The node month is also called the weekly month.Nodal moon refers to the moon's orbit around the earth, passing through the earth twice in successionBai DaoThe time required at the same intersection with the ecliptic.This period was 27.2122200 days, that is, 5:05:35.9 seconds on the 27th day.This cycle is of great significance for the speculation of solar and lunar eclipses.[1]
The orbital plane of the moon around the earth, that is, the white track plane.The white plane and the ecliptic plane do not coincide, but have an average intersection angle of 5 ° 9 ', which is called the yellow white intersection angle.These two planes intersect into a straight line, called the intersection line.There are two intersections between the intersection line and the celestial sphere. When the moon moves on the white path from the south of the ecliptic to the north of the ecliptic, this intersection is called the ascending intersection point. The other intersection point is the point where the moon moves from the north of the ecliptic to the south, called the descending intersection point.
The intersection point is a very important geometric point in the movement of the moon and the formation of solar and lunar eclipses.Another important feature of the intersection is that the intersection is constantly moving, not always unchanged.The movement of the intersection point is opposite to the movement direction of the moon, making a reverse movement.The moving period of the intersection is 18.6 years, that is, the intersection rotates once every 6793 days, with an average annual movement of 19 ° 21 '.[2]
The average intersection angle of yellow and white is 5 ° 09 ′, and the intersection angle of yellow and red is 23 ° 27 ′.Then the intersection angle of the white path and the equator is changing due to the movement of the intersection point, which indicates that the declination of the moon is changing. From a series of observation data, we can compare the path of the moon movement in each year, and find that the height of the moon on the ground is sometimes high and sometimes low.The change of lunar ground height is caused by the movement of intersection points.
When the ascending node coincides with the vernal equinox, the white path is higher than the ecliptic.The declination of the moon varies between 28 ° 36 'and - 28 ° 36'.When the descending node coincides with the vernal equinox, the lunar equator changes between 18 ° 18 'and - 18 ° 18'.It can be seen that the angle of intersection between the white path and the equator varies from 18 ° 18 'to 28 ° 36'.This shows that the maximum declination difference of the lunar sphere can reach 10 ° 18 '.
Intersection Moon and Solar Eclipse
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The eclipse of the sun and the moon must occur near the intersection of the ecliptic and the white path.Because only in such a narrow area can the three celestial bodies be arranged in a straight line.
The time interval that the sun passes through the same intersection of the ecliptic and the white path twice in a row is called the intersection year.It is also called Shinian.
The time interval that the moon passes through the same intersection of the ecliptic and the white path twice in a row is called the intersection month.
The restriction of the same intersection point is necessary because there should be two intersections between the ecliptic and the white planes.One is called the ascending node, and the other is called the descending node.
Due to the perturbation of the sun to the moon in the Earth Moon system, the intersection of the ecliptic and the white track moves 19 ° 21 'westward every year on the ecliptic, so the length of the intersection month is shorter than the length of the new moon, and the length of the intersection year is shorter than the length of the regression year.The length of the intersection month and the intersection year are two astronomical constants with the yellow white intersection moving as the background.According to modern measurement.For 2000:
1 node year - 346.620 030 9
1 intersection month - 27.212 2200
Since the necessary conditions for a solar lunar eclipse to occur are: 1. It must occur in the new moon (solar eclipse) and the moon (lunar eclipse);2. It must occur near the intersection, so the solar lunar eclipse cycle S is actually an integral multiple of both the new moon and the intersection month, namely:
Therefore, the determination of the solar lunar eclipse period is equivalent to the determination of the length of the intersection month (assuming that the length of the new moon is known).[3]
Discovery of the node month
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Liu Hong was the first person in ancient China to put forward the concept of the intersection moon and clarify the phenomenon of the yellow white intersection moving westward.Liu Hong gave his calculation method in compiling the duration of Ganxiang.According to Chen Meidong's research, Liu Hong actually proposed the formula for calculating the length of the intersection month in a feeding cycle:
Length of intersection month=number of synoptic months × length of synoptic months/number of intersection months
But Liu Hong did not actually calculate, while Chen Meidong checked the Ganxiang Calendar, Jingchu Calendar, Jiazi Calendar of the Third Period, Jiali Calendar of the Yuan Dynasty and Wuping Calendar according to the above formula, proving that Liu Hong's formula was indeed used.
Zu Chongzhi gave the value of the length of the intersection month for the first time in the Ming calendar, but did not specify the calculation method.Chen Meidong also calculated the Kaihuang Calendar, Dayan Calendar, Epoch Calendar, Huiyuan Calendar, Yitian Calendar, Tongtian Calendar, etc., and found a slight difference from the above formula.
Chen Meidong's research has clarified the main idea of the length of the intersection month given by ancient Chinese astronomers when they worked out the almanac, and proved their scientific concept.Since the specific almanac does not strictly point out the data source and its calculation method, it may be difficult to recover each almanac according to the modern method, but we will see from the following comprehensive table that the determination of the astronomical constant of the length of the intersection month in ancient China is very accurate.
In the same paper, Chen Meidong summarized the formula for the length of intersection year in various calendars as follows:
Annual length of intersection=number of synoptic months × length of synoptic months/number of intersection years;
or
Annual length of intersection=number of intersection months × length of intersection months/number of intersection years
This more clearly expresses the close relationship between the length of the intersection year and the feeding cycle.According to the records in the Book of the Continuing Han Dynasty - Records of the Legal Calendar:
If the rate of eating is twenty-three and the food is recovered, the month is one hundred and thirty-five. If the rate of eating is divided, the food can be eaten at the twenty fifth of May twenty-three.
