Astrologers knew that the orbital period of Jupiter is about 4,332 days. Since 4332 is 12 × 361, Jupiter's orbital period was divided into 12 years (; ; suì) of 361 days each. The stem-branches system solved the era system's problem of unequal reign lengths.

Continuous numbering
Nomenclature similar to that of the Christian era has occasionally been used:
  • Huángdì year (黄帝紀年), starting at the beginning of the reign of the Yellow Emperor with year 1 at 2697 (or 2698) BC
  • Yáo year (唐堯紀年), starting at the beginning of the reign of Emperor Yao (year 1 at 2156 BC)
  • Gònghé year (共和紀年), starting at the beginning of the Gonghe Regency (year 1 at 841 BC)
  • Confucius year (孔子紀年), starting at the birth year of Confucius (year 1 at 551 BC)
  • Unity year (統一紀年), starting at the beginning of the reign of Qin Shi Huang (year 1 at 221 BC)
No reference date is universally accepted. The most popular is the Gregorian calendar (公曆; 公历; gōnglì; 'common calendar'). 

On 2 January 1912, Sun Yat-sen announced changes to the official calendar and era. 1 January was 14 Shíyīyuè 4609 Huángdì year, assuming a year 1 of 2698 BC. The change was adopted by many overseas Chinese communities, such as San Francisco's Chinatown.

During the 17th century, the Jesuits tried to determine the epochal year of the Han calendar. In his Sinicae historiae decas prima (published in Munich in 1658), Martino Martini (1614–1661) dated the ascension of the Yellow Emperor to 2697 BC and began the Chinese calendar with the reign of Fuxi (which, according to Martini, began in 2952 BC. Philippe Couplet's 1686 Chronological table of Chinese monarchs (Tabula chronologica monarchiae sinicae) gave the same date for the Yellow Emperor. The Jesuits' dates provoked interest in Europe, where they were used for comparison with Biblical chronology.[citation needed] Modern Chinese chronology has generally accepted Martini's dates, except that it usually places the reign of the Yellow Emperor at 2698 BC and omits his predecessors Fuxi and Shennong as "too legendary to include".

Publications began using the estimated birth date of the Yellow Emperor as the first year of the Han calendar in 1903, with newspapers and magazines proposing different dates. The province of Jiangsu counted 1905 as the year 4396 (using a year 0 of 2491 BC), and the newspaper Ming Pao (明報; 明报) reckoned 1905 as 4603 (using a year 0 of 2698 BC). Liu Shipei (劉師培, 1884–1919) created the Yellow Emperor Calendar, with year 0 as the birth of the emperor (which he determined as 2711 BC). There is no evidence that this calendar was used before the 20th century.[20] Liu calculated that the 1900 international expedition sent by the Eight-Nation Alliance to suppress the Boxer Rebellion entered Beijing in the 4611th year of the Yellow Emperor. 

Chinese New Year

The date of the Chinese New Year accords with the patterns of the solar calendar and hence is variable from year to year. However, there are two general rules that govern the date. Firstly, Chinese New Year transpires on the second new moon following the December solstice. If there is a leap month after the eleventh or twelfth month, then Chinese New Year falls on the third new moon after the December solstice. Alternatively, Chinese New Year will fall on the new moon that is closest to lì chūn, or the solar term that begins spring (typically falls on February 4). However, this rule is not as reliable since it can be difficult to determine which new moon is the closest in the case of an early or late Chinese New Year.

It has been found that Chinese New Year moves back by either 10, 11, or 12 days in some years. If it falls before January 21, then it moves forward in the next year by either 18, 19, or 20 days.

Phenology

The plum-rains season (梅雨), the rainy season in late spring and early summer, begins on the first bǐng day after Mangzhong (芒种) and ends on the first wèi day after Xiaoshu (小暑). The Three Fu (三伏; sānfú) are three periods of hot weather, counted from the first gēng day after the summer solstice. The first fu (初伏; chūfú) is 10 days long. The mid-fu (中伏; zhōngfú) is 10 or 20 days long. The last fu (末伏; mòfú) is 10 days from the first gēng day after the beginning of autumn. The Shujiu cold days (數九; shǔjǐu; 'counting to nine') are the 81 days after the winter solstice (divided into nine sets of nine days), and are considered the coldest days of the year. Each nine-day unit is known by its order in the set, followed by "nine" ().

Tropical year

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Tropical_year

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. This differs from the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars (the sidereal year) by about 20 minutes because of the precession of the equinoxes.

Since antiquity, astronomers have progressively refined the definition of the tropical year. The entry for "year, tropical" in the Astronomical Almanac Online Glossary (2015) states:
the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.
An equivalent, more descriptive, definition is "The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever the longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox and a new tropical year begins" (Borkowski 1991, p. 122).

The mean tropical year in 2000 was 365.24219 ephemeris days; each ephemeris day lasting 86,400 SI seconds. This is 365.24217 mean solar days (Richards 2013, p. 587).
 
 

History


Origin

The word "tropical" comes from the Greek tropikos meaning "turn" (tropic 1992). Thus, the tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead, and where it appears to "turn" in its annual seasonal motion. Because of this connection between the tropics and the seasonal cycle of the apparent position of the Sun, the word "tropical" also lent its name to the "tropical year". The early Chinese, Hindus, Greeks, and others made approximate measures of the tropical year. 

Early value, precession discovery

In the 2nd century BC Hipparchus measured the time required for the Sun to travel from an equinox to the same equinox again. He reckoned the length of the year to be 1/300 of a day less than 365.25 days (365 days, 5 hours, 55 minutes, 12 seconds, or 365.24667 days). Hipparchus used this method because he was better able to detect the time of the equinoxes, compared to that of the solstices (Meeus & Savoie 1992, p. 40). 

Hipparchus also discovered that the equinoctial points moved along the ecliptic (plane of the Earth's orbit, or what Hipparchus would have thought of as the plane of the Sun's orbit about the Earth) in a direction opposite that of the movement of the Sun, a phenomenon that came to be named "precession of the equinoxes". He reckoned the value as 1° per century, a value that was not improved upon until about 1000 years later, by Islamic astronomers. Since this discovery a distinction has been made between the tropical year and the sidereal year (Meeus & Savoie 1992, p. 40). 

Middle Ages and the Renaissance

During the Middle Ages and Renaissance a number of progressively better tables were published that allowed computation of the positions of the Sun, Moon and planets relative to the fixed stars. An important application of these tables was the reform of the calendar.

The Alfonsine Tables, published in 1252, were based on the theories of Ptolemy and were revised and updated after the original publication; the most recent update in 1978 was by the French National Centre for Scientific Research. The length of the tropical year was given as 365 solar days 5 hours 49 minutes 16 seconds (≈ 365.24255 days). This length was used in devising the Gregorian calendar of 1582 (Meeus & Savoie 1992, p. 41). 

In the 16th century Copernicus put forward a heliocentric cosmology. Erasmus Reinhold used Copernicus' theory to compute the Prutenic Tables in 1551, and gave a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days), based on the length of a sidereal year and the presumed rate of precession. This was actually less accurate than the earlier value of the Alfonsine Tables.

Major advances in the 17th century were made by Johannes Kepler and Isaac Newton. In 1609 and 1619 Kepler published his three laws of planetary motion (McCarthy & Seidelmann 2009, p. 26). In 1627, Kepler used the observations of Tycho Brahe and Waltherus to produce the most accurate tables up to that time, the Rudolphine Tables. He evaluated the mean tropical year as 365 solar days, 5 hours, 48 minutes, 45 seconds (365.24219 days; Meeus & Savoie 1992, p. 41).

Newton's three laws of dynamics and theory of gravity were published in his Philosophiæ Naturalis Principia Mathematica in 1687. Newton's theoretical and mathematical advances influenced tables by Edmund Halley published in 1693 and 1749 (McCarthy & Seidelmann 2009, pp. 26–28) and provided the underpinnings of all solar system models until Albert Einstein's theory of General relativity in the 20th century. 

18th and 19th century

From the time of Hipparchus and Ptolemy, the year was based on two equinoxes (or two solstices) a number of years apart, to average out both observational errors and periodic variations (caused by the gravitational pull of the planets, and the small effect of nutation on the equinox). These effects did not begin to be understood until Newton's time. To model short-term variations of the time between equinoxes (and prevent them from confounding efforts to measure long-term variations) requires precise observations and an elaborate theory of the apparent motion of the Sun. The necessary theories and mathematical tools came together in the 18th century due to the work of Pierre-Simon de Laplace, Joseph Louis Lagrange, and other specialists in celestial mechanics. They were able to compute periodic variations and separate them from the gradual mean motion. They could express the mean longitude of the Sun in a polynomial such as:
L0 = A0 + A1T + A2T2 days
where T is the time in Julian centuries. The derivative of this formula is an expression of the mean angular velocity, and the inverse of this gives an expression for the length of the tropical year as a linear function of T.

Two equations are given in the table. Both equations estimate that the tropical year gets roughly a half second shorter each century. 

Tropical year coefficients
Name Equation Date on which T = 0
Leverrier (Meeus & Savoie 1992, p. 42) Y = 365.24219647 − 6.24×106 T January 0.5, 1900, Ephemeris time
Newcomb (1898) Y = 365.24219879 − 6.14×106 T January 0, 1900, mean time

Newcomb's tables were sufficiently accurate that they were used by the joint American-British Astronomical Almanac for the Sun, Mercury, Venus, and Mars through 1983 (Seidelmann 1992, p. 317).

20th and 21st centuries

The length of the mean tropical year is derived from a model of the solar system, so any advance that improves the solar system model potentially improves the accuracy of the mean tropical year. Many new observing instruments became available, including
The complexity of the model used for the solar system must be limited to the available computation facilities. In the 1920s punched card equipment came into use by L. J. Comrie in Britain. For the American Ephemeris an electromagnetic computer, the IBM Selective Sequence Electronic Calculator was used since 1948. When modern computers became available, it was possible to compute ephemerides using numerical integration rather than general theories; numerical integration came into use in 1984 for the joint US-UK almanacs (McCarthy & Seidelmann 2009, p. 32). 

Einstein's General Theory of Relativity provided a more accurate theory, but the accuracy of theories and observations did not require the refinement provided by this theory (except for the advance of the perihelion of Mercury) until 1984. Time scales incorporated general relativity beginning in the 1970s (McCarthy & Seidelmann 2009, p. 37).

A key development in understanding the tropical year over long periods of time is the discovery that the rate of rotation of the earth, or equivalently, the length of the mean solar day, is not constant. William Ferrel in 1864 and Charles-Eugène Delaunay in 1865 predicted that the rotation of the Earth is being retarded by tides. This could be verified by observation only in the 1920's with the very accurate Shortt-Synchronome clock and later in 1930s when quartz clocks began to replace pendulum clocks as time standards (McCarthy & Seidelmann 2009, ch. 9).

Time scales and calendar

Apparent solar time is the time indicated by a sundial, and is determined by the apparent motion of the Sun caused by the rotation of the Earth around its axis as well as the revolution of the Earth around the Sun. Mean solar time is corrected for the periodic variations in the apparent velocity of the Sun as the Earths revolves in its orbit. The most important such time scale is Universal Time, which is the mean solar time at 0 degrees longitude (the Greenwich meridian). Civil time is based on UT (actually UTC), and civil calendars count mean solar days.

However the rotation of the Earth itself is irregular and is slowing down, with respect to more stable time indicators: specifically, the motion of planets, and atomic clocks.

Ephemeris time (ET) is the independent variable in the equations of motion of the solar system, in particular, the equations from Newcomb's work, and this ET was in use from 1960 to 1984 (McCarthy & Seidelmann 2009, p. 378). These ephemerides were based on observations made in solar time over a period of several centuries, and as a consequence represent the mean solar second over that period. The SI second, defined in atomic time, was intended to agree with the ephemeris second based on Newcomb's work, which in turn makes it agree with the mean solar second of the mid-19th century (McCarthy & Seidelmann 2009, pp. 81–2, 191–7). ET as counted by atomic clocks was given a new name, Terrestrial Time (TT), and for most purposes ET = TT = International Atomic Time + 32.184 SI seconds. Since the era of the observations the rotation of the Earth has slown down and the mean solar second has grown somewhat longer than the SI second. As a result the time scales of TT and UT1 build up a growing difference: the amount that TT is ahead of UT1 is known as ΔT, or Delta T. As of January 2017, TT is ahead of UT1 by 69.184 seconds (International Earth Rotation Service 2017; McCarthy & Seidelmann 2009, pp. 86–7).

As a consequence, the tropical year following the seasons on Earth as counted in solar days of UT is increasingly out of sync with expressions for equinoxes in ephemerides in TT.

As explained below, long-term estimates of the length of the tropical year were used in connection with the reform of the Julian calendar, which resulted in the Gregorian calendar. Participants in that reform were unaware of the non-uniform rotation of the Earth, but now this can be taken into account to some degree. The table below gives Morrison and Stephenson's (S & M) 2004 estimates and standard errors (σ) for ΔT at dates significant in the process of developing the Gregorian calendar.

Event Year Nearest S & M Year ΔT σ
Julian calendar begins −44 0 2h56m20s 4m20s
First Council of Nicaea 325 300 2h8m 2m
Gregorian calendar begins 1582 1600 2m 20s
low-precision extrapolation 4000
4h13m
low-precision extrapolation 10,000
2d11h

The low-precision extrapolations are computed with an expression provided by Morrison & Stephenson (2004)
ΔT in seconds = −20 + 32t2
where t is measured in Julian centuries from 1820. The extrapolation is provided only to show ΔT is not negligible when evaluating the calendar for long periods; Borkowski (1991, p. 126) cautions that "many researchers have attempted to fit a parabola to the measured ΔT values in order to determine the magnitude of the deceleration of the Earth's rotation. The results, when taken together, are rather discouraging."

Length of tropical year

One definition of the tropical year would be the time required for the Sun, beginning at a chosen ecliptic longitude, to make one complete cycle of the seasons and return to the same ecliptic longitude. 

Mean time interval between equinoxes

Before considering an example, the equinox must be examined. There are two important planes in solar system calculations: the plane of the ecliptic (the Earth's orbit around the Sun), and the plane of the celestial equator (the Earth's equator projected into space). These two planes intersect in a line. One direction points to the so-called vernal, northward, or March equinox which is given the symbol ♈︎ (the symbol looks like the horns of a ram because it used to be toward the constellation Aries). The opposite direction is given the symbol ♎︎ (because it used to be toward Libra). Because of the precession of the equinoxes and nutation these directions change, compared to the direction of distant stars and galaxies, whose directions have no measurable motion due to their great distance (see International Celestial Reference Frame).

The ecliptic longitude of the Sun is the angle between ♈︎ and the Sun, measured eastward along the ecliptic. This creates a relative and not an absolute measurement, because as the Sun is moving, the direction the angle is measured from is also moving. It is convenient to have a fixed (with respect to distant stars) direction to measure from; the direction of ♈︎ at noon January 1, 2000 fills this role and is given the symbol ♈︎0.

There was an equinox on March 20, 2009, 11:44:43.6 TT. The 2010 March equinox was March 20, 17:33:18.1 TT, which gives an interval - and a duration of the tropical year - of 365 days 5 hours 48 minutes 34.5 seconds (Astronomical Applications Dept., 2009). While the Sun moves, ♈︎ moves in the opposite direction . When the Sun and ♈︎ met at the 2010 March equinox, the Sun had moved east 359°59'09" while ♈︎ had moved west 51" for a total of 360° (all with respect to ♈︎0; Seidelmann 1992, p. 104, expression for pA). This is why the tropical year is 20 min. shorter than the sidereal year.

When tropical year measurements from several successive years are compared, variations are found which are due to the perturbations by the Moon and planets acting on the Earth, and to nutation. Meeus & Savoie (1992, p. 41) provided the following examples of intervals between March (northward) equinoxes:


days hours min s
1985–1986 365 5 48 58
1986–1987 365 5 49 15
1987–1988 365 5 46 38
1988–1989 365 5 49 42
1989–1990 365 5 51 06

Until the beginning of the 19th century, the length of the tropical year was found by comparing equinox dates that were separated by many years; this approach yielded the mean tropical year (Meeus & Savoie 1992, p. 42). 

Different tropical year definitions

If a different starting longitude for the Sun is chosen than 0° (i.e. ♈︎), then the duration for the Sun to return to the same longitude will be different. This is a second-order effect of the circumstance that the speed of the Earth (and conversely the apparent speed of the Sun) varies in its elliptical orbit: faster in the perihelion, slower in the aphelion. Now the equinox moves with respect to the perihelion (and both move with respect to the fixed sidereal frame). From one equinox passage to the next, the Sun completes not quite a full elliptic orbit. The time saved depends on where it starts in the orbit. If the starting point is close to the perihelion (such as the December solstice), then the speed is higher than average, and the apparent Sun saves little time for not having to cover a full circle: the "tropical year" is comparatively long. If the starting point is near aphelion, then the speed is lower and the time saved for not having to run the same small arc that the equinox has precessed is longer: that tropical year is comparatively short. 

The following values of time intervals between equinoxes and solstices were provided by Meeus & Savoie (1992, p. 42) for the years 0 and 2000. These are smoothed values which take account of the Earth's orbit being elliptical, using well-known procedures (including solving Kepler's equation). They do not take into account periodic variations due to factors such as the gravitational force of the orbiting Moon and gravitational forces from the other planets. Such perturbations are minor compared to the positional difference resulting from the orbit being elliptical rather than circular.(Meeus 2002, p. 362)


Year 0 Year 2000
Between two Northward equinoxes 365.242137 days 365.242374 days
Between two Northern solstices 365.241726 365.241626
Between two Southward equinoxes 365.242496 365.242018
Between two Southern solstices 365.242883 365.242740
Mean tropical year
(Laskar's expression)
365.242310 365.242189

Mean tropical year current value

The mean tropical year on January 1, 2000 was 365.2421897 or 365 ephemeris days, 5 hours, 48 minutes, 45.19 seconds. This changes slowly; an expression suitable for calculating the length of a tropical year in ephemeris days, between 8000 BC and 12000 AD is
where T is in Julian centuries of 36,525 days of 86,400 SI seconds measured from noon January 1, 2000 TT (in negative numbers for dates in the past; McCarthy & Seidelmann 2009, p. 18, calculated from planetary model of Laskar 1986).

Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360°. The process for finding an expression for the length of the tropical year is to first find an expression for the Sun's mean longitude (with respect to ♈︎), such as Newcomb's expression given above, or Laskar's expression (1986, p. 64). When viewed over a one-year period, the mean longitude is very nearly a linear function of Terrestrial Time. To find the length of the tropical year, the mean longitude is differentiated, to give the angular speed of the Sun as a function of Terrestrial Time, and this angular speed is used to compute how long it would take for the Sun to move 360° (Meeus & Savoie 1992, p. 42; Astronomical Almanac for the year 2011, L8). 

The above formulae give the length of the tropical year in ephemeris days (equal to 86,400 SI seconds), not solar days. It is the number of solar days in a tropical year that is important for keeping the calendar in synch with the seasons (see below). 

Calendar year

The Gregorian calendar, as used for civil and scientific purposes, is an international standard. It is a solar calendar that is designed to maintain synchrony with the mean tropical year (Dobrzycki 1983, p. 123). It has a cycle of 400 years (146,097 days). Each cycle repeats the months, dates, and weekdays. The average year length is 146,097/400 = ​365 97400 = 365.2425 days per year, a close approximation to the mean tropical year (Seidelmann 1992, pp. 576–81). 

The Gregorian calendar is a reformed version of the Julian calendar. By the time of the reform in 1582, the date of the vernal equinox had shifted about 10 days, from about March 21 at the time of the First Council of Nicaea in 325, to about March 11. According to North (1983), the real motivation for reform was not primarily a matter of getting agricultural cycles back to where they had once been in the seasonal cycle; the primary concern of Christians was the correct observance of Easter. The rules used to compute the date of Easter used a conventional date for the vernal equinox (March 21), and it was considered important to keep March 21 close to the actual equinox (North 1983, pp. 75–76).

If society in the future still attaches importance to the synchronization between the civil calendar and the seasons, another reform of the calendar will eventually be necessary. According to Blackburn and Holford-Strevens (who used Newcomb's value for the tropical year) if the tropical year remained at its 1900 value of 365.24219878125 days the Gregorian calendar would be 3 days, 17 min, 33 s behind the Sun after 10,000 years. Aggravating this error, the length of the tropical year (measured in Terrestrial Time) is decreasing at a rate of approximately 0.53 s per century. Also, the mean solar day is getting longer at a rate of about 1.5 ms per century. These effects will cause the calendar to be nearly a day behind in 3200. The number of solar days in a "tropical millennium" is decreasing by about 0.06 per millennium (neglecting the oscillatory changes in the real length of the tropical year). This means there should be fewer and fewer leap days as time goes on. A possible reform would be to omit the leap day in 3200, keep 3600 and 4000 as leap years, and thereafter make all centennial years common except 4500, 5000, 5500, 6000, etc. But the quantity ΔT is not sufficiently predictable to form more precise proposals (Blackburn & Holford-Strevens 2003, p. 692).

Equality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Equality_...