Lunar algorithm for leap month

1949 leap July 1952 leap may 1955 leap March 1957 leap August 1960 leap June.

1963 leap April 1966 leap March 1968 leap July 197 1 leap may 1974 leap April.

1976 leap August 1979 leap June 1982 leap April 1984 leap October 1987 leap June.

1990 leap may 1993 leap March 1995 leap August 1998 leap may 200 1 leap April.

Leap in February 2004, leap in July 2006, leap in May 20 12, leap in April 20 14, leap in September.

20 17 leap in June 2020 leap in April.

Why is there a leap month in the lunar calendar? The lunar leap month is to coordinate the contradiction between the tropic year and the lunar year.

What is the contradiction between the tropic year and the lunar year? Remember first: the total length of the tropic year is 365.2422 days, and the length of the first lunar month is 29.5306 days.

12 lunar months constitute a lunar year, with a length of 29.5306× 12=354.3546 days, which is 10.88 days less than the regression and about 1/kloc-0 less than the monthly 0.9 1 day.

Accordingly, if the Spring Festival in one year of the lunar calendar is a snowy winter, the Spring Festival in the next year will be 1 1 day earlier than the season, and 16 Lunar New Year will appear in the hot summer.

If the lunar year consists of thirteen lunar months, the length is 29.5306× 13=383.8978 days, which is more than the tropic year 18 days.

If the calendar is made according to the above regulations, there will be a strange phenomenon that the weather is inconsistent with the calendar and the time order is disordered and reversed-this is contradiction.

In order to overcome this shortcoming, our ancestors found the method of "leap month" on the basis of astronomical observation, ensuring that the first month to March is spring, April to June is summer, July to September is autumn, and October to December is winter, while ensuring that the first year of the lunar calendar is in late winter and early spring.

The mid-year month of the lunar calendar is based on the length of 29.5306 days in the first lunar month, so the big month is 30 days and the small month is 29 days. In order to ensure that the first day of each month (the first day) must be a new moon, the arrangement of large and small months is not fixed and needs to be determined through strict observation and calculation. Therefore, it is very common to be big or small for two consecutive months in the lunar calendar, and even there are rare exceptions, such as 1990 in which March and April are small, and 9, 10,1,1February are big for four consecutive months.

So how often do you add leap months? The best way is to find the least common multiple of the number of days in the tropical year and the number of days in the lunar month: we hope that the number of days in m tropical years is equal to the number of days in n lunar months, that is, there should be an equation:

m×365.2422=n×29.5306

In this equation, we can't directly find out m and n, but we can find out their proportions:

The approximate value of this ratio is:

In these fractions, the numerator represents the number of tropical years and the denominator represents the number of moons. For example, the sixth score means that seven leap months must be added to 19 tropical year.

Comparison of the results of adding 7 leap months in 19 tropical year;

19 tropical year =19× 365.2422 = 6939.438+018 (days)

A lunar month has 29.5306 days, and 235 lunar months = 235× 29.5306 = 6939+38 days.

19 tropic year plus 7 leap months, the contradiction is eliminated: 6939.438+00-6939.18 = 0.0892 (days)-that is, more than 2 hours and 9 minutes, which is accurate enough.

Therefore, the lunar calendar adopts the method of 19 plus 7 leap months, that is, the "19 7 leap month method", which well coordinates the return year and the lunar year, so that the New Year's Day (Spring Festival) of the lunar calendar is always kept in the late winter and early spring. The ancients called 235 new moons "leap weeks".

The method of placing leap in the lunar calendar can make the average length of the lunar year close to the tropic year. The moon in the lunar calendar has distinct moon phase characteristics, which keeps the best characteristics of both the solar calendar and the lunar calendar.

At present, the method of setting leap is between two winter solstice. If it is only 12 months, it is not a leap; if it is 13 months, it is a leap. The leap month begins on the "winter solstice". When there is no "neutral spirit" in the first month, this month is a leap month, and its name is to add the word "leap" before the previous month.

What month is the lunar leap month? It depends on the 24 solar terms in a year.

In the China lunar calendar, 24 solar terms are divided into 12 solar terms and 12 neutral terms.

The lunar calendar takes the moon as the cycle (lunar calendar), and the December calendar is about 354 days. Combined with the almanac (solar calendar), the almanac is compiled according to the four-season cycle formed by the revolution of the earth. The monthly calendar is shorter than the annual calendar by 1 1 day. Therefore, it is necessary to add 7 leap months every 19 years to make up for the error. Deciding which month is a leap month depends on 24 solar terms. Lunar months usually include a solar term and a neutral atmosphere, such as the autumnal equinox. If a lunar month has only solar terms but no neutral atmosphere, one more month will be added to the calendar as a leap month. Taking 2006 as an example, July of the lunar calendar happened to be a month with solar terms but no neutral atmosphere, so there was an adjustment error in July.

The date of the twenty-four solar terms of the lunar calendar is postponed month by month, so in some lunar months, the gas falls at the end of the month, and it will be out of gas next month.

Generally, there will be a month without gas every two years, which coincides with the year when leap months are needed. Therefore, the lunar calendar stipulates that non-neutral months are leap months.

For example, April 29th of the 200 1 lunar calendar is full of breath, and the first day of every other month is the solstice of the next summer. If there is no gas this month, it will be a leap month, after April, so it is called leap April.