First, let's determine the positions of the sun and the planets. Subtract the planet's speed from the sun's speed, and if the remainder can be evenly divided by the sun's speed, you get an integer. Then, according to the previous calculation method, you can calculate the distance between the planet and the sun when the planet appears. Multiply the planet's speed's denominator by the previously calculated distance. If the remainder can be evenly divided by the sun's speed, you get an integer; if not, consider it an integer if it exceeds half. Then add this integer to the speed of the planet. If the sum equals the planet's speed's denominator, it means the planet has moved one degree. During direct and retrograde motion, the denominators are different, so you need to multiply the value previously calculated by the denominator of the current speed, then divide by the original denominator to obtain the correct planet speed. The remainder carries over from the previous calculations; subtract if it is retrograde. If the calculated degree is not enough, use the constellation "Dou Su" (one of the 28 lunar mansions) to divide this value, based on the denominator of the planet's speed, so that the calculated value will have adjustments, which need to be corrected back and forth. In short, terms like "Ying," "Yue," and "Man" are used to seek precise division results, while "Qu," "Ji," and "Chu" are used to seek whole division results.
Next, let's look at the situation of Jupiter. Jupiter is together with the sun in the morning, then it begins its retrograde motion, with direct motion lasting 16 days, traversing a distance of 1,742,323 minutes. The planet moves 2 degrees and 323,467 minutes, then appears in the east, lagging behind the sun. During direct motion, it moves quickly, covering 58 minutes and 11 seconds each day, and 11 degrees over 58 days. Then the speed slows down, covering 9 minutes each day, and traversing 9 degrees over 58 days. It then stops, resuming motion 25 days later. During retrograde motion, it moves 1/7 of a minute each day, retreating 12 degrees in 84 days. Then it stops again and begins direct motion 25 days later, covering 9 degrees over 58 days at a speed of 58 minutes and 9 seconds each day. The speed increases during direct motion, covering 11 degrees over 58 days at a speed of 11 minutes each day; at this point, it is ahead of the sun and sets in the west in the evening. After 16 days, having covered a distance of 1,742,323 minutes, the planet moves 2 degrees and 323,467 minutes, then meets with the sun again. One complete cycle lasts a total of 398 days and 3,484,646 minutes, with the planet covering 43 degrees and 2,509,956 minutes.
Sun: In the morning, it rises with the sun and then goes into hiding. Its trajectory is as follows: it moves forward for 71 days, traveling a distance equivalent to 1,489,868 minutes of planetary motion, with the planet moving 55 degrees and 242,860.5 minutes of arc. Then it appears in the east in the morning, behind the sun. During its forward motion, it travels 23 minutes and 14 seconds of arc each day, which amounts to 112 degrees over 184 days. It then continues moving forward, but at a slower pace, traveling 23 minutes and 12 seconds of arc each day, covering 48 degrees in 92 days. It stops for eleven days before moving in reverse, traveling 62 minutes and 17 seconds of arc each day, moving back 17 degrees in 62 days. It stops again for eleven days before resuming forward motion, traveling 12 minutes of arc each day, covering 48 degrees in 92 days. It moves forward again, this time faster, traveling 14 minutes of arc each day, covering 112 degrees in 184 days; at this point, it appears in front of the sun and sets in the west during the evening. After 71 days, traveling a distance equivalent to 1,489,868 minutes of planetary motion, with the planet moving 55 degrees and 242,860.5 minutes of arc, it appears with the sun again. After completing one full cycle, it totals 779 days and 973,113 minutes, with the planet moving 414 degrees and 478,998 minutes of arc.
Saturn: In the morning, it rises with the sun and then goes into hiding. Its trajectory is as follows: it moves forward for 16 days, traveling a distance equivalent to 1,122,426.5 minutes of planetary motion, with the planet moving 1 degree and 1,995,864.5 minutes of arc. Then it appears in the east in the morning, behind the sun. During its forward motion, it travels 35 minutes and 3 seconds of arc each day, which amounts to 7.5 degrees over 87.5 days. It stops for 34 days before moving in reverse, traveling 17 minutes and 1 second of arc each day, moving back 6 degrees in 102 days. After another 34 days, it resumes forward motion, traveling 3 minutes of arc each day, covering 7.5 degrees in 87 days; at this point, it appears in front of the sun and sets in the west during the evening. After 16 days, traveling a distance equivalent to 1,122,426.5 minutes of planetary motion, with the planet moving 1 degree and 1,995,864.5 minutes of arc, it appears with the sun again. After completing one full cycle, it totals 378 days and 166,272 minutes, with the planet moving 12 degrees and 1,733,148 minutes of arc.
Venus, when it conjoins with the sun in the morning, first "submerges," which means it goes retrograde, retreating four degrees over five days, and then it can be seen in the eastern sky behind the sun. Continuing retrograde, it moves three-fifths of a degree each day, retreating six degrees in ten days. Then it "stays," remaining stationary for eight days. Next, it "revolves," which means it turns to direct motion, moving three minutes of a degree each day, covering thirty-three degrees in forty-six days, and begins direct motion. The speed increases, moving one degree and fifteen minutes each day, covering one hundred sixty degrees over ninety-one days. It moves even faster, traveling one degree and twenty-two minutes each day, covering one hundred thirteen degrees over ninety-one days; at this point, it is behind the sun, appearing in the eastern sky in the morning. Finally, in direct motion for forty-one days, it travels one 56,954th of a circle, and the planet also moves fifty degrees and one 56,954th of a circle, conjoining with the sun again. One conjunction totals two hundred ninety-two days and one 56,954th of a circle, with Venus following the same trajectory.
When Venus conjoins with the sun in the evening, it first "submerges," this time in direct motion, covering one 56,954th of a circle over forty-one days, and the planet moves fifty degrees and one 56,954th of a circle, appearing in the west in front of the sun in the evening. Then it continues in direct motion, speeding up, moving one degree and twenty-two minutes each day, covering one hundred thirteen degrees over ninety-one days. The speed increases again, but the rate of acceleration slows, moving fifteen minutes each day, covering one hundred sixty degrees over ninety-one days, continuing in direct motion. The speed slows down, moving thirty-three minutes of a degree each day, covering thirty-three degrees in forty-six days. Then it "stays," remaining stationary for eight days. It "revolves," turning retrograde, moving three-fifths of a degree each day, retreating six degrees over ten days; at this point, it is positioned in front of the sun, appearing in the west in the evening. "Retrograde," the speed increases, retreating four degrees over five days, and ultimately, it conjoins with the sun again. The two conjunctions are considered one full cycle, totaling five hundred eighty-four days and one hundred thirteen thousand nine hundred eight-one-th of a circle, with Venus following the same trajectory.
Mercury, when it conjuncts with the sun in the morning, first "descends," retrogrades seven degrees in nine days, and then appears in the east behind the sun in the morning. It continues to retrograde, speeding up, moving back one degree a day. It "stays," pausing for two days. Then it "turns," shifting to direct motion, moving at three-quarters of a degree per day, covering eight degrees in nine days, and begins to move forward. The speed increases, moving one degree and a quarter a day, covering twenty-five degrees over twenty days, at which point it appears in the east behind the sun in the morning. Finally, it moves forward for sixteen days, traversing six million four hundred one thousand nine hundred sixty-seven parts of a circle, with the planet also covering thirty-two degrees and six million four hundred one thousand nine hundred sixty-seven parts of a circle, and then it conjoins with the sun again. One conjunction lasts fifty-seven days and includes six million four hundred one thousand nine hundred sixty-seven parts of a circle, with the planet following the same trajectory.
The sunset and the sun set simultaneously, and then the sun moves, sequentially traversing three hundred sixty-four million nine hundred sixty-six thousand six hundred sixty-seven parts of a circle over sixteen days, which is thirty-two degrees and three hundred sixty-four million nine hundred sixty-six thousand six hundred sixty-seven parts of a degree. At this point, it can be seen in the evening in the west, positioned in front of the sun. When it moves quickly, it covers one degree and a quarter a day, totaling twenty-five degrees over twenty days. When moving slowly, it covers seven-eighths of a degree a day, totaling eight degrees over nine days. When stationary, it remains still for two days. When moving in reverse, it retreats one degree a day, appearing in front of the sun, setting in the west in the evening. When moving in reverse at a slow speed, it retreats seven degrees over nine days, and then sets simultaneously with the sun. Two simultaneous sunsets are counted as one cycle, totaling one hundred fifteen days and six million twelve thousand five hundred five parts of a day, with the planet following the same pattern.
Calculate the remaining degrees of the sun's orbit plus the remaining degrees until the celestial body conjuncts with the sun. When the remaining degrees reach a complete cycle according to the daily method, calculate as before to obtain the time and remaining degrees of the celestial body's appearance. Multiply the denominator of the celestial body's orbit by the observed degrees. If the result equals a complete cycle according to the daily method and the denominator cannot be divided evenly, or if it exceeds half of a full circle, then take a full cycle, add the degrees of the orbit, and when the degrees equal the denominator, it represents one degree. The denominators for forward and backward orbits are different. Multiply the denominator of the current orbit by the remaining degrees. If the result equals the original denominator, it is the current orbit degrees. When stagnant, inherit the previous degrees. When in reverse orbit, subtract. If the degrees are not enough for a full circle, divide by the Dipper divisions and use the orbit denominator as a proportion. The degrees will increase and decrease, mutually constraining each other.
During Emperor Wu's reign, Liu Zhi, the attendant from Pingyuan, modified the calendar using the Dipper calendar and calculated the "Four Divisions Method." Every three hundred years, one day is subtracted, using one hundred and fifty as the rule for degrees and thirty-seven as the Dipper divisions. It was determined that the Jiazi year marks the beginning, reaching the tenth year of Taishi, with the year being Jiawu, totaling ninety-seven thousand four hundred eleven years. The Jiazi year's winter solstice began in the middle of the night, and the sun, moon, and five stars began in the Xingji, obtaining the starting point of the era. After embellishing it with some exaggerated expressions, it was titled the "Zhengli."
Duyu, the Marquis of Dangyang, wrote the "Chunqiu Changli," stating: The sun travels one degree per day, and the moon travels thirteen degrees and nineteen minutes, which is an unusual measurement. Officials in charge of astronomical calendars should calculate the speed of the moon's movement to determine the new moon and full moon and set leap months. The leap month does not have a solar term, and the direction of the Big Dipper lies between two solar terms, making it different from other months. Accumulating these interconnected data, the four seasons and eight festivals will remain consistent, forming a year with the utmost precision. By mastering these subtleties in line with the natural order, things can proceed in order without error. Thus, the "Chunqiu" states: "Leap months are meant to correct time, and time is used to organize affairs." However, the operation of yin and yang will produce differences with movement, accumulating deviations that eventually deviate from the calendar. Therefore, Confucius and Qiu Ming often wrote about the new moon and leap months, probably to correct mistakes and clarify the calendar.
Liu Zijun created a "Three Correct Calendars" (三正历) to study the "Spring and Autumn Annals" and calculated that there were a total of 34 solar eclipses with two types, Type A and Type B. However, his "Three Correct Calendars" only produced accurate results once, and compared to others' results, it was the furthest off. Moreover, his calendar also states that an extra day must be added every 6000 years, and as this accumulates year by year, the dates become increasingly inaccurate, which is utterly absurd!
Since ancient times, many who studied the "Spring and Autumn Annals" have erred, either by creating their own methods or by using various calendars from the era of the Yellow Emperor to calculate the new moons recorded in the scriptures (the first day of each lunar month), leading to significant discrepancies. Solar eclipses happen during new moons, which serve as a verification of celestial events. The "Spring and Autumn Annals" also records these solar eclipses occurring on new moons, showing that the "Spring and Autumn Annals" correspond with celestial events. However, Confucian scholars such as Liu Xiang and Jia Kui insist that solar eclipses occur on the second or third day of each month, contradicting the clear records of the sages. The issue stems from their rigid adherence to a single calendar, refusing to adapt based on celestial events.
Because of these matters in the "Spring and Autumn Annals," I wrote an article titled "Historical Discussion," which detailed the principles of the calendar. My main point is: the movement of celestial bodies is continuous; the sun, moon, and stars each travel in their own orbits, as they are all moving bodies. The state of a moving object can never be exactly the same; although the laws and speeds of their motion can generally be determined, as time accumulates year by year and month by month, there will always be subtle differences, which is a natural law. Therefore, the solar eclipses recorded in the "Spring and Autumn Annals" vary from year to year—some years have many, while others may go several years without any. This is completely normal and cannot be explained by a single fixed number, so the calendar will always have discrepancies. The initial error might be small and nearly imperceptible, but over time, the error will grow larger, leading to incorrect calculations of the new moon and full moon days (the last day of each month in the lunar calendar), at which point the calendar must be adjusted to reflect the actual conditions. The "Book of Documents" says, "Honor the vast heavens and align the calendar with the sun, moon, and stars," while the "Book of Changes" says, "Manage the calendar and clarify the times," meaning that the calendar should be based on celestial phenomena, rather than being created to validate them. Based on this reasoning, there must have been many adjustments and changes to the calendar during the over two hundred years of the Spring and Autumn period. Even if the ancient methods have been lost, we can still find some clues in the "Commentaries on the Spring and Autumn Annals" to estimate the general situation. The errors in the calendar calculations are documented in the "Commentaries on the Spring and Autumn Annals." Therefore, those who study the "Spring and Autumn Annals" should carefully check the new moons and solar eclipses according to the dates recorded in the "Commentaries" to infer the dates at that time; however, they do not do this, insisting on their own views and using their own methods to calculate the history of the "Spring and Autumn Annals." This is like measuring your own feet to make shoes but trying to carve someone else's feet to fit them.
After I completed "The Theory of Calendars," during the Xianning era, two skilled calculators, Li Xiu and Bu Xian, developed a new calendar based on my theories in "The Theory of Calendars," called the "Qiandu Calendar," and presented it to the court. This calendar calculates the sun's daily movement at a quarter degree and slightly adjusts the moon's movement. It adjusts the calendar every three hundred years using a binary approach, and after more than seventy years, it is adjusted again based on the magnitude of the gains and losses. The difference is minimal, but enough to ensure the accuracy of long-term calculations. At that time, officials and historians compared the "Qiandu Calendar" with the then-current "Taishi Calendar," cross-referenced with ancient records, and found that the "Qiandu Calendar" was much better than the "Taishi Calendar," with forty-five additional accurate instances compared to the official calendar. The calculation method of this calendar is still preserved today. We also verified it against ten ancient and modern calendars and found that the "Santong Calendar" showed the greatest discrepancies.
The "Spring and Autumn Annals" recorded a total of seven hundred and seventy-nine solar eclipses, with three hundred and ninety-three in the "Classic" section and three hundred and eighty-six in the "Commentary" section, totaling thirty-seven solar eclipses, with three instances lacking specific dates.
The "Huangdi Calendar" recorded four hundred and sixty-six solar eclipses, noting just one recorded solar eclipse.
The "Zhuanxu Calendar" recorded five hundred and ninety solar eclipses, with records of eight solar eclipses noted.
The "Xia Calendar" recorded five hundred and thirty-six solar eclipses, noting fourteen solar eclipses.
The "Zhenxia Calendar" (Xia Calendar revised by Song Zhongzi) recorded four hundred and sixty-six solar eclipses, noting just one solar eclipse.
The "Yin Calendar" recorded five hundred and three solar eclipses, noting thirteen solar eclipses.
The "Zhou Calendar" recorded five hundred and sixty solar eclipses, noting thirteen solar eclipses.
The "Zhenzhou Calendar" (Zhou Calendar revised by Song Zhongzi) recorded four hundred and eighty-five solar eclipses, noting just one solar eclipse.
The "Lu Calendar" recorded five hundred and twenty-nine solar eclipses, noting thirteen solar eclipses.
The "Santong Calendar" recorded four hundred and eighty-four solar eclipses, noting just one solar eclipse.
The "Qianxiang Calendar" recorded four hundred and ninety-five solar eclipses, noting seven solar eclipses.
The "Taishi Calendar" records five hundred and ten solar eclipses, including nineteen recorded solar eclipses. The "Qiandu Calendar" records five hundred and thirty-eight solar eclipses, including nineteen recorded solar eclipses. The commonly used "Chang Calendar" records seven hundred and forty-six solar eclipses, indicating a discrepancy of thirty-three, attributed to inaccuracies in the "Classic of History"; there are also records of four solar eclipses, three of which are not recorded with the cyclical characters. At the end of the Han Dynasty, Song Zhongzi collected seven different calendars to verify the records of the "Spring and Autumn Annals" and found that the calculation methods of the Xia and Zhou calendars differed from those documented in the "Yiwen Zhi", so he renamed them "True Xia Calendar" and "True Zhou Calendar". In the eighth year of Emperor Mu's Yonghe reign, the author Langya Wang Shuo created a new calendar called the "Tong Calendar", using the cyclical characters as the starting point, with a cycle lasting ninety-seven thousand years, counting years using the number four thousand eight hundred and eighty-three, and using one thousand two hundred and five as the division of the twenty-eight constellations. He believed this starting point marked the beginning of the universe's creation.
After the fall of the Western Jin Dynasty, during the reign of Yao Xing of the Later Qin, in the year 404 AD (9th year of the Taiyuan era of Emperor Xiaowu of the Eastern Jin Dynasty), Jiang Ji, a native of Tianshui, wrote a calendar book called "Sanji Jiazi Yuanli." The book states: "In order to establish a calendar, it is necessary to first accurately grasp the laws of the sun and moon's movements, to calculate celestial phenomena and understand earthly changes. If there are mistakes from the beginning, the four seasons would be thrown into chaos. Therefore, Confucius compiled the 'Spring and Autumn Annals' in the order of day by day, month by month, season by season, and year by year, which shows that understanding the changes in celestial phenomena is the basis of managing human affairs, which is why emperors have always placed great importance on it. From the era of Fu Xi through the Han and Wei dynasties, each dynasty has established its own calendar, in pursuit of accuracy. The primary criterion for assessing accuracy is whether it accurately predicts solar and lunar eclipses. However, in ancient literature, only the 'Spring and Autumn Annals' detailed the phenomena of solar eclipses. From Duke Yin to Duke Ai, a total of 36 solar eclipses were recorded over a period of 242 years, but it remains unclear which calendar the 'Spring and Autumn Annals' employed to calculate these solar eclipses. Ban Gu believed that the 'Spring and Autumn Annals' was compiled using the calendar of the state of Lu, and the calendar of Lu was inaccurate, so the arrangement of intercalary months was chaotic. The Lu calendar began its count with the intercalary year, however, the arrangement of intercalary months in the 'Spring and Autumn Annals' does not align with the Lu calendar’s starting point. The 'Mingli Xu' states that to compile the 'Spring and Autumn Annals', Confucius reexamined the old calendar of the Yin and Shang periods, ensuring that its calculation methods could be passed down through generations. Thus, it appears that the 'Spring and Autumn Annals' should be calibrated according to the Yin calendar."
However, when we use the Yin calendar to calculate the astronomical conjunction of the sun and moon as recorded in the "Spring and Autumn Annals," we find that many instances do not align with the Yin calendar. When using the Yin calendar to check the "Spring and Autumn Annals," many new moons (the first day of each month) do not align with the dates recorded in the "Spring and Autumn Annals"; some are one day earlier, while others are one day later. The new moons recorded in the scriptures and transmissions of the "Spring and Autumn Annals" are also different. Logically, one can be chosen, but the scriptures provide verification of solar eclipses, whereas the transmissions contain errors. Fu Qian explained that the "Spring and Autumn Annals" transmissions used the Taiji Shangyuan calendar, which corresponds to the epoch of the "San Tong Calendar" established by Liu Xin. Is it overly far-fetched to interpret the "Spring and Autumn Annals" through the lens of the Han Dynasty calendar? The transmissions of the "Spring and Autumn Annals" contain numerous errors, not limited to this instance. In the 27th year of Duke Xiang, on the new moon of the eleventh month of Yihai, a solar eclipse occurred. The transmissions of the "Spring and Autumn Annals" said, "The morning star is positioned in Shen, the calendar officials are negligent, and both attempts to arrange a leap month were wrong." However, calculations indicate that the conjunction of the sun and moon should indeed occur in this month, and there was no situation where two attempts to arrange a leap month were wrong. Liu Xin's calendar and the solar eclipse recorded in the "Spring and Autumn Annals" align with the new moon only once, while the rest differ by two days. Liu Xin also referenced a statement in the "Five Elements Transmission," claiming that during the Spring and Autumn period, most feudal lords were ineffective in governance, so the movement of the moon was always slower. Liu Xin did not think there was a problem with the calendar itself, but instead fabricated this strange explanation. A solar eclipse serves as a direct verification of celestial phenomena, yet Liu Xin employed his own calendar to refute it, which misrepresents celestial phenomena and misleads future generations!
Du Yu also believed that during the decline of the Zhou Dynasty, the world was thrown into chaos, and scholars were unable to grasp the true calendar. The seven calendars we have today may not have all been in use by the emperors of that era. When we use these seven calendars to calculate both ancient and modern solar and lunar eclipses, we find them to be inaccurate, all due to the differing values of the *doufen*. The 'Yin Calendar' has a *doufen* of one-quarter, the 'Three Unified Calendar' has a *doufen* of 385 out of 1539, the 'Qianxiang Calendar' has a *doufen* of 145 out of 589, and the 'Jingchu Calendar' has a *doufen* of 455 out of 1843. These calendars have different sizes of *doufen* and different methods of calculation. The *doufen* of the 'Yin Calendar' is too coarse, making it unsuitable for now; the *doufen* of the 'Qianxiang Calendar' is too fine, making it unsuitable for ancient times; although the *doufen* of the 'Jingchu Calendar' is relatively moderate, the sun's position is off by four degrees, resulting in inaccurate calculations of solar and lunar eclipses. For example, if a solar eclipse occurs near the eastern star Jing, and we use the position of the moon to calculate it, but find it near the star Shen, the discrepancy is so significant that it undermines its use in predicting celestial events and human affairs.
Now I have developed a new calendar, with a *doufen* of 605 out of 2451, and the sun at 17 degrees of the Dou Star, which marks the starting point for observing celestial events. It can be used to calculate the solar eclipses recorded in the 'Spring and Autumn Annals' as well as to verify current celestial phenomena. When using this calendar to analyze the 36 solar eclipses recorded in the 'Spring and Autumn Annals,' 25 were found to be accurate, 2 were off by a day, 2 occurred at the end of the month, and 5 had discrepancies, making a total of 34 that were relatively accurate. The remaining two instances do not have specific dates for the solar eclipses recorded in the texts, so their accuracy cannot be verified. Various geographical and astronomical texts record: "The calendar was revised every three hundred years."
If we were to use this new calendar we currently have in the Spring and Autumn period, most solar eclipses would occur on the new moon (the first day of the lunar calendar). From the Spring and Autumn period to now, over a thousand years have passed, and the occurrence of solar eclipses has consistently varied around three eclipses occurring near the new and full moons (the first and fifteenth days of the lunar calendar). Therefore, this method can be applied indefinitely, unlike the old hassle of having to revise the calendar every three hundred years!
Look, the calendar we currently use, if we were to apply it to the Spring and Autumn Period, most solar eclipses would occur on the first day of the lunar calendar. From the Spring and Autumn Period to now, over a thousand years have passed, and the timing of solar eclipses tends to fluctuate around the first and fifteenth days of the lunar calendar. Therefore, this calendar can still be used, unlike the previous system that required changing the calendar every three hundred years, which was quite cumbersome.
From the beginning of the Jiazi era to the first year of Duke Yin of Lu, in the Jiwei year, a total of 82,736 years have passed. Counting up to the ninth year of Taiyuan in the Jin Xiaowu period, Jiashen year, a total of 83,841 years have passed.
The Yuan law is 7,353; the Ji law is 2,451; bringing the total to 179,044. The Ri law is 6,602; the month cycle is 32,766; the Qi division is 12,860; the Yuan month is 99,045; the Ji month is 3,315; the Mei division is 44,761; the Mei law is 643; the Dou division is 605; the Zhou Tian is 89,520 (also known as the Ji Ri); the Zhang month is 235; the Zhang year is 19; the Zhang leap month is 7; the year midpoint is 12; the meeting number is 47 (the sun and moon complete a cycle every 893 years, a total of 47 meetings, which divide evenly); the Qi midpoint is 12.
The Jiazi era's exchange is 9157; the Jiashen era's exchange is 6337; the Jiachen era's exchange is 3517; the Zhou half is 127; the total for the new moon is 941; the total for the meeting year is 893; the total for the meeting month is 11,045; the small fraction (1) is 2196; the number of chapters is 129; the small fraction (2) is 2183; the large leap fraction of the week is 76,269; the historical cycle is 447,610 (half a week); the total for the meeting is 38,134; the difference is 11,986; the meeting rate is 1882; the method of small fraction is 2209; the entry limit is 11,104; the small week is 254; the rate of the Jiazi era is 49,178; the rate of the Jiashen era is 58,231; the rate of the Jiachen era is 67,284; the total week is 167,063; the remaining days of the week are 3362; the week void count is 2701.
This text records a series of astronomical calendar calculations, including various chronological methods, cycles, and numerical values, demonstrating the complexity and precision of ancient astronomical calendar calculations. These numbers represent the profound understanding ancient astronomers had of time and the laws of the universe and their precise calculation skills. Let's first talk about the "Five-Star Convergence Method." This method is based on actual observed results, rather than rigidly applying previous theories. As you can see, determining the starting point of celestial movements requires tracing back a long time; while the simplified algorithms we use today are adjusted according to actual conditions. Both methods have their own advantages, which is why the author discusses both.
This guy is impressive; he uses lunar eclipses to measure the angle of the sun's movement, which serves as a benchmark for calendar researchers. He also authored "On the Celestial Sphere," using precise calculations to determine the sun's position on the ecliptic, correcting errors made by earlier Confucian scholars and providing a comprehensive understanding of this topic. "The five-star method is based on what is observed to be correct, not tied to the original. However, the calculations are grounded in the original, and the method is applied to the present context. Each approach is appropriate, which is why the author presents two methods. Using lunar eclipses to determine the position of the sun's movement is fundamental to calendar experts. Furthermore, he wrote "On the Celestial Sphere," tracing the sun's path along the ecliptic, addressing the errors of earlier Confucian scholars and gaining deeper insights from this.
