Why is the new calendar and the old calendar in 19 the same day?

Why is there no "leap first month" in the lunar calendar?

Zhao, Shanghai Observatory, Chinese Academy of Sciences

The lunar calendar in China has a long history, and its origin can be traced back to the Xia Dynasty, so it is also called the "Summer Calendar". As we all know, the average lunar year is 12 months, and the leap year is 13 months. However, do you know how to set the leap month in the lunar calendar? Why leap months are mostly located in summer and less in winter? It seems that there has never been a leap month in our memory, so there is no "leap spring festival" Why? The problem has to start with the movement of the earth and the moon.

Definition of year, month and day

Since ancient times, all human activities have been inseparable from time. In order to calculate time, we must introduce time units. All human activities are carried out on the stage of the earth, so the phenomenon of alternating day and night and changing seasons is naturally regarded as the most basic unit of time.

The rotation of the earth has brought us the first natural unit of time, that is, "day". The rotation of the earth around its axis is a "day", which is a cycle of alternating day and night. The revolution of the earth around the sun brings the second unit of time, which is the year. One revolution of the earth is a year, a cycle of four seasons. Finally, the movement of the moon around the earth established the third time unit "the moon" for us.

Any movement is relative, and the movement of celestial bodies is no exception. Whether it is the rotation, revolution of the earth or the movement of the moon, it is necessary to observe it relative to some reference points. So in astronomy, there are different "years", "months" and "days" because of the different reference points used. The "day" used in our life is equal in length every day, which is called flat sun day. Flat solar day is no longer a natural time unit, but the time when the earth rotates once relative to the sun when its orbit is a perfect circle and its axis of rotation is perpendicular to the plane of the orbit. The time period that determines the change of the four seasons is called tropic year, and its length is equal to 365.422 flat solar days. Finally, the cycle of the moon is called the new moon, and its length is equal to 29.5306 flat solar days. Obviously, the length of years and months is not an integer multiple of days, which brings some troubles to the timing problem in daily life. How to calculate time with three units of year, month and day is called calendar, including the number of days in a year, how to determine the number of days in different months of a year, and the law of leap.

Solar calendar and lunar calendar

The length of months and years in a calendar is an integer multiple of days. They are no longer natural time units, they are called calendar year and calendar month respectively. The solar calendar, also known as the solar calendar, is a calendar based on the period of the earth's revolution around the sun. Every calendar year in the solar calendar is close to the tropic of Capricorn. For a long time, the average length of the calendar year should be as equal as possible to the tropic year. Under this premise, every year is divided into 12 calendar months, which has no astronomical significance. Therefore, in the solar calendar, the length of a year is calculated by the number of days closest to the tropic year, which is 365 days a year.

Obviously, if the Gregorian calendar year is 365 days per year, then because each Gregorian calendar year is 0.2422 days shorter than the tropic year, if the difference keeps accumulating, the season will continue to be postponed. For example, after 720 years, the cumulative difference reaches about half a year, when the vernal equinox appears in 10, and July becomes the coldest month of the year. In this way, it will inevitably lead to the reversal of cold and summer, 18 years old chaos. In order to overcome this, the Gregorian calendar stipulates the setting of leap years, which is 366 days, and a year with 365 days is called a normal year. The rules for setting leap years can be expressed in three sentences: a leap year is a year in which the number of AD years in non-century years is evenly divided by 4, a leap year is a year in which the number of AD years in century years (such as 1900 and 2000) is evenly divided by 400, and the rest years are flat years. Therefore, there are 97 leap years and 303 average years in 400 years, with an average length of 365.2425 days, which is only 26 seconds different from the length of the tropic year, and it takes more than 3,000 years to 1 day, which is very accurate. The current solar calendar was promulgated by Pope Gregory VIII in 1582, and has been adopted by countries all over the world since the second year, so it is also called Gregorian calendar or Gregorian calendar.

The lunar calendar, also known as the lunar calendar, is a calendar based on the cycle of the moon. The principle of making lunar calendar is to make each calendar month close to the new moon, and the average length of each calendar month should be equal to the new moon. Then, make the length of the calendar year as close as possible to the tropic year. Because the length of the first lunar month is 29.5306 days, the calendar months of the lunar calendar are the 30th day of the first lunar month and the 29th day of the second lunar month, alternating with each other, so that the average length of the calendar months is close to that of the first lunar month. Of course, there is a big difference in this way. Therefore, in the current Muslim calendar, it is stipulated that there are 19 1 month and 169 month in 360 calendar months (that is, 30 calendar years), thus greatly improving the coordination between calendar months and the first month of the lunar calendar.

There are even years and leap years in the pure lunar calendar. It has an average of 354 days a year, including six big months and six small months. The leap year is 355 days.1One day is added at the end of February, including 7 big months and 5 small months. This calendar does not take into account the coordination between the average length of calendar years and the length of tropical years. Over time, there is a big difference between the two. For example, for a 68-year-old Hui man who uses the lunar calendar to record the years, he actually lived only 66 spring and autumn periods.

Because the basic feature of the lunar calendar is that the average length of the calendar month is equal to the new moon, each date should correspond to a certain moon phase, for example, the fifteenth day of the lunar calendar is roughly the full moon. The months in the solar calendar cannot reflect this natural phenomenon. However, the calendar year of the lunar calendar can't reflect the seasonal changes, and it is out of touch with agricultural production and people's daily life, so it is rarely used.

Lunar calendar and solar terms

The lunar calendar is based entirely on the movement of the moon, while the solar calendar is based entirely on the revolution of the earth around the sun. The lunar calendar, which has been used for a long time in China, is not based entirely on the lunar calendar or the solar calendar, but both. On the one hand, the lunar calendar takes the moon orbiting the earth as a month, and the average calendar month length is equal to the first month of the lunar calendar; This is the same as the lunar calendar, so it is also called the lunar calendar. On the other hand, the leap month is set in the lunar calendar, so that the average length of each calendar year is as close as possible to the tropic of Capricorn, and the 24 solar terms is set to reflect the characteristics of seasonal changes. The lunar calendar combines the characteristics of the lunar calendar, so it is called the "lunar calendar".

The length of the calendar month of the Yin-Yang calendar is the same as that of the Hijri calendar, and there are big and small months: the 30th day of the big month and the 29th day of the small month, which is called the Moon Building. However, the arrangement of the lunar calendar is different from that of the hijri calendar, which arranges the months alternately mechanically, and the size of the lunar calendar is determined after calculation, which is more accurate than the hijri calendar. The lunar calendar stipulates that the first day of each month must be combined with the new moon, and the day of the new moon is designated as the first day. The size of the moon building depends on the date of the new moon, that is, according to the number of days contained in the two-month new moon. Because the length of two months is not exactly 59 days, the number of months in a year is not necessarily equal. Sometimes, two months, big or small, may appear one after another, so that the average length of a calendar month is as close as possible to the average length of the moon, and the remaining difference depends on the arrangement of leap months and leap months.

The first month of the lunar calendar and the year of the tropic are two cycles that are difficult to overlap, and their remainders are very fragmentary. However, the China lunar calendar successfully reconciled these two natural cycles, which is the basis of the lunar calendar and the solar calendar. As early as the Spring and Autumn Period, it was found that if seven leap months were inserted into 19 lunar year, the total length was almost equal to 19 solar year. This "19-year seven-leap method" is called "leap chapter" in the ancient calendar. In fact, 19 tropical year = 6939.60 days, while 235 (12× 19+7) months = 6939.69 days, and the difference between them is only 2 hours, 9 minutes and 36 seconds. In order to further explain the rules for setting leap months in the lunar calendar, let's explain the solar terms first.

Twenty-four solar terms are a major feature of the China lunar calendar. Because the lunar calendar has long been called the lunar calendar, many people mistakenly believe that solar terms belong to the lunar calendar. In fact, solar terms completely revolve around the earth and can be called a part of the solar calendar. Solar terms reflect the different positions reached by the earth when it runs in orbit. Because of the relativity of motion, they are different positions that the sun reaches when it moves on the ecliptic. It is called vernal equinox to stipulate that the meridian of the sun is equal to zero. Since then, the temple has a solar term every 15 and * * * has 24 solar terms. Starting from the vernal equinox, they are Qingming, Grain Rain, Changxia, Xiaoman, Mangzhong, Summer Solstice, Slight Summer, Great Summer, beginning of autumn, Early Summer, Bailu, Autumn Equinox, Cold Dew, Early Frost, beginning of winter, Light Snow, Heavy Snow, Winter Solstice, Slight Cold, Severe Cold, beginning of spring, Rain and Sting. Because of this, the dates of solar terms in the solar calendar are relatively fixed. For example, the vernal equinox always falls on March 2 1 or 22. A few changes are caused by the unequal length of the solar calendar and the increase of one day in leap years. On the contrary, the dates of lunar solar terms are changeable, and the dates when the same solar term appears in different years of the lunar calendar can differ by up to one month. Now we can clearly see that solar terms belong to the solar calendar rather than the lunar calendar.

Setting rules of lunar leap

24 solar terms can be divided into "solar terms" and "moderate qi", which are called "festival" and "qi" for short. From the winter solstice, the ancients alternately arranged the middle qi and solar terms, so slight cold is the solar term, great cold is the middle qi, and so on. There are 12 solar terms and 12 solar terms in a year. Generally, there is a solar term and a solar term every month. Every gas belongs to a certain month and cannot be confused.

There are two ways to determine the solar terms. The ancient calendar used the word "constant qi", that is, a year was divided into 24 equal parts according to time, and each solar term exceeded 15 days on average, so it was also called "flat qi". The modern lunar calendar uses the word "fixed qi", that is, according to the position of the earth in orbit, the period is 360, and the interval between two solar terms is 15. Because the earth is near the perihelion during the winter solstice, and the movement speed is relatively fast, the sun travels on the ecliptic for less than 15 days. From summer to around, the situation is just the opposite. The sun moves slowly on the ecliptic, and a solar term reaches 16 days. When using fixed air, it can be guaranteed that the spring and autumn can be divided into two days under the condition of equal day and night.

The method of setting leap in lunar calendar is closely related to the division of qi and the method of setting qi. Because the average length of the two solar terms is about 30.5 days, and the average lunar month is only about 29.5 days, the date of each solar term will inevitably be delayed by 1~2 days from the previous month. If this goes on, there will always be a month when there is only solar terms and no gas. This month is designated as "leap month" and is regarded as1March of the lunar calendar. Since solar terms appear repeatedly in strict accordance with the length of the tropic year, setting leap months in accordance with the above provisions will inevitably ensure that the average length of the lunar year is very close to the tropic year. 19 Seven-leap Method is how to set leap.

Due to the constant gas method, the average length of a festival in winter is about 29.74 days, which is not much longer than the first month of the lunar calendar, and the solar terms are slowly delayed month by month, so it is very unlikely to set up a leap month in winter. On the contrary, the earth moves slowly near the summer solstice, and the solar terms are also slow, reaching as many as 16 days at a time. Therefore, there are many leap months in summer and the months around it, such as March, April, May, June and July in the lunar calendar. In the 200 years from 182 1 to 2020, there are 74 leap months. Among them, 1 month, 1 1 month and1February have no leap, and the most leap is in May, reaching 16 times. No wonder we can't spend the first month and the Spring Festival.