Algorithm series (18) using astronomical method to calculate Shiber (upper)

Shiber plays a very important role in the Chinese ancient calendar, this article will introduce the basic knowledge of Shiber and how to calculate the exact time of Shiber occurrence using vsop82/87 planetary operation theory.

The ancient Chinese calendars are dominated by the laws of the moon's operation, strictly according to synodic length definition month, but because the length of synodic and the length of the Earth's return can not be coordinated, will lead to the lunar calendar and the actual cold weather can not correspond, so the Wise Ancients of the Moon and the operation of the laws of the sun to develop the rules of the Chinese calendar. In this special combination of yin and yang of the calendar rules, Shiber plays a very important role, it is linked to the operation of the Moon and the law of the Sun link. It is precisely because of the Shiber combination of rules, so that the lunar calendar Four seasons and the Earth around the sun caused by the weather changes in the temperature and cold change, become China's thousands of years of production, the basis for life.

Shiber originated in the Yellow River basin of China. Far away in the spring and Autumn Period, the Ancients began to use Mid-spring, Midsummer, mid-autumn and midwinter four solar terms to guide the cultivation of farming. Later, after continuous improvement and improvement, to the Qin and Han dynasties, Shiber has been basically established. Before 104 A.D., Emperor Han Dynasty promulgated by Deng Ping and other people made "too early", formally Shiber set in the calendar, clear 24 solar terms of the astronomical position. The definition of Shiber astronomical position is that from the beginning of the sun yellow through zero, along the yellow through every 15 degrees of experience known as "a solar term." The Sun a return year running 360 degrees, a total of 24 solar terms, each Gregorian calendar month corresponds to 2 solar terms. Among them, the first solar term of the month is "seasonal", namely: beginning of spring, insects, qingming, summer, grain, slight heat, the beginning of autumn, Lu, dew, Winter, snow and Xiaohan and other 12 seasons; The second solar term for the month is "gas", namely: Rainwater, vernal equinox, Rain, Xiaoman, Summer solstice, great heat, Chushu, Autumnal Equinox, Frost, Snow, Winter solstice and Dahan 12 of the gas. "Season" and "gas" alternately appear, each lasted 15 days, people used to "seasonal" and "gas" collectively referred to as "solar terms."

In order to better understand the astronomical position of Shiber, we must first explain several astronomical concepts. The celestial sphere is an imaginary sphere introduced by people in order to study the position and movement of celestial bodies, and according to the position of the observation point (i.e. the center of the sphere), it can be divided into "celestial sphere" and "inner Earth" etc. Figure (1) is a simple sketch of the celestial sphere concept:

Fig. (1) schematic diagram of celestial sphere concept

One of the most commonly used coordinate systems in astronomy is the "inner Earth Sphere", which has the same autobiographical axis as the Earth and has an infinitely large radius in theory. The Earth's equator and north-south poles extend to the celestial sphere, corresponding to the equator and the poles of the north-South Sky. And the earth with latitude and longitude as the location, the celestial sphere also divides the latitude and longitude, named "Red Classics" and "Red latitude", the Earth on the longitude of the degree (seconds) as the unit, the Red by the time (minutes) as a unit. All celestial objects in the sky can be projected onto the celestial sphere, with the Red Meridian and the red Latitude as the celestial body position on the celestial sphere. The ecliptic (ecliptic) is a great circle of the Earth's orbit around the sun and the celestial sphere, and because the Earth orbits the Moon and other planets, the Earth's orbit is not strictly planar, Therefore, the definition of the ecliptic is as follows: The instantaneous mean orbital plane of the Earth-Moon's centroid around the sun and the great Circle of the celestial sphere. The two planes of the ecliptic and the celestial equator do not overlap, and there is an intersection of 23 degrees and 26 points, called the "obliquity angle". Due to the existence of the obliquity angle, the ecliptic and the celestial equator have two intersections on the Orb, which are the vernal equinox and autumnal equinox points. The ecliptic coordinate system can be formed on the celestial sphere, and the concept of latitude and longitude is also used in the ecliptic coordinate system, which is called "Huang Jing" and "Huang Wei" respectively. Celestial body from the vernal equinox point from the ecliptic to the east, the vernal equinox is 0 degrees yellow, along the ecliptic week is 360 degrees, the use of units is degrees, minutes and seconds. Huang Wei to the ecliptic measurement plane, north to 0 degrees to 90 degrees, south to 0 degrees to-90 degrees.

The plane of the ecliptic can be approximately understood as the plane of the Earth's orbit around the sun, the ecliptic coordinate system with the ecliptic as the base circle according to the observation center is the sun or the earth can also be divided into the daily heart coordinate system and the geocentric coordinate system, the corresponding celestial ecliptic coordinates are called "Japanese Heart Huangching, Japanese heart Huang Wei" and "Inner Earth Huangching, Inner Earth Huang Wei". Japanese heart Huangching and Huang Wei are easier to understand, because planets in the solar system orbit the sun, and the sun-centric projection of these planets into the celestial sphere is the simplest way to determine the position of a planet. However, the annual movement of human observation of the sun, is based on the earth as a reference to the Sun's annual position to calculate the movement of the Sun's orbit, the use of the Earth is actually Huangching and Geocentric Huang Wei, to understand the ancient calendar, understand this is very important. Figure (2) explains the cause of this visual illusion:

Fig. (2) schematic diagram of the visual position of the solar ecliptic