How to reorganize the calendar of ancient astronomy in China?

In a sense, the history of ancient astronomy in China is a history of calendar reform.

According to the ancient book Shang Shu Yao Dian in the Spring and Autumn Period, Emperor Yao organized a group of astronomical officials to observe the stars in the east, south, west and north directions for compiling calendars and forecasting seasons.

Summer, which was written at the latest in the Spring and Autumn Period, recorded the activities of astrology, meteorology, phenology, agriculture and so on in the order of 12 months.

The basic outline of the Xia calendar is that a year is divided into 12 months. Except for February 1 1 month and1February, the season and climate are all represented by the twilight, zenith, morning light and sunset of some remarkable stars every month.

Although this is not a scientific calendar, it is ok to call it a combination of phenological calendar and astronomical calendar, or more accurately, we have some experience in observing images and timing.

Yao Dian in Shangshu also records the ancient method of forecasting seasons by using prominent astrology to appear in the southern sky at dusk, which is the famous "four satellites". That is, knowing the four seasons, accurately dividing the solar terms of a year and applying them to social production.

It can be seen that at the latest in the late Shang Dynasty and early Zhou Dynasty, people have been quite sure to use astrology to predict the seasons.

As for the official calendar, there was a heavenly stems and earthly branches calendar in the Xia Dynasty, that is, the calendar was recorded repeatedly on the days of A, B, C, D, E, J, G, Xin, Ren and Q 10.

On the basis of heavenly stems and earthly branches in Xia Dynasty, Shang Dynasty developed into heavenly stems and earthly branches, that is, A, B, C, D 10 trunk and Zi, Ugly, Yin, Mao 12 branch were paired in turn, forming 60 trunk branches of A, Ugly, Bingyin and Ding Mao, which were circulated once a week for 60 days.

Scholars have the same view on the calendar of the Shang Dynasty: the Shang Dynasty recorded the day with branches, and the month with numbers; There are big moon and small moon, big moon 30, small moon 29; There are leap months and even big months; The leap month is placed at the end of the year and is called "March"; There is a fixed relationship between seasons and months.

On the basis of inheriting and developing the achievements of the Shang Dynasty in observing images and timing, the Zhou Dynasty promoted the production of calendars. The Zhou Dynasty invented a method to determine the important solar terms such as winter solstice and summer solstice by measuring the sun shadow with soil gauge, so as to set the length of the tropic year more accurately by calculation.

Astronomers in the Zhou Dynasty have mastered the method of calculating the full moon, the sun and the moon, and can determine the date of the new moon, which can be confirmed from the Book of Songs, reflecting the data of the Zhou Dynasty and even before it.

The book Xiaoya at the turn of October records:

At the turn of October, the new moon shines high and there is food every day.

This is the first time that the word "Shuoyue" appeared in China's classics, and it is also the first time that China clearly recorded an eclipse in 776 BC.

By the end of the Spring and Autumn Period to the Warring States Period, the regression period had been set at 365 days, and the method of setting seven leap months by 19 was found. On the basis of these achievements, the historical scientific calendar "seasonal calendar" was born. From the Warring States to the early Han Dynasty, the four-season calendar was widely used.

The emergence and application of seasonal calendar indicates that China calendar has entered a quite mature period. It embodies the wisdom and astronomical calendar level of ancient China people, and has very precious value in the world.

The first reform of the calendar was the "eighty-one-minute calendar" put forward by Luo and others during the period of Emperor Wu of the Western Han Dynasty. Because Emperor Wu of the Han Dynasty ordered the creation of a new calendar in the seventh year of Yuanfeng, namely 104 BC, the seventh year of Yuanfeng was changed to the first year of Taichu, and the end of 12 was defined as the end of Taichu Yuan, from the first month to the end of 12 every year.

This kind of calendar is called the original calendar. This calendar is 29 days long, so it is called "8 1 minute method" or "8 1 minute calendar".

Taichu calendar is the first calendar handed down in China with complete data. Compared with the quarterly calendar, its progress is as follows:

Taking the first month as the beginning of a year, the original 24 solar terms in China are distributed in 12 months, and the months without neutral atmosphere are regarded as leap months, thus making the months and seasons more reasonable.

Accurately measure the rendezvous period of planets. For example, Mercury is 1 15.87 days, which is only 0.0 1 day less than the current measured value1/5.88 days.

The mating cycle of 135 months is adopted, that is, the annual eclipse is 346.66 days, which is only 0.04 days different from the current measured value.

At the end of the Eastern Han Dynasty, the "dry elephant calendar" formulated by astronomer Liu Hong reduced the mantissa of the tropical year to 365,462 days for the first time. For the first time, the change of the speed of the moon movement was introduced into the calendar, which became the first calendar with the algorithm of determining the new moon.

This calendar also shows that the intersection angle between the ecliptic and the ecliptic is about 6 degrees, and it is inferred that an eclipse can only occur when the intersection angle between the moon and the ecliptic is within 15 degrees, which actually puts forward the concept of "food limit".

Zu Chongzhi, an astronomer in the Northern and Southern Dynasties, first quoted the precession discovered by Yu in the Eastern Jin Dynasty into his Da Ming Calendar, and determined that the annual difference of 45 years was 1 1 month. Although this figure is on the high side, Pioneer's performance is great.

The monthly length of the intersection measured in Zu Chongzhi is 27.2 1223 days, which is only one thousandth of the current measured value.

In the Sui Dynasty, when astronomer Liu Zhuo calculated the emperor's calendar, the age difference was more accurate, which was 75 years old. Liu Zhuo's "Emperor's Calendar" also takes into account the inconsistency between the sun and the moon. In order to get the exact time of the new moon, he created a quadratic difference interpolation formula with equal spacing.

This creation is of great significance not only in the history of ancient systems, but also in the history of Chinese mathematics.

The calendars worth introducing in Tang Dynasty are Dayan calendar and Xuan Ming calendar.

On the basis of large-scale astrometry, astronomers in the Tang Dynasty wrote the first draft of Great Yan Li in 727. After they died, Chen and I compiled it into a book.

"Dayan Calendar" compiled the solar motion table with constant air, and completed this calculation with one action, and invented the unequal interval quadratic difference interpolation method. Dayanli also uses the table of sine function properties and the approximate interpolation method of cubic difference to deal with the uneven motion of planets.

Dayan calendar is known as the "crown of the Tang Dynasty" because of its innovation, and it has become a model of later calendars because of its clear organization.

In 822 AD, the Xuan Ming Calendar compiled by Xu Ang, an official of the Tang Dynasty, came out, which is another excellent calendar after Dayan Calendar in the Tang Dynasty.

It gives the number of days in the near month and the intersection month, which are 27.55455 days and 27.25438+022 days respectively. In particular, it is famous for putting forward three differences of solar eclipse, namely instantaneous difference, gas difference and engraving difference, which improves the accuracy of calculating solar eclipse.

In the Song Dynasty, there were 18 kinds of calendars published in more than 300 years, among which the Unified Calendar formulated by the astronomer Yang Zhongfu in the Southern Song Dynasty was the best.

The regression age of the Unified Calendar was 365.2425 days, which was the most accurate value in the world at that time. The calendar also points out that the length of the tropic year is gradually changing, and its value was large in ancient times, but it is small today.

The most innovative calendar in the Song Dynasty is the "Twelve-Qi Calendar" proposed by Shen Kuo, a famous scientist in the Northern Song Dynasty.

In the calendar issued by China in the past dynasties, 12 months are distributed in four seasons: spring, summer, autumn and winter, and each season has three months. In the case of leap month, the leap month season is four months. There are four solar terms in astronomy: beginning of spring, Changxia, beginning of autumn and beginning of winter, namely beginning of spring, long summer, beginning of autumn and beginning of winter. Therefore, it is difficult to unify the contradictions between the two on the calendar.

In view of this shortcoming, Shen Kuo proposed a calendar with "Twelve Qi" as the year, which was later called "Twelve Qi Calendar". It is a kind of solar calendar, which not only conforms to the actual horoscope and season, but also serves the production activities more conveniently. Unfortunately, traditional habits are too powerful to be promulgated and implemented.

The calendar in ancient China reached its peak in the Yuan Dynasty, when astronomers such as Guo Shoujing and Xun Wang worked out the calendar.

Guo Shoujing, Wang Xun and others not only summarized and used for reference the experience of predecessors, but also developed a large number of sky-observing instruments in the process of formulating the calendar method.

On this basis, Guo Shoujing presided over and participated in nationwide astronomical observation. He established 27 observation points all over the country, which were called "Four Seas Survey" at that time, and the distribution scope was unprecedented. The observation results of these stations laid a foundation for making an excellent time service calendar.

There are many innovations in Shoushi Calendar, such as abandoning the long-used Chronology of Shang Yuan; The old method of expressing the mantissa of astronomical data by fraction is cancelled; The apparent velocity of the sun on the ecliptic and the daily velocity of the moon around the earth are obtained by cubic difference interpolation. By using the sagittal cyclotomic method similar to a spherical triangle, the right and left latitudes of the sun can be obtained from the longitude of the yellow meridian, and the intersection angle of the right and left latitudes can be calculated.

The chronograph calendar was made in 1280, officially promulgated and implemented in the following year, and has been in use until 1644. After more than 360 years, it can be seen that the chronograph calendar is precise.

Emperor Chongzhen accepted the suggestion of does, and authorized Xu Guangqi to organize the calendar bureau and revise the calendar.

Besides choosing his own calendar, Xu Guangqi also hired Jesuits Deng, giacomo Rowe and others to work in the Origin Bureau. After five years of hard work, 46 kinds of 137 volumes of "Chongzhen almanac" were compiled.

The almanac introduces European astronomical knowledge, calculation methods and measurement units, such as Tycho's cosmic system and geometric calculation system; This paper introduces the clear concepts of circular earth, geographical longitude and geographical latitude.

The exact formulas of spherical triangle and plane triangle are introduced. The European common unit of measurement is adopted, with a circumference of 360 degrees, 96 minutes and 24 hours a day, and the hexadecimal number is below degrees and hours.

Xu Guangqi's calendar compilation is not only a major reform in China's ancient calendar compilation, but also lays a certain theoretical and ideological foundation for the development of ancient astronomy in China.

Tang Ruowang, an Italian Jesuit missionary in the early Qing Dynasty who was named "Doctor Guanglu" by Yongzheng Dynasty, revised the book to volume 103 and renamed it "Western New Law Almanac", which was presented to the Qing court together with his new law almanac, and was promulgated and implemented.

In the early Qing Dynasty, the new calendar was originally named "Book of Poets and Immortals". The book "Constitution" became the basic work for Qin officials and students to learn the new law and the theoretical basis for calculating the folk almanac at that time. It was used for more than 80 years before and after the early Qing Dynasty.