Chapter 30 Chapter 8: A Calendar in Its Own

The time interval required for the sun to pass through the winter solstice twice in a row is called the return year, which was called Suishi in ancient times. Using the gauge, it is possible to directly determine the day when the sun reaches the winter solstice point, because the shadow at noon on that day is longer than that on other days of the year.However, the winter solstice may occur at any time of the day, not necessarily at noon, so a long period of observation is required to know the time of the winter solstice. Before the Spring and Autumn Period and the Warring States Period, astronomers had grasped the value of the return year of 3651/4 days, writing "one quarter day of three hundred and sixty-five days".Where this value comes from is not clearly documented.They may have discovered it after summarizing the length of the shadow at noon on the winter solstice for hundreds of years. If the shadow at noon on the winter solstice is the longest in the first year, it will be slightly shorter in the second year, shorter in the third year, and almost the same as in the second year. Years are equal in length, the fifth year basically returns to the length of the first year, and then the number of days between the winter solstice of the first year and the winter solstice of the fifth year is divided by four years, and the above value will be obtained.Although this is speculation, it will not be too far from the truth.

A calendar that uses this regression to an older age is called a quarter calendar.The modern measurement value of the length of the tropical year is 365.242217 days, the quarter calendar year can exceed 0.007783 days, and the four-year period can exceed 0.031132 days, which is less than 45 minutes. For the ancient times more than 2,000 years ago, it is very difficult to achieve this step. easy. However, after the quarter calendar has been used for a long time, the accumulation of errors is more obvious, and the phenomenon of calendar acquisition often occurs, that is, the predicted time of the calendar is later than the actual time of occurrence of astronomical phenomena.This requires retesting the regression year value and replacing the intercalation method.Comparing the regression year values ​​of previous calendars, it can be found that the general trend is that the error gradually becomes smaller and approaches the true length.The closest value is 365.242190 days, the error is 0.000027 days, and the difference is only 2.3 seconds a year. This was measured by Xing Yunlu with his six-foot altimeter in the late Ming Dynasty.

It is worth mentioning that the data measured by Yang Zhongfu in the Southern Song Dynasty is 365.2425 days, which is exactly the same as the current Gregorian calendar (that is, the Gregorian calendar), but it is used 350 years earlier than the Gregorian calendar.At the same time, Yang Zhongfu noticed that the length of the return year is not static.Although the change value he measured is larger than the modern theoretical value, the modern theoretical value was calculated after the development of astronomical telescopes and with the help of celestial mechanics and advanced mathematics. Moon and moon are two positions on the orbit of the moon.At Shuo time, the center of the moon and the center of the sun are in the same celestial longitude, and the celestial longitude difference is equal to 0°. At this time, the moon cannot be seen from the earth.When looking at the moon, the moon and the sun face each other across the earth, and the celestial longitude difference is equal to 180°. At this time, the shape of the moon is perfect when viewed from the earth.The time interval between two consecutive moons or two consecutive moons is called a synodic month.

The synodic month value in the quadrant calendar is not obtained from observation, but is calculated from the length of the tropical year according to the 19-year seven-leap method.China's earliest intercalation cycle is 19 years and seven leaps, that is, 19 tropical years are equal to 19 lunar years plus seven leap months.In other words, 19 tropical years equal 235 synodic months.Since the regression year value of the quadrant calendar is relatively large and the synodic month value is relatively small, when the precision of the regression year is increased, the precision of the synodic month will be reduced, and vice versa.Until the Southern and Northern Dynasties, this problem had not been resolved. The seven leaps in 19 years are the key to hindering the solution of the problem.Zhao (bandit owed) [fei Fei] of Beiliang modified the intercalation period and adopted 221 leap in 600 years, which improved the accuracy of both the tropic year and the synodic month.

Originally, the tropical year and the synodic month are two independent cycles, and there is no need to link them together.From the Linde calendar of Li Chunfeng in the Tang Dynasty, the intercalary cycle was abolished, and the month without middle energy was used as the intercalary month. When astronomers gradually grasp the law of solar and lunar eclipses, they can directly obtain the synodic monthly value by dividing the number of days between two eclipses by the number of months.The longer the time between eclipses, the more precise the synodic month value.