Algorithm series (20) Calculation of Chinese lunar calendar (ii.)

The so-called "astronomical algorithm", is to use the classical law of mechanics to deduce the orbit of the planets, the exact calculation of the position of the planet at any time, so as to obtain the time when an astronomical phenomenon occurs, such as the Sun and Moon, the celestial phenomenon is the Huangching (depending on the Yellow Sutra) to 0 of the moment. A set of theories capable of calculating the position of a planet at any given time is called the Ephemeris, and the more famous Ephemeris is the de series Ephemeris published by NASA's JPL, as well as the Swiss Ephemeris, which is extended by the Swiss observatory on the basis of DE406. It is usually not convenient to calculate the planet's position directly from the planet's orbit, what's more, most civil astronomical calculations do not use so many precise orbital parameters, so astronomers have deduced a lot of VSOP82 on the basis of these ephemeris, which can be used to make simple calculations, but can guarantee a certain precision of the planetary operation theory. /87 Solar System planetary Operation theory and elp-2000/82 theory of lunar movement, both sets of theories are already close to the De series Ephemeris in precision. On how to apply these two sets of ethics for Almanac, please refer to the third article in the "Calendar Generation Algorithm" series, "Shiber by astronomical methods" and the fourth article, "Using astronomical methods to calculate the sun and moon", This paper introduces the lunar calendar projection is based on the astronomical algorithm has been obtained by the precise throttle time and sun-Moon combined time of the moon.

China's official age is used in the Chinese Gregorian calendar (Gregorian), so the derivation of the lunar calendar should be based on the Gregorian calendar year cycle, accompanied by the lunar calendar year of information, that is, the calendar in the Gregorian calendar January 1 as the beginning, to the end of December 31, according to the lunar calendar derived from the lunar Append on Gregorian date information to form a double calendar. Typically, a Gregorian calendar year cycle cannot be fully mapped to a lunar calendar year cycle, the difference between the two is not fixed, so there is no stable correspondence, that is, there is no conversion formula from the Gregorian calendar date to the lunar date, only according to the calendar rules of lunar calendar to derive the corresponding relationship between the lunar date and the Gregorian calendar date. By the rules of the lunar calendar, the synodic of the last Gregorian year () is the November of the previous lunar year (winter months), so in terms of solar terms, it is necessary to calculate the 25 solar terms including the last year's winter solstice, in order to correspond to the last lunar year of November and the current agricultural calendar November. When calculating the corresponding Shuori, considering the situation of the leap month, it is necessary to calculate 15 consecutive Shuori from the first shuori before the winter solstice of the last year to guarantee a full year of two winter solstice, figure (1) shows the relationship between Shuori and the winter solstice without a leap month in 2011 years:

Figure (1) Shuori and winter solstice solar terms without leap month

The figure above is the number of the Gregorian calendar month, the black dot represents Shuori, and the black triangle represents the winter solstice solar term. Figure (2) shows the relationship between the Shuori and the winter solstice with a leap month in 2012 years:

Fig. (2) Shuori and Winter solstice solar terms in the event of a leap month