Chapter 47 Third Eclipse and Lunar Eclipse

Solar and lunar eclipses are collectively called eclipses.The eclipse is not only related to the movement of the moon, but also related to the movement of the sun. The accuracy of the eclipse forecast has become an important criterion for testing the quality of the calendar. "The key to imitating the calendar is the solar eclipse" ("Book of Jin·Lv Li Zhi"), which expresses this meaning. Calendarists of all dynasties have recognized and applied this standard, thus objectively admitting that solar and lunar eclipses have laws to follow.But at the same time, there are always astrologers taking advantage of the inaccurate forecasts of astronomical officials to mystify solar and lunar eclipses to show God's will.This shows that the law of solar and lunar eclipses is very complicated and cannot be grasped by short-term observation.

A solar eclipse must occur on a lunar eclipse, and a lunar eclipse must occur on a lunar eclipse, but not all synodic eclipses occur.The reason is very simple, because the apparent orbit of the moon and the apparent orbit of the sun have an included angle of 5°09′, and the maximum angular diameters of the sun and the moon are 32′32″ and 33′26″ respectively.When the sun and the moon are close to intersect at the position of the celestial longitude, the distance between the center of the sun and the moon is about 33′.That is to say, when the distance between the centers of the sun and the moon is greater than 33', eclipses will not occur even at synodic positions.The distance between the center of the sun and the moon is directly related to the distance between the sun and the moon from the node of the orbit. The distance from the node when the sun and the moon are critical is usually used as the condition for judging whether to eclipse or not. This limit is called the eclipse limit.The Qianxiang calendar of the Eastern Han Dynasty used the yellow longitude 15.5 degrees as the criterion for the occurrence of solar eclipses, which was not far from the modern value and was adopted by many calendars of later generations.

Experience is constantly accumulating and awareness is constantly improving.According to the statistics of the Three Traditions of the Western Han Dynasty, there are about 23 eclipses in 135 synodic months, and the eclipses that occur after 135 synodic months will be repeated in very similar order and interval.This is the first record of the eclipse cycle in China.The time interval between the sun passing through the yellow and white nodes twice in a row is called a node year.The ancients realized that since the eclipse must meet the two conditions of synodic and near the node, then the cycle of eclipse must be closely related to the synodic month and the year of the node.This is exactly the case. From a mathematical analysis, the eclipse cycle should be the least common multiple of the synodic month and the node year.However, since neither the synodic month nor the node year is an integer value, it is not easy to obtain an accurate eclipse cycle.Therefore, there is only one approximate calculation method in ancient China.The Tongtian calendar of the Song Dynasty calculated that the eclipse cycle was 223 synodic months, which is 0.46 days different from 19 node years, which is equivalent to the Saros cycle of the ancient Babylonians.The Tang Dynasty's Wuji calendar calculated that the eclipse cycle is 358 synodic months, which is only 0.04 days different from the 30.5 node years.The West did not achieve such precision until the 19th century.