Chapter 45 Chapter 12 Sun and Moon Motion and Position Calculation

Studying the law of the apparent motion of the sun means knowing when and where the sun is going.Although the armillary sphere can help astronomers directly measure the depolarization of the sun, it cannot directly measure the occlusal degree, because there is no starry sky as the background during the day.The ancients used the moon to deduce the right ascension of the sun, but this was only limited to a few special cases of the moon phase, and the inferred results were not precise enough.For the position of the sun at other times, it is often calculated by the average degree of the sun every day.In the quadrant calendar, the sun travels by an average of one degree per day.As the accuracy of the regression year increases, the mean value also changes.Therefore, on this basis, the twenty-four solar terms are equally divided into return years, and each solar term occupies 15.2 days, which is called Pingqi.

As early as before the Spring and Autumn Period and the Warring States Period, astronomers knew that the sun had a separate orbit, called the ecliptic.Zhang Heng, an astronomer in the Eastern Han Dynasty, once measured that the sun’s motion was non-uniform, but he attributed it to the uneven projection of the ecliptic on the equator. In fact, projection is only one of the reasons for the uneven motion of the sun. Therefore, Zhang Heng did not actually Did not realize that the sun itself has a regular slow motion. The inhomogeneity of the sun's motion is the reflection of the inhomogeneity of the earth's revolution.The orbit of the earth is an ellipse, which is close to a circle. The sun is located at one focus of the ellipse. According to the law of celestial body motion, the earth moves faster near the perihelion and slower near the aphelion.

Zhang Zixin, a native of the Northern Qi Dynasty, was proficient in astronomy and mathematics. To escape the war, he settled on the island and observed the sun, moon and planets for 30 years.He was the first to affirm that there is a real inhomogeneity in the motion of the sun, moon, and planets. After considering the unevenness of the solar movement, the time occupied by each solar term is no longer equal, as short as more than 14 days and as long as nearly 16 days, which is called fixed gas.The calculation method of fixed qi is: first measure the fastest position and slowest position of the sun's movement, and then compile the speed correction value table of each solar term according to the actual speed, the absolute value of the correction value is based on the fastest and slowest position is the upper limit, and the correction value of the calming time is the calming time.

The Dayan calendar of a line in the Tang Dynasty used fixed qi as a reference value, and used the quadratic difference interpolation formula with unequal intervals to calculate the correction value at any position between the solar terms and the solar average movement. Add and subtract the correction value to get The actual position of the sun. The ecliptic is the orbit of the sun's annual apparent motion.The ecliptic and the equator do not coincide. There is an angle between them, which is called the yellow-equatorial angle. The sun moves to the farthest distance from the equator. In ancient China, it was called the yellow-equatorial distance.As mentioned in the first section, the ancient Chinese observation instruments are equatorial devices, but the ecliptic is the basic circle for measuring the positions of the sun, moon and planets, so it is necessary to convert the equatorial degrees into ecliptic degrees. Indispensable elements in the conversion process.

It is precisely because of the high degree of attention that the ancients have always been very accurate in measuring the intersection angle of the yellow and the red.As early as the 1st century BC, the value of the intersection angle between yellow and red in "Zhoubi Suanjing" was 23°39′18″.1, which is only 3′23″.9 different from today’s theoretically estimated value.The error of the data in the Yitian Calendar of the Northern Song Dynasty is 23″.9, which is less than half an arc minute. However, 600 years later, the intersection angle between the yellow and the red measured by the Danish Tycho, who is famous for his good observations, is still 2′. error.

Modern scientific research has proved that the shape and density distribution of the earth is not spherically symmetrical. After being affected by the gravitational force from the sun, moon and planets, the direction of the earth's rotation axis in space will change. The direction of the celestial equator perpendicular to the rotation axis The direction will also change.The consequence of this change is that the vernal equinox, one of the intersection points of the ecliptic equator, slowly moves westward along the ecliptic, and the winter solstice, which is 90° from the vernal equinox, also moves westward.When the sun moves from the winter solstice point to the next winter solstice point after one tropical year, the winter solstice point has moved a certain distance relative to the background of the starry sky, and there is a phenomenon that the tropical year is shorter than the sidereal year, and the difference between the two is "precession".