First, we need to calculate the time frame using various methods to clarify the days, months, and years. You see, this method is quite complex, taking into account the variations in the lengths of day and night, as well as monthly gains and losses, using various coefficients for multiplication and division to calculate the accurate date. For example, calculating the daily lunar cycles, adjusting with the lunar weeks, and finally determining the date. Then, we need to calculate the lengths of day and night, using various ratios to calculate the accurate dawn and dusk moments.
Next, calculate the distance of the moon from the ecliptic plane. This requires many complex calculations, including addition, subtraction, multiplication, and division, considering positive and negative signs, combining similar terms and accounting for differences; overall, it's quite troublesome to calculate. From the Jichou year in the Shangyuan era to the Bingxu year in the Jian'an era, a total of 7,378 years have passed. The following years are: Jichou, Wuyin, Dingmao, Bingshen, Yisi, Jiawu, Guiwei, Renshen, Xinyou, Gengxu, Jihai, Wuzi, Dingchou, Bingshen.
Then, we need to consider the movements of the five stars (Jupiter, Mars, Saturn, Venus, Mercury). Each star has its own movement rules, calculating their positions based on their orbital cycles and daily motion. This requires many coefficients such as orbital rates, daily rates, lunar calculations, and so forth; it's quite laborious to calculate. Also, calculating the new and old moon positions of the five stars, their entry dates into each month, and the remaining days. Finally, calculating the degrees and degree remainders of the five stars involves the concepts of weekly and constellation divisions, a highly intricate calculation process.
Lastly, summarizing the important numbers: Jiyue (纪月) is 7,285, Zhangrun (章闰) is 7, Zhangyue (章月) is 235, Suizhong (岁中) is 12, Tongfa (通法) is 43,026, Rifan (日法) is 1,457, Huisu (会数) is 47, Zhoutian (周天) is 215,130, Doufen (斗分) is 145, and the weekly rate of Jupiter is 6,722. These numbers are intermediate results obtained during the calculation process, ultimately aiming to determine the accurate dates and star positions. As you can see, these ancient astronomers truly dedicated immense effort to make these calculations!
Wow, these dense numbers are overwhelming! I'll break it down for you in simple terms.
First paragraph: Walking seven thousand three hundred forty-one (the unit isn’t specified, probably steps or distance) every day totals to thirteen days in a month (possibly referring to a cycle), walking an extra sixty-four thousand eight hundred one in a month (same unit). The total for the month is one hundred twenty-seven thousand seven hundred eighteen (same unit), and the average daily walk is three hundred ninety-five thousand nine hundred fifty-eight (same unit). On the first day of the lunar month, there are twenty-three days left until the next new moon, and on the first day, there are one thousand three hundred seventy (unit unclear). The fifteenth day of the lunar month marks the beginning of the new month, leaving three hundred forty-eight million four hundred sixty-six (same unit) remaining. The virtual division is one hundred fifty, the 斗分 (doufen) is nine hundred seventy-four thousand six hundred ninety, the degree is thirty-three, and the remaining degrees are two hundred fifty million nine hundred ninety-five thousand six (unit unclear).
Second paragraph: Next is fire (possibly referring to a celestial body or cycle): the weekly rate is three thousand four hundred seventy, the daily rate is seven thousand two hundred seventy-one, totaling twenty-six days in a month, with an extra twenty-five thousand six hundred twenty-seven in a month (same unit). The total is sixty-four thousand seven hundred thirty-three, and the average daily walk is two million six thousand seven hundred twenty-three (same unit). On the first day of the lunar month, there are forty-seven days remaining, and on the first day, there are one thousand one hundred fifty-seven (unit unclear). The twelfth day of the lunar month marks the beginning of the new month, leaving ninety-seven million three thousand thirteen remaining. The virtual division is three hundred, the 斗分 (doufen) is four hundred ninety-four thousand one hundred fifteen, the degree is forty-eight, and the remaining degrees are one hundred ninety-nine thousand one hundred six.
Paragraph 3: Next is Earth (which could also refer to celestial bodies or cycles): the lunar rate is three thousand five hundred twenty-nine, the daily rate is three thousand six hundred fifty-three, totaling twelve days in a month, with an additional fifty-three thousand eight hundred forty-three units in a month. Calculated based on a month, the total for the month is sixty-seven thousand fifty-one, with an average daily rate of two hundred seventy-eight thousand five hundred eighty-one units. There are fifty-four extra new moons, and five hundred thirty-four fewer new moons. The 24th day of the lunar month marks the start of the new month, leaving one hundred sixty-six thousand two hundred seventy-two remaining, with nine hundred twenty-three virtual parts, fifty-one thousand one hundred seventy-five actual parts, twelve degrees, and one hundred seventy-three thousand one hundred forty-eight degree remainders.
Paragraph 4: Finally, the next element is Metal (which could also refer to celestial bodies or cycles): the lunar rate is nine thousand twenty-two, the daily rate is seven thousand two hundred thirteen, totaling nine days in a month, with an additional one hundred fifty-two thousand two hundred ninety-three units in a month. Calculated based on a month, the total is one hundred seventy-one thousand four hundred eighteen, with an average daily rate of five hundred thirty-one thousand three hundred fifty-eight units. There are twenty-five extra new moons, and one thousand one hundred twenty-nine fewer new moons. The 27th day of the lunar month marks the start of the new month, leaving fifty-six thousand nine hundred fifty-four remaining, with three hundred twenty-eight virtual parts, one hundred thirty thousand eight hundred nineteen actual parts, two hundred ninety-two degrees, and fifty-six thousand nine hundred fifty-four degree remainders.
In summary, this text records a series of results from astronomical or calendar calculations, filled with various numbers. The specific meanings need to be interpreted in conjunction with the background and professional knowledge at that time. I am currently unable to determine what units these numbers represent and what relationships exist between them. The lunar rate is eleven thousand five hundred sixty-one, the daily rate is one thousand eight hundred thirty-four, and the monthly total is one. The remainder for the month is two hundred eleven thousand three hundred thirty-one, the total monthly method is two hundred nineteen thousand six hundred fifty-nine, and the daily degree method is six hundred eighty-nine thousand four hundred twenty-nine. There are twenty-nine large new moon remainders, seven hundred seventy-three small new moon remainders, the day marking the start of the new month is the 28th, and the daily remainder is six hundred forty-one thousand nine hundred sixty-seven. The new moon virtual parts are six hundred eighty-four, the actual parts are one hundred sixty-seven thousand six hundred thirty-four, the degree is fifty-seven, and the degree remainder is six hundred forty-one thousand nine hundred sixty-seven.
The method of calculating the conjunction of stars is as follows: first, multiply the year you want to calculate by the number of weeks. If the result can be divided by the rate of days, it means the conjunction equals one. If it cannot be divided, the remainder is the conjunction remainder. Then divide the conjunction remainder by the number of weeks. If the quotient is one, it indicates the conjunction year; if the quotient is two, it indicates the year before the conjunction; if the quotient is zero, it is the conjunction year itself. Subtract the number of weeks from the conjunction remainder to obtain the degrees and minutes. For the conjunction of Venus and Mercury, odd numbers indicate morning and even numbers indicate evening.
Next, multiply the total number of months by the conjunction and the remaining months by the conjunction. If the result can be divided by the month calculation method, the quotient is the month, and the remainder is the new remaining month. Subtract the month calculation method from the conjunction of months, and the remaining value is the entry of months. Then multiply the intercalary month by the entry of months. If the result can be divided by the intercalary month, it means there is an intercalary month. Subtract it from the entry of months, and the remaining is used in the middle of the year, which is the conjunction of the Tianzheng calculation. If it falls on an intercalary month, adjust it with the new moon. Multiply the common method by the remaining months, multiply the month calculation method by the remaining small remainder, and then simplify the fraction. If the result can be divided by the rate of days, the quotient is the conjunction of stars and months, and the remainder that cannot be divided is the remaining days, recorded outside the Tianzheng calculation. Multiply the number of weeks by the degrees and minutes. If the result can be divided by the rate of days, the quotient represents one degree, while the remainder is the degree remainder, starting from the fifth ox. The above is the method of calculating the conjunction of stars.
The method of calculating the year is as follows: add the total number of months to the remaining months, and add the remaining months to the remaining months. If the result can be divided by the month calculation method, the quotient is a month. If it cannot be divided, it is the year itself. If it can be divided, subtract it. Consider leap years, and the remaining is the following year; if it exceeds, it indicates the following two years. For Venus and Mercury, morning plus morning equals evening, evening plus evening equals morning.
The method of calculating the remaining new moons and full moons is: add the remaining new moons and full moons to their conjunction. If the result can form a month, add twenty-nine (full moon) or seven hundred and seventy-three (new moon). If the new moon can be divided by the rate of days, subtract it from the full moon, as described above.
The method of calculating the entry of months and remaining days is: add the entry of months and remaining days to the conjunction of the entry of months and remainder. If the remainder can be divided by the rate of days, the quotient is one day. If the previous new moon can fill the virtual points, subtract one day. If the remaining small remainder exceeds seven hundred and seventy-three, subtract twenty-nine days. If it is not enough, subtract thirty days. The remaining value is the entry date for the next conjunction of months.
The method for calculating degrees is as follows: add the degrees and the degree remainders. If the result can be divided by the rate of days, the quotient is one degree.
Jupiter: It is hidden for 32 days and 3,484,646 minutes, and visible for 366 days. Speaking of these five celestial bodies, their movements are quite complex. Jupiter is in retrograde for 5 degrees, totaling 2,509,956 minutes. When it appears, it is at 40 degrees, but after subtracting the retrograde of 12 degrees, it ends up at 28 degrees. As for Mars, it is in retrograde for 143 days and 973,113 minutes; visible for 636 days. It is in retrograde at 110 degrees, 478,998 minutes; then it appears at 320 degrees, and after subtracting the retrograde of 17 degrees, it ends up at 303 degrees. Saturn is in retrograde for 33 days and 166,272 minutes; visible for 345 days. It is in retrograde at 3 degrees, 1,731,148 minutes; then it appears at 15 degrees, and after subtracting the retrograde of 6 degrees, it ends up at 9 degrees. Venus is quite special; it is in retrograde in the east for 82 days, 11,398 minutes; then it appears in the west for 246 days, subtracting the retrograde of 6 degrees, it is still at 246 degrees. When it is in retrograde in the east, it is at 100 degrees, 11,398 minutes; then it appears in the east, and at this time, the daily position is the same as in the west, remaining for 10 days and retreating 8 degrees. Mercury is in retrograde for 33 days and 601,255 minutes; then appears in the west for 32 days, subtracting the retrograde of 1 degree, it ends up at 32 degrees. It is in retrograde at 65 degrees, 601,255 minutes; then it appears in the east, where the daily position is the same as in the west, remaining for 18 days and retreating 14 degrees.
This calculation method sounds daunting. First, you need to add the number of days of the solar period and the remainder, then add that to the number of days and the remainder of the conjunction of the stars, resulting in one. By following these steps, you can calculate the number of days and degrees when the stars appear. Then, multiply the denominator of the star's movement by the observed degrees, and if the remainder can be evenly divided by the number of days, it will yield one. If the remainder is over half, it will also count as one. Add the number of days to the fraction; when the fraction equals the denominator, it amounts to one degree. The denominators for retrograde and direct motion are different, so you need to multiply by the current denominator and divide by the original denominator to get the current fraction. The remaining numbers need to be connected to the previous ones, subtracting for retrograde motion. If the retrograde degrees are not enough, use the dip to divide the fraction, using the current denominator as the rate, and the fraction will increase or decrease, balancing each other. Any mention of "如盈约满" pertains to precise division, while "去及除之" and "取尽之除之" refer to taking the full division.
In the morning when Jupiter and the sun are aligned, Jupiter becomes obscured. Then it starts moving forward, traversing a distance of 1,742,323.2 minutes and moving 2 degrees and 323 minutes and 467 seconds in planetary motion. After that, it becomes visible in the east, positioned behind the sun. It moves quickly forward, traversing 11 degrees and 58 minutes each day. Afterward, its forward speed slows down to 9 minutes and 9 degrees per day for 58 days. Then it stops moving for twenty-five days before starting retrograde motion. During retrograde motion, it moves one-seventh of a degree each day, moving back 12 degrees over eighty-four days. It stops again for twenty-five days before resuming forward motion, covering 58 minutes and 9 degrees each day for 58 days. Then its forward speed increases to 11 minutes and 11 degrees per day for 58 days. At this point, it moves ahead of the sun and can be seen hiding in the west in the evening. Sixteen days later, traversing a distance of 1,742,323.2 minutes and moving 2 degrees and 323 minutes and 467 seconds in planetary motion, it aligns with the sun again. The entire cycle lasts 398 days, covering a distance of 3,484,646 minutes and moving 43 degrees and 250,956 minutes in planetary motion.
The situation on Mars is similar. In the morning, Mars aligns with the Sun and goes into hiding. It then moves forward for 71 days, traveling a distance of 1,489,868 minutes of travel and covering an angle of 55 degrees. In the morning, it can be seen in the east, behind the Sun. While moving forward, it covers 14/23 of a degree each day, totaling 112 degrees over 184 days. After that, its forward speed slows down, covering 12/23 of a degree each day, totaling 48 degrees over 92 days. It then pauses for 11 days. After that, it begins to move backward at a rate of 17/62 of a degree per day for 62 days, covering a total of 17 degrees. It then pauses again for 11 days, and then resumes moving forward, covering 12 minutes each day, totaling 48 degrees over 92 days. Next, its forward speed increases again, covering 14 minutes each day, totaling 112 degrees over 184 days. At this point, it has moved in front of the Sun, and in the evening, it can be seen in the west, becoming less visible. After 71 days, covering a distance of 1,489,868 minutes of travel and covering an angle of 55 degrees, it aligns with the Sun once more. Thus, one complete cycle takes a total of 779 days, covering a total travel time of 970,313 minutes, with the planet moving 414 degrees and 478,998 minutes.
In the morning, the Sun and Saturn appear simultaneously. Saturn first moves forward, and then within sixteen days, Saturn moves 1,122,426.5 minutes (angle), while the planet moves 1,995,864.5 minutes (angle). At this point in the morning, Saturn can be seen in the east, behind the Sun. During its forward motion, Saturn moves 3/35 minutes of angle each day, and can move 7.5 degrees over 87.5 days. Then Saturn stops moving for 34 days. Saturn then retrogrades, moving 1/17 degrees per day, and can move back 6 degrees over 102 days. After 34 days, Saturn resumes its forward motion, moving 3 minutes of angle each day, and can move 7.5 degrees over 87 days, at which point Saturn is positioned in front of the Sun and can be seen in the west during the evening. Within sixteen days, Saturn moves 1,122,426.5 minutes (angle), while the planet moves 1,995,864.5 minutes (angle), and then Saturn and the Sun appear simultaneously. In one complete cycle, the total duration is 378 days and 166,272 minutes (angle), while the planet covers 12 degrees and 173,148 minutes (angle).
In the morning, the sun and Venus appear simultaneously. The orbit of Venus is retrograde at first, moving back four degrees over five days, then in the morning you can see Venus in the east, behind the sun. During its retrograde phase, Venus moves back by five-thirds of a degree each day and can move back six degrees in ten days. Then Venus stops moving for eight days. After that, Venus moves forward, but at a slower speed, covering forty-six and one-third arcminutes each day, and can move thirty-three arcminutes in forty-six days. Then the speed increases to one degree and fifteen ninety-firsts each day, covering one hundred and six arcminutes in ninety-one days. The speed continues to increase, moving one degree and twenty-two ninety-firsts each day, covering one hundred and thirteen arcminutes in ninety-one days, at which point Venus is behind the sun and can be seen in the east in the morning. After moving forward for forty-one days, Venus covers fifty-six thousand nine hundred and fifty-four arcminutes, while the planet covers fifty degrees and fifty-nine thousand nine hundred and fifty-four arcminutes. Then Venus and the sun appear together. In one complete cycle, a total of two hundred and ninety-two days and fifty-six thousand nine hundred and fifty-four arcminutes are covered, with the planet moving the same number of arcminutes.
In the evening, the sun and Venus appear simultaneously. The orbit of Venus is direct at first, covering fifty-six thousand nine hundred and fifty-four arcminutes in forty-one days, while the planet covers fifty degrees and fifty-nine thousand nine hundred and fifty-four arcminutes. Then in the evening, Venus can be seen in the west, in front of the sun. During direct movement, the speed is very fast, covering one degree and twenty-two ninety-firsts each day, and can move one hundred and six arcminutes in ninety-one days. Then the speed slows down, moving one degree and fifteen minutes each day, covering one hundred and six arcminutes in ninety-one days. The speed continues to slow down, covering thirty-three arcminutes each day, and can move thirty-three arcminutes in forty-six days. Then Venus stops moving for eight days. After that, Venus retrogrades, moving back by five-thirds of a degree each day, moving back six degrees in ten days, at which point Venus is in front of the sun and can be seen in the west in the evening. During its retrograde phase, Venus moves back four degrees in five days, then Venus and the sun appear together. In two complete cycles, a total of five hundred eighty-four days and one hundred thirty-nine thousand eight arcminutes are covered, with the planet moving the same number of arcminutes.
In the morning, Mercury meets the sun, hides away first, then moves in the opposite direction, moving back seven degrees in nine days. Then you can see it in the eastern sky, positioned behind the sun. It then continues moving quickly in the opposite direction, retreats one degree in a day. Then it stops, does not move for two days. Then it turns, this time running in the same direction, moving slowly, traversing eight-ninths of the sun's path in a day, covering twenty-five degrees in twenty days, running to the back of the sun. It appears in the eastern sky in the morning, then runs in the same direction for sixteen days, covering one four-hundred ninety-six thousandths of a circle, which amounts to thirty-two degrees and an additional four-hundred ninety-six thousandths of a degree. Then it meets the sun again; in total, it takes fifty-seven days to complete one four-hundred ninety-six thousandths of a circle. Mercury also travels like this.
In the evening, Mercury meets the sun, hides away first, then runs in the same direction for sixteen days, covering one four-hundred ninety-six thousandths of a circle, which amounts to thirty-two degrees and an additional four-hundred ninety-six thousandths of a degree. Then you can see it in the western sky, positioned in front of the sun. Running in the same direction, its speed decreases, covering one and a quarter degrees in a day, covering twenty-five degrees in twenty days, continuing in the same direction. Its speed decreases, traversing eight-ninths of the sun's path in a day, covering eight degrees in nine days. It stops, does not move for two days. Then it turns, this time running in the opposite direction, retreats one degree in a day, running in front of the sun, hiding away in the western sky at night. Running in the opposite direction, moving slowly, retreats seven degrees in nine days, and then meets the sun again. Both encounters are complete; in total, this takes one hundred fifteen days to complete one two-hundred fifty-five thousandths of a circle. Mercury also travels like this.
