First, we need to calculate how many days are in a given period. The method is as follows: first, multiply a certain ratio by the nighttime duration of the nearest solar term (节气), then divide by 200 to get the daytime duration; subtract the daytime duration from the nighttime duration using the same ratio to get the nighttime duration; finally, add the daytime and nighttime durations together and divide by two to get the average length of a day. Next, calculate the extra days as a percentage of the average length of a day, then divide by 12 to get a degree. If the remainder of dividing this degree by 3 is 1, it is called "strong"; if it is 2, it is called "weak"; and if it is 0, it is called "few." This degree represents the angle between the moon and the ecliptic. For the solar calendar, add the moon's position on the ecliptic to the extreme point (position of the extremity), and for the lunar calendar, subtract the extreme point to get the moon's angle from the extreme point. Remember, "strong" is positive, "weak" is negative; add the same signs and subtract the different signs. The subtraction is the same: subtract the same signs and add the different signs; there's no additive inverse; two "strong" values are greater than one "few," and one "strong" plus one "weak" cancels each other out.
From the year of Ji Chou in the Shangyuan period to the year of Bing Xu in the Jianan period, a total of 7378 years have passed. The following years are Ji Chou, Wu Yin, Ding Mao, Bing Chen, Yi Si, Jia Wu, Gui Wei, Ren Shen, Xin You, Geng Xu, Ji Hai, Wu Zi, Ding Chou, and Bing Yin. The five elements are associated with the five planets: Jupiter, Mars, Saturn, Venus, and Mercury. Each planet has a fixed value for its orbital cycle and daily angle of movement, referred to as the orbital rate and daily rate. Multiply the number of years by the orbital rate to obtain the lunar method, then multiply the lunar method by the daily rate to get the lunar part; divide the lunar part by the lunar method to get the lunar number. Multiply the total number of days by the lunar method to obtain the daily degree method. Multiply the Dipper fraction by the orbital rate to get the Dipper fraction. (The daily degree method is obtained by multiplying the chronological method by the orbital rate, so here we also use fractions to multiply.)
Next, we need to calculate the major and minor remainders of the five planets. Multiply the common method by the lunar number, divide the daily method by the lunar number to get the major remainder; the leftover part is the minor remainder. Subtract the major remainder from 60. We also need to calculate the entry date and day remainder of the five planets. Multiply the common method by the lunar remainder, then multiply the combined lunar method by the major minor remainder, add them together, simplify, and finally divide the daily degree method by the simplified result to arrive at the final value.
Then calculate the degrees and the remainder of the five degrees. (Use the week cycle multiplied by the remainder, then simplify using the solar method to get the degrees; the part that cannot be divided is the remainder. If it exceeds the week cycle, subtract the week cycle and the Doufen.)
Year: 7285
Month of the chapter: 7
Chapter month: 235
Within the year: 12
General method: 43026
Solar method: 1457
Meeting number: 47
Week cycle: 215130
Doufen: 145
Jupiter: Week ratio 6722, solar ratio 7341, total month number 13, month remainder 64810, total month method 127718, solar degree method 3959258
New moon large remainder: 23
New moon small remainder: 1370
Day of entering the month: 15
Goodness, these dense numbers are overwhelming! This is probably a record of ancient astronomical calculations, right? Let's go through it sentence by sentence.
First, "solar remainder, three million four hundred eighty-four thousand six hundred forty-six." This means that the remaining value of the solar is three million four hundred eighty-four thousand six hundred forty-six. It's hard for us to understand what specific unit this refers to now, but it's probably a result of astronomical calculations.
"New moon Xu Fen, one hundred fifty." The new moon Xu Fen is one hundred fifty. What "new moon Xu Fen" means can only be explained in conjunction with the calendar knowledge of the time.
"Doufen, nine hundred seventy-four thousand six hundred ninety." Doufen is nine hundred seventy-four thousand six hundred ninety. This "Doufen" likely refers to some astronomical unit.
"Degree, thirty-three." The degree is thirty-three.
"Degree remainder, two million nine thousand nine hundred fifty-six." The remaining value of the degree is two million nine thousand nine hundred fifty-six. These numbers give the impression of calculating the positions of stars.
Next is the calculation result regarding "Fire." "Fire: Week ratio, three thousand four hundred seven. Solar ratio, seven thousand two hundred seventy-one. Total month number, twenty-six. Month remainder, twenty-five thousand six hundred twenty-seven. Total month method, sixty-four thousand seven hundred thirty-three. Solar degree method, two million six thousand seven hundred twenty-three. New moon large remainder, forty-seven. New moon small remainder, one thousand one hundred fifty-seven. Day of entering the month, twelve." This section contains various astronomical parameters related to "Fire," including week ratio, solar ratio, total month number, etc. The precise meanings would require explanation from a professional astronomer. In any case, it's a collection of astronomical calculations that can be quite overwhelming.
Then there are calculations regarding the planet "Earth." "Earth: orbital circumference, 3529. daily orbital period, 3653. total lunar months, 12. lunar remainder count, 53843. total lunar calculation, 6751. daily calculation, 278581. major lunar remainder count, 54. minor lunar remainder count, 534. lunar day count, 24." Similar to the section about the planet "Mars," this is also a series of astronomical data.
Next is "Venus." "Venus: orbital circumference, 9022. daily orbital period, 7213. total lunar months, 9. lunar remainder count, 152293. total lunar calculation, 171418. daily calculation, 5313958. major lunar remainder count, 25. minor lunar remainder count, 1129. lunar day count, 27." The astronomical calculations are similar to the previous planets.
Lastly, "Mercury." "Mercury: orbital circumference, 11561. daily orbital period, 1834. total lunar months, 1. lunar remainder count, 211331. total lunar calculation, 219659. daily calculation, 6809429. major lunar remainder count, 29." This data is also similar to the calculations of the previous planets. In summary, this passage records the ancient astronomical calculations of several planets, and the specific meanings must be interpreted alongside the calendar and astronomical knowledge of that era. This is essentially an ancient astronomical data report!
Wow, this really looks like ancient astronomical calculations! Let’s look at some basic data: the minor lunar remainder count is 773, the lunar day count is 28, the daily remainder count is 6419967, the major lunar fraction count is 684, the Dipper fraction count is 1676345, the degree count is 57, and the degree remainder count is also 6419967. I'm not quite sure what these numbers specifically refer to, but I'll note them down for now.
Next, calculate the conjunction of stars. Multiply pi (π) by the "year of the Upper Yuan" (what year this "year of the Upper Yuan" refers to is not clear in the original text, let's not worry about it for now) to get a "conjunction total." If the result is a whole number, then it's simple; if it's not a whole number, the leftover portion is referred to as "conjunction remainder." Then divide the conjunction total by pi to obtain a number, which represents the year of the star conjunction. If the result is 1, it's the previous year; if it's 2, it's two years ago; if it's neither 1 nor 2, then it's the current year. Subtract pi from the "conjunction remainder" to get the "degree fraction." If the "conjunction total" of Venus and Mercury is an odd number, it's in the morning; if it's even, it's in the evening.
Next, calculate the conjunction of the moon. Multiply the number of months and the month remainder by the "conjunction total." If the result is a whole number, it indicates compliance with the conjunction of the moon rule; otherwise, the remaining part is the month remainder. Subtract the product of the month from the conjunction of the moon result; the remainder is the month of entry. Also consider the impact of leap months; finally, calculate the conjunction of the moon result. If it's at the boundary of a leap month, adjust it using the new moon.
Next, calculate the conjunction of stars and the entry date of the moon. Use specific methods mentioned in the original text, such as "common method," "conjunction method," and "association number," which would require further explanation to fully understand. Ultimately, obtain the conjunction of stars and entry date of the moon; if the result is not a whole number, the leftover portion is referred to as the day remainder.
Then, calculate the degrees. Multiply the days of the week by the degree fraction; if the result is a whole number, then you get one degree; if it's not a whole number, the remaining part is the remainder. The original text states, "measure the degree using the five steps of the ox," but I find this difficult to understand without additional context.
The above is the part about calculating the conjunction of stars; next is to calculate the positions of Jupiter and Mars.
Jupiter: retrograde for 32 days, moving for 3,484,646 minutes; direct for 366 days; retrograde by 5 degrees, moving for 2,509,956 minutes; direct by 40 degrees (after subtracting 12 degrees from retrograde, the actual movement is 28 degrees).
Mars: retrograde for 143 days, moving for 973,113 minutes; direct for 636 days; retrograde by 110 degrees, moving for 478,998 minutes.
In summary, this passage outlines a complex method for astronomical calculations, involving many professional terms and calculation steps. To fully understand it, more detailed background information and professional knowledge are required. I have tried to translate it into modern language, but some professional terms and calculation methods I cannot fully explain.
This thing makes one complete turn at 320 degrees. (But subtracting 17 degrees due to retrograde motion, so it is actually 303 degrees.) Saturn, hiding underground for 33 days, a total of 166,272 minutes. It can be seen for 345 days. During retrograde, it turns 3 degrees, totaling 1,731,148 minutes. It progresses 15 degrees. (Subtracting 6 degrees for retrograde, it actually moves 9 degrees.)
Second paragraph:
As for Venus, it appears in the east in the morning for 82 days, a total of 113,908 minutes. Then it can be seen in the west, visible for 246 days. (Subtracting 6 degrees for retrograde, it actually moves 240 degrees.) In the morning, when it lurks, it turns 100 degrees, which is also 113,908 minutes. Then it can be seen in the east. (Its daily motion is the same in the west. It lurks for 10 days, retrograding 8 degrees.)
Third paragraph:
Mercury, visible in the morning for 33 days, a total of 6,012,505 minutes. It can be seen in the west for 32 days. (Subtracting 1 degree for retrograde, it actually moves 32 degrees.) When it is retrograde, it turns 65 degrees, a total of 6,012,505 minutes. It can be seen in the east, with the same daily motion as in the west, visible for 18 days, retrograding 14 degrees.
The calculation method is as follows: add the days of the occulted planets and the remaining degrees, then add the remaining degrees of the stars and the sun. If the remainder equals a full day's worth of degrees, you complete a cycle. As mentioned earlier, this can be used to calculate the days and degrees of the appearance of the stars. Multiply the denominator of the star's movement by the visible degrees, and the remainder is calculated as a day's degree. If the remainder is less than half, it is discarded; if it exceeds half, it is treated as a unit. Add this unit to the fraction of its movement, and when the fraction reaches the denominator, one degree is obtained. The denominators for direct and retrograde movements are different. Multiply the current denominator by the original fraction, and if the result equals the original denominator, it is the current fraction. The remaining part carries over from before, subtracted if retrograde. If the hidden degrees don't complete a cycle, divide by the fraction using the movement's denominator as a ratio, allowing for fluctuations in the fractions. Terms like surplus and full are for precise division; "go" and "divide" refer to exhaustive division.
In the morning, when the sun and Jupiter appear simultaneously, Jupiter begins to hide. Then Jupiter starts moving forward, and after 16 days, it has traveled 1,742,323.2 minutes (degrees), while the planet has moved 2 degrees and 323,467 minutes. Then, Jupiter can be seen in the east in the morning, behind the sun. Next, Jupiter's speed increases, moving 58 minutes and 11 degrees per day for 58 days. Afterwards, the speed slows down, moving 9 minutes and 9 degrees per day for 58 days. Jupiter then stops moving, and only starts moving backwards 25 days later. During retrograde motion, it moves back 7 minutes and 1/7 of a degree per day for 84 days. It stops again, and 25 days later starts moving forward again, moving 58 minutes and 9 degrees per day for 58 days. The speed then increases, moving 11 minutes and 11 degrees per day for 58 days, with Jupiter now appearing in front of the sun and can be seen hiding in the west in the evening. After 16 days, having traveled 1,742,323.2 minutes, and the planet moving 2 degrees and 323,467 minutes, Jupiter appears simultaneously with the sun again. One complete cycle is completed in a total of 398 days, 3,484,646 minutes, and the planet moving 43 degrees and 2,509,956 minutes.
In the morning, when the sun and Mars appear at the same time, Mars remains hidden. Then Mars starts to move forward; after 71 days, it has traveled 1,489,868 arcminutes, while the planet has traveled an additional 55 degrees and 1,242,860.5 arcminutes. Then in the morning, Mars can be seen in the east, behind the sun. Next, Mars moves 23 arcminutes and 14 arcseconds each day, covering 112 degrees in 184 days. After that, the speed slows down, moving 23 arcminutes and 12 arcseconds each day, covering 48 degrees in 92 days. After stopping, Mars begins to move backward 11 days later. During the backward movement, it moves 62 arcminutes and 17 arcseconds backward each day, covering 17 degrees in 62 days. After stopping again, it resumes forward motion 11 days later, moving 12 arcminutes each day, covering 48 degrees in 92 days. Then the speed increases, moving 14 arcminutes each day, covering 112 degrees in 184 days. At this point, Mars is positioned in front of the sun and can be seen lurking in the west during the evening. After 71 days, having covered 1,489,868 arcminutes, the planet has traveled an additional 55 degrees and 1,242,860.5 arcminutes, at which point Mars appears at the same time as the sun. One cycle is completed, totaling 779 days and 973,130 arcminutes, with the planet having traveled 414 degrees and 47,998 arcminutes.
In the morning, when Saturn and the sun appear at the same time, Saturn remains hidden. It moves forward, covering a distance of 1,122,426.5 arcminutes every sixteen days, while the planet travels one degree and 1,995,864.5 arcminutes. Then in the morning, it can be seen in the east, behind the sun. During the forward movement, it moves 35 arcminutes and 3 arcseconds each day, covering seven and a half degrees in 87 and a half days. Then it stops for 34 days. After that, it moves backward, moving 17 arcminutes and 1 arcsecond each day, covering six degrees in 102 days. After another 34 days, it resumes forward motion, traveling one-third of an arcdegree each day, covering seven and a half degrees in 87 days. At this point, it is positioned in front of the sun and can be seen lurking in the west during the evening. After sixteen days, having covered 1,122,426.5 arcminutes, the planet has traveled one degree and 1,995,864.5 arcminutes, then it appears at the same time as the sun again. After one complete cycle, totaling 378 days and 166,272 arcminutes, the planet has traveled 12 degrees and 173,148 arcminutes.
In the morning, Venus and the Sun appeared simultaneously, and Venus slipped into the background. It went retrograde, retreating four degrees in five days, then it was seen in the morning in the east, behind the Sun. During its retrograde motion, it retreated 0.6 degrees each day, retreating six degrees after ten days. Then it remained stationary for eight days. After that, it went direct, moving relatively slowly at a rate of thirty-three degrees and forty-six minutes each day, covering a total of thirty-three degrees over forty-six days while moving direct. Its speed increased, moving one degree, fifteen minutes, and ninety-one seconds each day, covering one hundred six degrees in ninety-one days. It then continued to move direct, increasing its speed further to twenty-two degrees and ninety-one minutes each day, covering one hundred thirteen degrees in ninety-one days; at this point, it was behind the Sun, concealed in the eastern sky. While going direct, it traversed a distance of fifty-six thousand nine hundred fifty-four minutes over forty-one days, and the planet also covered a distance of fifty degrees in the same fifty-six thousand nine hundred fifty-four minutes, and then appeared simultaneously with the Sun again. This conjunction lasted a total of two hundred ninety-two days and fifty-six thousand nine hundred fifty-four minutes, with the planet traveling the same distance.
In the evening, Venus and the Sun appeared simultaneously, and Venus slipped into the background. It went direct, traversing a distance of fifty-six thousand nine hundred fifty-four minutes over forty-one days, while the planet covered a distance of fifty degrees in fifty-nine thousand nine hundred fifty-four minutes, and then it was visible in the evening sky to the west, positioned in front of the Sun. While going direct, it moved very quickly, traveling twenty-two degrees and ninety-one minutes each day, covering one hundred thirteen degrees in ninety-one days. It then continued to move direct, but its speed slowed down, traveling one degree and fifteen minutes each day, covering one hundred six degrees in ninety-one days while going direct. Its speed decreased further, moving thirty-three degrees and forty-six minutes each day, covering thirty-three degrees in forty-six days. Then it remained stationary for eight days. After that, it went retrograde, retreating 0.6 degrees each day, retreating six degrees after ten days, at which point it was in front of the Sun, hiding in the west in the evening. While going retrograde, it moved very quickly, retreating four degrees after five days, and then appeared simultaneously with the Sun again. Thus, after two conjunctions, a complete cycle lasted a total of five hundred eighty-four days and one hundred thirteen thousand nine hundred eight minutes of travel, with the planet traveling the same distance.
In the morning, Mercury and the Sun were conjunct. Then it appeared to be dormant, starting to retrograde, having retreated seven degrees over nine days, and it could be seen in the east in the morning, located behind the Sun. Continuing to retrograde at a fast speed, it retreated one degree each day. It stopped, remaining stationary for two days. Then it turned to direct motion, moving slowly, covering seven-eighths of the Sun's daily path, traversing eight degrees in nine days, moving in the direct direction. The speed increased, traveling one and a quarter degrees each day, covering twenty-five degrees in twenty days, still located behind the Sun. In the morning, Mercury appeared in the east, starting direct motion; after sixteen days, six hundred forty-one thousand nine hundred sixty-seven minutes, it traveled thirty-two degrees, six hundred forty-one thousand nine hundred sixty-seven minutes, and ultimately aligned with the Sun once more. One conjunction took a total of fifty-seven days, six hundred forty-one thousand nine hundred sixty-seven minutes, and Mercury's travel distance was the same.
In the evening, Mercury and the Sun were conjunct. Then it appeared to be dormant, starting direct motion; after sixteen days, six hundred forty-one thousand nine hundred sixty-seven minutes, it traveled thirty-two degrees, six hundred forty-one thousand nine hundred sixty-seven minutes, and was visible in the west at dusk, located in front of the Sun. Continuing in direct motion at a fast speed, it traveled one and a quarter degrees each day, covering twenty-five degrees in twenty days. The speed slowed down, covering seven-eighths of the Sun's daily path, traversing eight degrees in nine days. It stopped, remaining stationary for two days. Then it turned to retrograde, retreating one degree each day, located in front of the Sun, dormant in the west at dusk. Retrograding at a slow speed, it retreated seven degrees after nine days, ultimately being in conjunction with the Sun again. Two conjunctions completed one cycle, taking a total of one hundred fifteen days, six hundred twelve thousand five hundred five minutes, and Mercury's travel distance was also the same.
