How many years will the solar birthday and the lunar birthday overlap?

First, the lunar calendar (strictly speaking, the lunar calendar used in China is not the real lunar calendar, but the lunar calendar) and the solar calendar to deal with leap years. The lunar calendar is treated as 65438+7 leap in 2009, and the solar calendar is treated as 4 years 1 leap, which is exactly the same in the corresponding relationship between the lunar calendar and the solar calendar in 19.

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 one day in four years, plus February, so the normal year is 365 days, February is 28 days, leap year is 366 days, and February is 29 days. So every 400 years, there are 97 leap years, with one day added at the end of February and 366 days in leap years. Calculation method of leap year: the number of years in the calendar year can be divisible by four, which is a leap year; Divided by 100 but not divided by 400 is an average year; Leap years can be divisible by 100 or 400. For example, 2000 is a leap year, and 1900 is not.

In the China lunar calendar, a year with a leap month is called a leap year. The general year is 12 months, 354 or 355 days, and the leap year is 13 months, 383 or 384 days. As a kind of lunar calendar, the number of days in each month depends on the monthly loss, and the time of one year is based on 12 months. In order to close the earth's cycle around the sun, that is, the tropic year, one month is added every two to four years, and the added month is a leap month, so the leap year of the lunar calendar is 13 months.

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 August is called leap August.

Second, the calculation

The most important feature of coincidence is the unity of heaven (just like some common multiples)

Lunar day matrix:

384, 354, 355, 383, 354, 355, 384, 354, 355, 384, _

354, 384, 354, 354, 384, 354, 355, 384, 355, 384, _

354, 354, 384, 354, 354, 385, 354, 355, 384, 354, _

383, 354, 355, 384, 355, 354, 384, 354, 384, 354, _

354, 384, 355, 354, 385, 354, 354, 384, 354, 384, _

354, 355, 384, 354, 355, 384, 354, 383, 355, 354, _

384, 355, 354, 384, 355, 353, 384, 355, 384, 354, _

355, 384, 354, 354, 384, 354, 384, 354, 355, 384, _

355, 354, 384, 354, 384, 354, 354, 384, 355, 355, _

384, 354, 354, 383, 355, 384, 354, 355, 384, 354, _

354, 384, 354, 355, 384, 354, 385, 354, 354, 384, _

354, 354, 384, 355, 384, 354, 355, 384, 354, 354, _

384, 354, 355, 384, 354, 384, 354, 354, 384, 355, _

354, 384, 355, 384, 354, 354, 384, 354, 354, 384, _

355, 355, 384, 354, 384, 354, 354, 384, 354, 355

Gregorian calendar days matrix:

365, 365, 366, 365, 365, 365, 366, 365, 365, 365-

366, 365, 365, 365, 366, 365, 365, 365, 366, 365-

365, 365, 366, 365, 365, 365, 366, 365, 365, 365-

366, 365, 365, 365, 366, 365, 365, 365, 366, 365-

365, 365, 366, 365, 365, 365, 366, 365, 365, 365-

366, 365, 365, 365, 366, 365, 365, 365, 366, 365-

Interested students can use computer programming to calculate.

The number of days is the same every 19 years.

It should be noted that the lunar July of 19 is compiled manually, which makes the lunar calendar and solar calendar basically coincide. However, due to the particularity of leap years in the solar calendar, the lunar calendar may not overlap every day after 19.

Third, other calculations.

The lunar calendar is based on the time when the moon revolves around the earth and the earth revolves around the sun respectively. Because both of them run in elliptical orbits, one day can be recorded as the included angle between the sun-earth connection and the earth-moon connection, and the question becomes when the included angle appears for the second time. It should be solved by analytic geometry. (The data is too large and the formula is extremely complicated, so I have to give up after solving it for a long time _)

The revolution of the earth 1 week-the return year is 365.2422 days, and the revolution of the moon 1 week-the first month of the lunar calendar is 29.53059 days, which can be divided into three calendars: lunar calendar-Islamic calendar, single month, 30th, bimonthly, 29th and 30th (360th month)/kloc. Gregorian calendar-Gregorian calendar has 365 days in normal year, 366 days in leap year, four years 1 leap, but minus 3 leap in 400 years, with an average of nearly tropic year every year; Yin-Yang calendar —— The summer calendar (commonly called "lunar calendar", but not called "lunar calendar") is similar to the lunar month every month, and the winter solstice to the next year (the end of the year) is similar to the tropic year. Leap months lack neutral energy (key solar terms), and the tropic year of 19 is shorter than 235 lunar months in 2009.