How to calculate leap month?

How did the lunar leap month come about? How to calculate leap month? Leap moon refers to a phenomenon in the lunar calendar. The lunar calendar arranges the big moon and the small moon, that is, the moon, according to the full and short moon. The length of a moon is 29.5306 days, which is the cycle of the moon's profit and loss. According to the lunar calendar, there are 30 days for the big moon and 29 days for the small moon, and a year is 12 months * * 354 days. The lunar month has no seasonal significance, so just after 17, the date of the lunar calendar will be reversed with the seasons. For example, one year's New Year is spent in the snow, and after 17, the vermicelli will be shaken to celebrate the New Year. The use of such a calendar naturally cannot meet the needs of agricultural production, so the lunar calendar in China has been in parallel with the 24 solar terms since the Qin and Han Dynasties, and the 24 solar terms are used to guide agricultural production.

Twenty-four solar terms can be divided into two groups: "solar terms" and "middle qi": the ancients regarded every 300 meridian from slight cold as a solar term; From the winter solstice, every 300 meridian is a neutral gas, and there are 12 solar terms and 12 neutral gas in a year. 12 solar terms divide a year into 12 months, and each month has a solar term and a neutral atmosphere. Solar term is the starting point of solar term month; Zhongqi is the midpoint of the festival. The traditional calendar in China does not adopt the method of day-to-day and month-to-month sequence and long-term arrangement of big month, small month, normal year and leap year, but emphasizes the calculation from year to month. The state sets up special institutions to calculate calendars.

(1) Set the date order according to the moon phase. It calculates the date and time of the conjunction of the sun and the moon one by one, and the first day of each month is the date of the conjunction; Determine the size of last month according to the number of days included in the second conjunction. If the interval between this new moon and the next one is 30 days, then this month is the big moon; If it is only once every 29 days, it is an abortion.

(2) Set the month order with neutral gas. First of all, the calendar month and leap month are distinguished by whether the calendar month is neutral or not. We know that there are 12 neutral gases in a tropical year, but it contains 365.2422 ÷ 29.5306 = 2.3682 satellites. After several calendar months of rotation, there must be a calendar month without neutral gas. Hanshu? The calendar says, "The new moon cannot be obtained, so it is called leap moon". This month without neutrality is a leap month. When the previous calendar day is a few months, it is a leap month. For example, the leap month of 1984 appears after October of the old calendar, so it is called "leap October". Leap months are calculated, not fixed in the monthly order of the year. In addition to 1 1 month,1February and the first lunar month, leap month is possible, and it is the seventh leap month in the nineteenth year.

To sum up, leap year is a phenomenon in the solar calendar, which is fixed in February, 29 days longer than the normal year; Leaping moon is a phenomenon in the lunar calendar. This is a leap month. That year, there were 13 months in the lunar calendar, and that year was called leap month year. Leap Moon is 384 years old.

First, calculate the formula of annual trunk and branches.

From the palm of your hand, you can count the annual stems and branches, and the flowers in Zhi Zi begin.

Yangzhi began on the 10th and lasted for four years.

Every other position is reversed for ten years, and the end of the year is 503.

Sixty numbers are added and subtracted one by one, and thousands of years are counted in the palm of your hand.

Calculation method: "Palm counts one year of dry branches and Zhi Zi flower roots." This method is to arrange the branches on the palm of your hand and calculate the annual branches on the palm of your hand. First locate the ground branch on the palm of your hand (Figure 1), and then start with the ground branch position as Jiazi, which can be set to 1864, 1924, or 1984, all of which are Jiazi years. "Yangzhi is the beginning of ten days, and Tiangan is the end of four years." Zi, Yin, Chen, Wu, Shen and Xu in the earthly branches are all Yang branches, and they are also the beginning of every ten days. Everything is A, that is, Jia Zi, Jia Xu, Shen Jia, Wu Jia, Chen Jia and Jia Yin. The mantissa of the Gregorian calendar in these years is 4. "Every other place for ten years, 503 at the end of the year." There are ten days to dry twelve earthly branches, heavenly stems and earthly branches combination. Every time the heavenly stems are circulated, the soil branch is always connected with the next two branches (Xun Kong). The first branch left is the beginning of the later period. We start from the sub-position of the earthly branch and push back every other one, that is, from the sub-position to the tenth anniversary of JOE, and then from the tenth anniversary of JOE to Shenwei-the mantissa is four every year, and the annual interval is ten years. After the beginning of the tenth day is determined, the mantissa of the year is 4 as the starting point, and the mantissa of the calendar year is 5, 6, 8, 9, 0, 1, 2, 3 from the next branch, and then it is the beginning of the later period. According to this method, if the year of Jiazi is set to 1984, we can know that 1994 is JOE, 2004 is Shen Jia, and 20 14 is Wu Jia. After determining the number of Gregorian calendar years starting every ten days, we can push forward the trunk and branches of any year as needed. Although it is meaningful, it can push the trunks and branches of thousands of years forward.

Second, the formula for calculating months and hours.

Do it the day before the fifth day, and the order of months is from one to five. ......& gt& gt

How to calculate leap month is a way to set leap in calendar. In Asia (especially in China), leap month refers to one month added every leap year in the lunar calendar (in order to coordinate the contradiction between the tropic year and the lunar year and prevent the lunar year from being out of touch with the tropic year and the four seasons, 1 leap and 19 leap are set every two to three years). Sometimes, a leap month also refers to a month that includes a leap day in a leap year (especially in February of a leap year in the Gregorian calendar). A leap month is an additional month in every leap year. In the lunar calendar, the length of the first lunar month (29.5306 days) is the average of one month, which is 65438+February in the whole year, which is about 10 and 2 1 hour different from the tropic year (365.2422 days), so it is leap in turn, one month in three years, two months in five years and seven months in nineteen years. A leap month is called "leap month" after a certain month. For example, the last leap month in 2009 was May (June 23rd, 2009-July 2nd, 20091), and the upcoming leap month of 20 12 was April (20 12). What we usually call "leap year" is actually a rough figure. Then there are 365 days in a year, which is O.2422 days different from the actual year, so four years later, it is nearly one day less than the actual year. In order to make up for this difference, the calendar stipulates that four years is a leap year, that is, a year divisible by four is a leap year, and additionally stipulates that every century year (a year with two zeros at the end) must be divisible by 400 to be a leap year. For example, 1996 is a leap year, and 2000 is also a leap year, but 1700 is not. The leap year in the solar calendar has 29 days in February, the leap day is February 29 and the leap year in the solar calendar has 366 days. That is to say, February of leap year in the solar calendar is not called leap February, and leap month is unique to the lunar calendar. Now let's talk about "leap month". Leap moon refers to a phenomenon in the lunar calendar. The lunar calendar arranges the big moon and the small moon, that is, the moon, according to the full and short moon. The length of a moon is 29.5306 days, which is the cycle of the moon's profit and loss. According to the lunar calendar, there are 30 days for the big moon and 29 days for the small moon, and a year is 12 months * * 354 days. Lunar month has no seasonal significance, so its length is 29.5306× 12=354.3672 days, which is less than 365.2422 days in the tropic year (that is, near 1 1 day) 10.88 days, and 0.9/kloc per month. The difference between solar calendar year and year is 1 1 day. Only after 17 will the date of the lunar calendar be reversed in the same season. For example, a year's New Year is spent in the snow, and a new year comes after 17. The use of such a calendar naturally cannot meet the needs of agricultural production, so the lunar calendar in China has been in parallel with the 24 solar terms since the Qin and Han Dynasties, and the 24 solar terms are used to guide agricultural production. Many people misunderstand the lunar calendar in China and often confuse it with the lunar calendar. There are three calendars in the world: one is the solar calendar, in which the time for the earth to go around the sun is one year, and the number of months and days in a year can be specified artificially; One is the lunar calendar, in which the time for the moon to circle the earth is one month, and only a few months in a year can be designated artificially; The third is the yin-yang calendar, that is, the average time for the moon to orbit the earth is January, but by setting leap months, the average number of days in a year is equal to the average time for the earth to orbit the sun, such as the lunar calendar and Tibetan calendar in China. Therefore, the lunar calendar in China is not a lunar calendar, but a combination of yin and yang. The lunar and solar elements in the lunar calendar have their own uses. The lunar calendar can indicate the moon's profit and loss, and can also predict the tides. The solar calendar is more useful. Twenty-four solar terms are a great invention in ancient China. It shows the position of the earth in orbit, reflects the annual apparent movement of the sun, and is most suitable for guiding agricultural activities. Therefore, the traditional lunar calendar in China is called the lunar calendar. Therefore, the lunar calendar is different from the lunar calendar, and it is not appropriate to call the lunar calendar the lunar calendar. The sun and the moon are calendars that people hang in the sky. Year after year, the earth revolves around the sun, and everything on the earth lives and multiplies in the cycle of the sun and the moon. 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 the contradiction. In order to overcome this shortcoming, we ... >>

How did the lunar leap month come about? How to calculate leap month refers to a phenomenon in the lunar calendar. The lunar calendar arranges the big moon and the small moon, that is, the moon, according to the full and short moon. The length of a moon is 29.5306 days, which is the cycle of the moon's profit and loss. According to the lunar calendar, there are 30 days for the big moon and 29 days for the small moon, and a year is 12 months * * 354 days. Lunar months have no seasonal significance. Thus, the difference between a year and a year in the solar calendar is 1 1 day. Just after 17, the date of the lunar calendar is reversed in the same season. For example, a New Year is spent in the snow, and after 17, you should shake your fan to pay a New Year call. The use of such a calendar naturally cannot meet the needs of agricultural production, so the lunar calendar in China has been in parallel with the 24 solar terms since the Qin and Han Dynasties, and the 24 solar terms are used to guide agricultural production. Twenty-four solar terms can be divided into two groups: "solar terms" and "middle qi": the ancients regarded every 300 meridian from slight cold as a solar term; From the winter solstice, every 300 meridian is a neutral gas, and there are 12 solar terms and 12 neutral gas in a year. 12 solar terms divide a year into 12 months, and each month has a solar term and a neutral atmosphere. Solar term is the starting point of solar term month; Zhongqi is the midpoint of the festival. The traditional calendar in China does not adopt the method of day-to-day and month-to-month sequence and long-term arrangement of big month, small month, normal year and leap year, but emphasizes the calculation from year to month. The state sets up special institutions to calculate calendars. (1) Set the date order according to the moon phase. It calculates the date and time of the conjunction of the sun and the moon one by one, and the first day of each month is the date of the conjunction; Determine the size of last month according to the number of days included in the second conjunction. If the interval between this new moon and the next one is 30 days, then this month is the big moon; If it is only once every 29 days, it is an abortion. (2) Set the month order with neutral gas. First of all, the calendar month and leap month are distinguished by whether the calendar month is neutral or not. We know that there are 12 neutral gases in a tropical year, but it contains 365.2422 ÷ 29.5306 = 2.3682 satellites. After several calendar months of rotation, there must be a calendar month without neutral gas. Hanshu? The calendar says, "The new moon cannot be obtained, so it is called leap moon". This month without neutrality is a leap month. When the previous calendar day is a few months, it is a leap month. For example, the leap month of 1984 appears after October of the old calendar, so it is called "leap October". Leap months are calculated, not fixed in the monthly order of the year. In addition to 1 1 month,1February and the first lunar month, leap month is possible, and it is the seventh leap month in the nineteenth year. To sum up, leap year is a phenomenon in the solar calendar, which is fixed in February, 29 days longer than the normal year; Leaping moon is a phenomenon in the lunar calendar. This is a leap month. That year, there were 13 months in the lunar calendar, and that year was called leap month year. Leap Moon is 384 years old. First, calculate the annual trunk and branch formulas. Zhi Zi spent a lot of money on palm counting trunks and branches every year. Yangzhi began on the 10th and lasted for four years. Every other position is reversed for ten years, and the end of the year is 503. Sixty numbers are added and subtracted one by one, and thousands of years are counted in the palm of your hand. Calculation method: "Palm counts one year of dry branches and Zhi Zi flower roots." This method is to arrange the branches on the palm of your hand and calculate the annual branches on the palm of your hand. First locate the ground branch on the palm of your hand (Figure 1), and then start with the ground branch position as Jiazi, which can be set to 1864, 1924, or 1984, all of which are Jiazi years. "Yangzhi is the beginning of ten days, and Tiangan is the end of four years." Zi, Yin, Chen, Wu, Shen and Xu in the earthly branches are all Yang branches, and they are also the beginning of every ten days. Everything is A, that is, Jia Zi, Jia Xu, Shen Jia, Wu Jia, Chen Jia and Jia Yin. The mantissa of the Gregorian calendar in these years is 4. "Every other place for ten years, 503 at the end of the year." There are ten days to dry twelve earthly branches, heavenly stems and earthly branches combination. Every time the heavenly stems circulate, the earth branch is always with the next two branches (Xun Kong). The first branch left is the beginning of the later period. We start from the sub-position of the earthly branch and push back every other one, that is, from the sub-position to the tenth anniversary of JOE, and then from the tenth anniversary of JOE to Shenwei-the mantissa is four every year, and the annual interval is ten years. After the beginning of the tenth day is determined, the mantissa of the year is 4 as the starting point, and the mantissa of the calendar year is 5, 6, 8, 9, 0, 1, 2, 3 from the next branch, and then it is the beginning of the later period. According to this method, if the year of Jiazi is set to 1984, we can know that 1994 is JOE, 2004 is Shen Jia, and 20 14 is Wu Jia. After determining the number of Gregorian calendar years starting every ten days, we can push forward the trunk and branches of any year as needed. Although it is meaningful, it can push the trunks and branches of thousands of years forward. Second, calculate the monthly and hourly dry branch formulas, mainly five days before the dry, and the monthly dry order is one to five. ......& gt& gt

How are leap years and leap months calculated? First, leap years can be divided into solar calendar and lunar calendar.

The concepts of leap year in solar calendar and lunar calendar are different. The leap year we often talk about is actually the leap year of the Gregorian calendar.

A year with a leap day in the solar calendar is called a leap year.

A year with a leap month in the lunar calendar is called a leap year.

The leap years of the solar calendar and the lunar calendar do not coincide. For example, the lunar calendar 1995 and 200 1 are leap years, but the solar calendar is not. In 2000, the solar calendar was a leap year, but the lunar calendar was not. The following is a comparison of 1982-2042.

Second, the judgment of leap year in Gregorian calendar

Common sense is that every four years is a leap year, and a year divisible by four is a leap year. Actually, it's not. Which years are leap years? How to judge leap year?

In the Gregorian calendar year, a year with leap days is called leap year, which is generally 365 days and 366 days. Because the earth's cycle around the sun is 365 days, 5 hours, 48 minutes and 46 seconds (365,438+09 days), which is the tropic year, the Gregorian calendar sets a year as 365 days. The remaining time is about four years, plus it is fixed in February, so there are 365 days in a normal year, 28 days in February, 366 days in a leap year and 29 days in February. There are 97 leap years every 400 years.

The usual calculation method of leap year: the number of years in the calendar year can be divisible by 4, which is a leap year; But the year divisible by 4 is not necessarily a leap year, such as 1700, 1900, it is not a leap year. At the turn of the century, the year that can be divisible by 100 but not by 400 is a normal year; Leap years can be divisible by 100 or 400. For example, 2000 is a leap year, while 1000 and 3000 are not. Here is a leap year calculation formula, you can have a look if you are interested.

Third, the calculation of lunar leap month.

A year with a leap month in the lunar calendar is called a leap month year, but now it is also customarily called a leap year (so it is easily confused with a leap year in the Gregorian calendar). The general year is 12 months, 354 or 355 days, and the leap year is 13 months, 383 or 384 days.

There is no thirteenth month in the lunar calendar. According to the calendar rules, leap months are repeated from February to the same month after 10, and the repeated months are leap months. For example, the leap month after April is called leap April.

The law of lunar leap year is one leap in three years, two leap in five years and seven leap in 19. According to the laws of the lunar calendar, it is mainly determined according to the coincidence with the 24 solar terms of the lunar calendar. Usually, a month with only one solar term (usually a small month) is set as a leap month to make up for it. The number of leap months in the lunar calendar is 29 or 30 days, just like normal months.

The lunar calendar basically takes 19 as a cycle, corresponding to the same time in the Gregorian calendar. For example, in the Gregorian calendar, May 27th, 2006, 5438+0, May 27th 1982 and May 27th 1963 are the fifth day of leap April.

How to calculate leap month? Leap years are calculated according to the following rules: leap years should be divisible by 4 (for example, 2004 is a leap year, and 200 1 is not), but not all years divisible by 4 are leap years. In the year divisible by 100, the year divisible by 400 at the same time is a leap year (for example, 2000 is a leap year), and the year divisible by 100 but not by 400 (for example, 1800, 1900, 2/kloc) It is not accurate to say that "a year divisible by 4 is a leap year"

How to calculate leap month and judge leap year in Gregorian calendar is like this: leap once every four years, not leap for a hundred years, and leap again every four hundred years.

Simple calculation method of leap year in Gregorian calendar: (A year that meets one of the following conditions is a leap year)

1. It is divisible by 4, but not by 100. (For example, 2004 is a leap year, but 1900 is not. )

2. divisible by 400. (For example, 2000 is a leap year)

Here is a simple way to judge whether it is a leap year.

(1) To judge whether a year is a leap year, you only need to look at the last two digits of the year. If the last two digits are divisible by 4, it is a leap year, otherwise it is not.

(2) When the last two digits are all 0, we will look at the first two digits of the year; If the first two digits are divisible by 4, it is a leap year, and vice versa.

(3) If the two digits at the end of 2004 are 04, it can be directly regarded as 1 bit. If this number is divisible by 4, it is a leap year, otherwise it is not.

How to calculate the lunar leap month? Is there any formula? 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+38+08 (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 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.

When is February a leap month and how to calculate it? A year divided by 4 is a leap month, just like 2004, 2008, 20 12, etc.

Leap month, February has 2 days, one more day!