First, we need to calculate the specific days of this year. First, we calculate using the Gan method (a specific calculation method, not explained here), and if it is not enough, then we use the Ji method (another calculation method). If both methods are insufficient, then we apply the Neiji Jiazi system (a method of reckoning years) to calculate. After calculating enough, we then apply the Man method to adjust the results, and then calculate using the Waiji Jia Wu year (another method of reckoning years).
Next, based on the Neiji year and the days we need to calculate, we multiply the Zhangyue (a unit of month) by Zhangsui (a unit of year) to get an approximate number of months, with any remainder treated as leap residue (the remaining days of a leap month). If the leap residue exceeds twelve days, then there is a leap month in this year. Then we multiply by the Tong method (a calculation method) to get an approximate number of days. If it exceeds the Ri method (number of days in a day), we keep the accurate number of days, with any remaining counted as small remainder. We then divide the accurate number of days by sixty (sixty days) to get a big remainder. We write down the calculated Neiji year and big remainder, and the calculated day will be the 1st day of the 11th month in the Tianzheng calendar (lunar calendar 11th month 1st day).
To calculate the day of the next month, we add twenty-nine days to the big remainder and add seven hundred and seventy-three to the small remainder. If the small remainder exceeds the Ri method, we subtract from the big remainder. If the small remainder exceeds six hundred and eighty-four, then this month is a long month.
Next, we calculate the winter solstice. Using the same method, we multiply the small remainder by the Neiji year, with any excess over the Ji method considered a big remainder, and any shortfall counted as small remainder. We divide by sixty, record the result, and the calculated day will be the winter solstice in the Tianzheng calendar.
Then we calculate the small remainder of the winter solstice, add fifteen, then add five hundred and fifteen to the small remainder. If it exceeds two thousand three hundred and fifty-six, we subtract from the big remainder, and continue this process.
We subtract the Zhangsui from the leap residue, multiply the remaining number by Suizhong (a specific time point in a year). If it exceeds Zhangrun (a leap month in a year), we count it as one month. If it is not enough, then we count it as one month if it exceeds half; this method allows for some flexibility while preventing the occurrence of a nonexistent middle month.
In Danyu, add seven, and to Xiaoyu, add half of five hundred fifty-seven. If Xiaoyu exceeds the solar limit, subtract it from Danyu; the remainder can then be calculated using the previous method to find the first quarter moon. Using this method, you can also calculate the full moon, last quarter moon, and the first day of the next month. If the small remainder from the first quarter moon is less than four hundred and one, multiply by one hundred ke (a time unit); if it exceeds the solar limit, it counts as one ke; if it’s insufficient, use one-tenth to determine the fraction. Using the recent solar terms and the remaining time from the night leak (an ancient timekeeping device), one can determine the specific time.
Next, calculate the days without sunlight (the days when the sun's shadow is absent) after the winter solstice. Multiply the remainder by the lunar calendar year; if it exceeds the calendar limit, it counts as accumulated days without sunlight, and any remainder is added to the accumulated days. Use the convergence method multiplied by the accumulated days; if it exceeds the days without sunlight, leave the large remainder, and the insufficient part is the small remainder. Record the large remainder, and the calculated days will be the days without sunlight after the winter solstice.
To find the next day without sunlight, add sixty-nine to the large remainder and sixty-four to the small remainder; if it exceeds the law, deduct it from the large remainder. If there are no fractions, it indicates the end.
Multiply the calendar limit by the accumulated days (the total number of days); if it exceeds the cycle (360 degrees), subtract it, and the remainder divided by the calendar limit gives the degrees. Start counting from five degrees before the Ox constellation, divide by the order of the constellations; if it is less than one constellation, that is the position of the midnight of the lunar new year.
To calculate the next day, add one degree and divide by the fraction using the celestial measure (one of the twenty-eight constellations); if the fraction is small, subtract one degree and add it using the calendar limit.
Finally, calculate the moon's position at midnight of the lunar new year. Multiply the lunar cycle (the number of days in a month) by the accumulated days; if it exceeds the cycle, subtract it, and the remainder exceeding the calendar limit counts as degrees, while the insufficient part is the fraction. Using the previous method, you can obtain the result.
Next, calculate the upcoming month; for a small month, add 22 degrees and 258 minutes. For a large month, add one day, which equals 13 degrees and 217 minutes, completing a full degree. Winter is almost over, and the moon is near the Zhan and Xin constellations.
First, let's calculate the moon's position on the first day of next month. Multiply the number of days in a year by the decimal remaining from the new moon; a complete count is a large fraction; if insufficient, it is a small fraction. Use the large fraction to divide the degrees at the new moon's midnight; after completing the calendar limit, you'll get the degrees, and the method is the same as before, allowing you to calculate the accurate time of the solar and lunar conjunction.
Next month, add 29 degrees to the new moon's degree; the large division equals 312, and the small division equals 25. Subtract the small division from the large division when it is full, then obtain the degree after the full division, and then divide by the large division using the appropriate method.
Next, calculate the positions of the waxing and waning moons. First, calculate the waxing moon by adding 7 degrees to the new moon's degree, which is 225 minutes, and the small division is 17.5. Calculate the degree and small division as before, and you can then calculate the position of the waxing moon. You can also calculate the full moon, waning moon, and the timing of the next new moon.
To find the moon's orbit position, add 98 degrees to the new moon's degree; the large division is 480, and the small division is 41. Calculate the degree and small division as before, and you can calculate the position of the waxing moon. Adding more will allow you to calculate the full moon, waning moon, and the timing of the next new moon.
Next, calculate the time of solar and lunar eclipses. Use the solar method for the sun and the lunar method for the moon, multiply by the night leaking time of the nearest solar term, then divide by 200 to get the bright division. Subtract the solar method for the sun and the lunar method for the moon; the remainder represents the dark division. Add the time of midnight and calculate the degree according to the previous method.
First, determine the reference year; subtract the time to be calculated from the reference year. Multiply the remaining years by the meeting rate. If the result equals the meeting year, it is a cumulative eclipse; if there is a remainder, add 1. Then multiply by the meeting month; if the result equals the meeting rate, it is a cumulative month; if this is insufficient, begin your calculations from Tianzheng.
To calculate the next solar eclipse, add 5 months. The month remainder is 1635, and the full meeting rate gives one month; this is the full moon.
Because the winter solstice has a relatively large remainder, multiply the small remainder by 2; this corresponds to the day governed by the Kan hexagram. Add the small remainder of 175; subtract from the large remainder using the Gan method; this is the day governed by the Zhongfu hexagram.
Calculate the next hexagram by adding 6 to each; the large remainder is 6, and the small remainder is 13. From each of the four positive hexagrams, select one day and multiply the small remainder by 2.
First, determine the large and small remainders of the winter solstice. Add 27 to the large remainder and 927 to the small remainder; subtract from the large remainder using the full 2356, and get the day when the earth hexagram is in charge. Add 18 to the large remainder and 618 to the small remainder to get the day when the wood of Lichun is in charge. Add 73 to the large remainder and 116 to the small remainder to get the earth again. According to the order of the earth, you can calculate the days when fire, metal, and water are in charge.
Finally, multiply the small remainder by 12, and use the full method to get one Chen, starting from Zi. This is based on the small remainder, which is determined independently of the calculations for the new moon, waxing moon, and full moon.
First, we multiply one hundred by a decimal number, and then round the result according to the rules, with the remaining part, which is less than one-tenth, requiring further subdivision. The calculation method is based on the solar terms, starting from midnight and continuing until the water level stops rising at night, using approximate values to represent.
Next, the calculation process involves both progress and regression. Add the result for progress and subtract for regression. The difference between progress and regression begins at two degrees, decreasing by one point every four degrees, halving each time, decreasing again after three times until the difference reaches three. After five degrees, return to the initial state.
The moon's movement speed varies, but overall, it follows a repetitive cycle with a consistent pattern. The calculation method combines astronomical and daily numbers, multiplying the remainder by itself, then dividing by the total number of weeks to get the portion that exceeds one cycle. By adding this portion to a cycle and then dividing by the number of days it takes the moon to complete a cycle, you can determine the specific date. The changes in the moon's movement speed are due to natural laws. By adding the speed changes and the moon's movement speed, the degrees and minutes of movement for each day can be calculated. Adding the values of speed changes results in a profit and loss rate. Increases keep increasing, and decreases keep decreasing, allowing for the calculation of cumulative gains and losses. Multiplying half a small cycle by a common calculation method, then subtracting from the total number of weeks, and subtracting from the complete cycle days, will give the degree of the moon's movement on the new moon day.
Below are the specific numerical calculation results:
Day Rotation Degrees Minutes Rate of Loss/Gain Cumulative Gain/Loss Moon Movement Minutes
Day 1: 14 degrees 10 minutes, regression, loss 22, gain 22, 276
Day 2: 14 degrees 9 minutes, regression, loss 21, gain 22, 275
Day 3: 14 degrees 7 minutes, regression, loss 19, gain 43, 273
Day 4: 14 degrees 4 minutes, regression, loss 16, gain 62, 270
Day 5: 14 degrees, regression, loss 12, gain 78, 266
Day 6: 13 degrees 15 minutes, regression, loss 8, gain 90, 262
Day 7: 13 degrees 11 minutes, regression, loss 4, gain 98, 258
Day 8: 13 degrees 7 minutes, regression, loss 102, gain 102, 254
Day 9: 13 degrees 3 minutes, regression, gain 4, gain 102, 250
October 10th: 12 degrees 12 minutes, plus 3, minus 8, yielding 246.
October 11th: 12 degrees 15 minutes, plus 4, minus 11, yielding 243.
October 12th: 12 degrees 11 minutes, plus 3, minus 15, yielding 239.
October 13th: 12 degrees 8 minutes, plus 2, minus 18, yielding 236.
October 14th: 12 degrees 6 minutes, plus 1, minus 20, yielding 234.
October 15th: 12 degrees 5 minutes, minus 1, minus 21, plus 26, yielding 233.
This text describes an ancient astronomical calculation method, involving a series of addition, subtraction, multiplication, and division operations, ultimately obtaining the degrees and dates of the moon's daily movement. A deeper understanding of the specifics may require advanced astronomical knowledge.
On the 16th: 12 degrees 6 minutes, minus 20, plus 5 (since it is less than 20, subtract the deficit and add 5).
The remainder is 5, reducing the initial 20, yielding 234.
On the 17th: 12 degrees 8 minutes, minus 18, plus 5, reducing 15, yielding 236.
On the 18th: 12 degrees 11 minutes, minus 15, plus 5, reducing 23, yielding 239.
On the 19th: 12 degrees 15 minutes, minus 11, plus 5, reducing 48, yielding 243.
On the 20th: 12 degrees 18 minutes, minus 8, plus 5, reducing 59, yielding 246.
On the 21st: 13 degrees 3 minutes, minus 4, plus 5, reducing 67, yielding 250.
On the 22nd: 13 degrees 7 minutes, plus 5, minus 5, reducing 71, yielding 254.
On the 23rd: 13 degrees 11 minutes, plus 5, minus 4, reducing 71, yielding 258.
On the 24th: 13 degrees 15 minutes, plus 5, minus 8, reducing 67, yielding 262.
On the 25th: 14 degrees, plus 5, minus 12, reducing 59, yielding 266.
On the 26th: 14 degrees 4 minutes, plus 5, minus 16, reducing 47, yielding 270.
On the 27th: 14 degrees 7 minutes, this is the third initial increment, plus 3 major cycles, minus 19, reducing 31, yielding 273.
On Sunday, it was 14 degrees (9 minutes), subtract a certain number, add five, subtract twenty-one, decrease by twelve, and the result is two hundred and seventy-five. Points for Sunday: three thousand three hundred and three. Zhou Void: two thousand six hundred and sixty-six. Sunday standard: five thousand nine hundred and sixty-nine. For the entire week, the total is one hundred eighty-five thousand thirty-nine. Historical week: one hundred and sixty-four thousand four hundred and sixty-six. A minor adjustment: one thousand one hundred and one. Major points for the new moon: ten thousand one hundred and eighty-one. Small points: twenty-five. Half a week: one hundred and twenty-seven.
These numbers are used to calculate the new moon (the first day of each month in the lunar calendar). Multiply the accumulated days of each month by the size of the major points for the new moon. If the small points reach thirty-one, subtract from the major points. If the major points reach one hundred and sixty-four thousand four hundred and sixty-six, subtract. Divide the remaining by five thousand nine hundred and sixty-nine; the quotient is the day, and the remainder is the day residue. The day residue is set aside first, and the calculated day is the corresponding date of the new moon.
To calculate the new moon of the next month, add one day to this day. The current day residue is five thousand eight hundred and thirty-two, and the small points are twenty-five.
To calculate the first quarter moon (the fifteenth and thirtieth day of each month in the lunar calendar), add seven days to the new moon respectively. The current day residue is two thousand two hundred and eighty-three, and the small points are twenty-nine and a half. These points need to be converted into days according to the method mentioned above. If the total days reach twenty-seven, subtract twenty-seven days, and the remainder is the weekly count. If the weekly count is not enough for division, subtract one day, and then add two thousand six hundred and sixty-six (Zhou Void).
Wow, this ancient method is really complicated! Let's break it down and explain it in simple terms. First, it explains how to calculate the calendar. First, calculate the accumulated surplus and deficit days, then multiply this by a certain ratio to calculate the added or subtracted days; this is the so-called "time surplus and deficit." Then, it says to subtract the difference in the moon's movement, calculate the surplus and deficit; this surplus and deficit will impact the date of the new moon (the first day of the lunar calendar) and also affect the first quarter moon (the fifteenth and thirtieth day of the lunar calendar).
Next, it explains how to calculate the precise positions of the sun and moon. By multiplying the number of days in a year by the previously calculated time surplus or deficit, then dividing by a certain value, you can obtain a full value, which represents the specific value of the surplus or deficit. Adding or subtracting this value to the current positions of the sun and moon, adjusting according to certain rules, will give you the accurate positions of the sun and moon.
Then, it starts calculating the midnight moment. By multiplying half a day's time by the remainder of the new moon day, and then subtracting the calendar remainder. If the remainder is not enough, add a cycle value and subtract, then subtract a day, add the cycle value and its fraction, you can get the midnight moment.
After calculating the midnight moment, it continues to calculate the following day. The remainder of the calendar must be calculated every day; if the remainder exceeds a cycle, subtract the cycle, and if it is not enough, keep it to add to the next day.
Then, it calculates the surplus or deficit of the midnight moment. By multiplying the remainder of the midnight moment by a ratio, if the result is not a full cycle, use this remainder to adjust the accumulation of surplus or deficit. If the accumulation reaches a full cycle, round it up; if not enough, consider it as a fraction.
Next, it explains how to calculate the daily calendar changes. By multiplying the remainder of the calendar by a decay factor, if not a full cycle, keep the remainder to represent the daily changes. Then, it says to calculate the decay within a cycle; after completing a cycle, add this decay to the decay of the next cycle.
This part explains how to adjust the date based on calendar changes. Use the decay value to adjust the date calculation; if the remainder is not enough, adjust to the next cycle. Finally, it says if the calculated date is not an integer, subtract 1338, then multiply by a constant; if the result is an integer, add 837, then add the number 899, and finally add the decay of the next cycle, continuing the calculation loop.
Finally, it explains how to calculate the dusk and dawn moments. By multiplying the value of the moon's movement by the solar terms moment, then dividing by 200, obtaining a value, then subtracting the value of the moon's movement, obtaining another value. Both of these values are used to adjust the midnight moment to get the dusk and dawn moments. If there is excess value, if it exceeds half, keep it; otherwise, discard it.
In conclusion, this is essentially a comprehensive set of ancient astronomical calculation formulas, densely packed, enough to make anyone dizzy! The brilliance of this algorithm lies in considering various factors, aiming for precise calculations of the positions and times of the sun and moon.
This text describes the calculation methods of ancient calendars, which are quite complex. Let's break it down sentence by sentence and try to explain it in modern language as much as possible.
The first paragraph talks about the basic method of calculating the days of the calendar. "Four tables of the lunar cycle, in and out of three paths, intersecting days, dividing by the rate of the moon, for the day of the calendar." This means that based on the rules of the moon's movement (the specific calculation tables and steps referred to as four tables and three paths, which are quite professional and not necessary to delve into), divide a day into several parts and calculate each day based on the speed of the moon's movement. "Multiply the week by the new moon conjunction, when the moon is in conjunction, the new moon conjunction." This means multiplying the length of one cycle of the moon (synodic month) by a coefficient to get a value called "new moon conjunction." "Multiply the common number by the conjunction number; the remainder is similar to the number of conjunctions, referred to as 'retreat.'" This calculation step is more complex; in simple terms, it involves performing calculations with another coefficient to obtain a correction value called "retreat." "Calculate the daily increments based on the lunar cycle, with the number of conjunctions being the 'rate of difference.'" Finally, based on the moon's cycle, calculate the progress number for each day, as well as a value called "rate of difference." In summary, this paragraph explains the initial steps of calendar calculation and the calculation methods of some key parameters.
The following paragraphs list the daily "loss and gain rate" and "combined number," which are used to adjust the calendar calculation. "One day decrease by one, increase by seventeen on the first day" means decreasing by one on the first day and increasing by seventeen, and so on. The following lines list the values that need to be increased or decreased each day, some of which also include more detailed correction values such as "limit remainder" and "micro-adjustment." "Limit remainder" and "micro-adjustment" represent the remainder and smaller correction amount in the calculation, which involve more precise calendar adjustments. "Lesser Method, four hundred seventy-three" refers to a calculation method, where the value 473 is a parameter in this method. Understanding the specific meanings of these numbers requires deeper knowledge of ancient calendar systems to fully comprehend.
The last paragraph summarizes the entire calendar calculation process. "Using the meeting month to accumulate the lunar months, the remainder is multiplied by the new moon and the differentiation separately..." This paragraph describes using various parameters calculated earlier, as well as a value called "accumulated month of the meeting," to finally calculate the specific date. "The differentiation method is derived from the new moon; if the remainder does not complete the lunar cycle, it indicates a solar calendar; if it does, then it indicates a lunar calendar." This means judging whether it is a solar or lunar calendar based on the calculation results. "Add two days, the remaining days total two thousand five hundred and eighty; the differentiation is nine hundred and fourteen. According to the calculations, add two days, then adjust to thirteen, and subtract the remaining fraction." This paragraph describes a specific calculation example, explaining how to determine the date based on the calculation results. "The lunar and solar calendars eventually transition at specific points, with the lunar month running its course in between." This paragraph explains the alternation of the lunar and solar calendars and the phases of the moon's movement. The last few sentences describe how to adjust the date based on the calendar's gains and losses, and how to use the "profit and loss rate" and "accumulation number" to finally determine the date. In conclusion, this paragraph summarizes the final steps and results of the entire calendar calculation process. The entire text describes a complex calendar calculation method, involving many professional terms and complex calculation processes.
Let's first talk about how to calculate the new moon, which is the first day of the moon. First, use a difference value to multiply the remaining decimal part of the new moon, similar to calculus, calculate a value, then subtract this value from the remaining days calculated in the calendar. If it is not enough to subtract, then add the total days of a month before subtracting, and finally subtract one day. Add back the remaining part and then use an "accumulation number" to simplify this tiny fraction, so you can calculate which day the new moon occurs in the middle of the night.
Next, calculate the second day. Add one day; the remaining day is 31, and the decimal part is also 31. If this decimal part exceeds the accumulation number, subtract the total days of the month. Then continue adding one day until the end of the calendar. If the remaining day exceeds the fractional day, subtract the fractional day; this marks the beginning of the calendar. If the remaining day does not exceed the fractional day, keep it the same. Then, add 2720; if the decimal part is 31, this will give you the start date of the next calendar.
Then, we multiply a "common number" by the waxing and waning of the lunar calendar and the remaining days at midnight. If the remaining days exceed half of a week, it is considered the decimal part. Use the waxing and waning to adjust the remaining days of the lunar calendar; if there are too many or too few remaining days, adjust the remaining days using the monthly cycle, and finalize it. Next, multiply the finalized remaining days by the profit and loss rate; if the result equals the monthly cycle days, use the comprehensive value of profit and loss to determine the value at midnight.
Next, calculate the time of dusk and dawn. Multiply the profit and loss ratio by the number of time segments at night during the recent solar term, and divide by 200 to get the bright time. Subtract this value from the profit and loss ratio to get the dim time. Then use the profit and loss value at midnight to determine the time of dusk and dawn.
If overtime is to be calculated, divide the value of the dusk and dawn time by 12 to get an angle. One-third of the remainder represents "less," less than one minute represents "strong," and two "less" represent "weak." The result calculated this way is the angle of the moon's departure from the ecliptic. For the solar calendar, subtract the extreme angle from the ecliptic calendar, while for the lunar calendar, add the extreme angle to obtain the angle of the moon's departure from the extreme. "Strong" is positive, "weak" is negative; same names are added, different names are subtracted. When subtracting, same names cancel out, and different names are added, with no mutual cancellation; two "strong" plus one "less," minus one "weak."
Starting from the year of Jichou in the Yuan Dynasty to the year of Bingxu in the eleventh year of Jian'an, it totals 7,378 years.
Jichou Wuyin Dingmao Bingchen Yisi Jiwu Guiwei
Renshen Xinyou Gengxu Jihai Wuzi Dingchou Bingyin
Five Elements: Wood, the planet Jupiter; Fire, the planet Mars; Earth, the planet Saturn; Metal, the planet Venus; Water, the planet Mercury. The operational cycles and celestial degrees of each star must be calculated to derive the weekly and daily rates. Multiply the annual chapter by the weekly rate to get the lunar law, and multiply the monthly chapter by the daily rate to get the monthly fraction. If the monthly fraction equals the lunar law, the lunar number is obtained. Multiply the common number by the lunar law to get the daily degree law. Multiply the Dou fraction by the weekly rate to get the Dou fraction. (The daily degree law uses the chronicle law multiplied by the weekly rate, so fractions are also used for multiplication here.)
Finally, calculate the large remainder and small remainder for the five stars' new moon days. (Multiply the common law by the lunar number, and divide the daily law by the lunar number to get the large remainder; the remainder is the small remainder. Subtract the large remainder from 60 to find the small remainder.)
Calculate the degrees of the five planets along with the monthly and daily remainders. (Use the standard method to multiply by the remainder of the month separately, and use the combined month method to multiply by the small remainder of the new moon day, add them together, simplify using the meeting number, and finally divide by the obtained value using the day degree method to get the result.)
This text records some data on ancient astronomical calculations, appearing to be a record of a certain calendar or astrological prediction. Let's break it down sentence by sentence and explain what it means in modern terms.
First, "the degrees and remainders of the five planets. (Subtract the excess to obtain the remainder, multiply by the number of complete cycles, and simplify using the day degree method; the quotient is the degree, and the remainder is the degree remainder. If the degree exceeds a complete cycle, subtract the complete cycle number and add the Doufen.)" This part outlines the calculation method, similar to an instruction manual.
Next, the numbers are as follows:
- Record month: seven thousand two hundred eighty-five (7285)
- Leap month: seven (7)
- Total months: two hundred thirty-five (235)
- Months in a year: twelve (12)
- Standard method: forty-three thousand twenty-six (43026)
- Day method: one thousand four hundred fifty-seven (1457)
- Meeting number: forty-seven (47)
- Complete cycle: two hundred fifteen thousand one hundred thirty (215130)
- Doufen: one hundred forty-five (145)
This resembles a table that catalogs various astronomical parameters.
"Wood: Orbital period, six thousand seven hundred twenty-two; daily orbital rate, seven thousand three hundred forty-one; total number of days, thirteen; remaining days, sixty-four thousand eight hundred one; total lunar calculation, one hundred twenty-seven thousand seven hundred eighteen; daily calculation method, three hundred ninety-five million nine thousand two hundred fifty-eight; major lunar remainder, twenty-three; minor lunar remainder, one thousand three hundred seven; entry month day, fifteen; daily remainder, three hundred forty-eight million four thousand six hundred forty-six; lunar virtual division, one hundred fifty; Dou division (a traditional Chinese astronomical term), nine hundred seventy-four thousand six hundred ninety; degree number, thirty-three; degree remainder, two hundred fifty-nine thousand nine hundred fifty-six." This is a detailed record of the calculation results of Jupiter's orbit, including orbital period, daily orbital rate, total number of days, etc., all of which are parameters related to the movement of Jupiter and can be understood in conjunction with the calendar system at the time. This part is like a detailed record of the calculation results of Jupiter's orbit.
"Fire: Orbital period, three thousand four hundred seven; daily orbital rate, seven thousand two hundred seventy-one; total lunar calculation, twenty-six; remaining days, twenty-five thousand six hundred twenty-seven; total lunar calculation, sixty-four thousand seven hundred thirty-three; daily calculation method, two million six thousand seven hundred twenty-three; major lunar remainder, forty-seven; minor lunar remainder, one thousand one hundred fifty-seven; entry month day, twelve; daily remainder, ninety-seven thousand three hundred thirteen; lunar virtual division, three hundred; Dou division, forty-nine thousand four hundred fifteen; degree number, forty-eight; degree remainder, one hundred ninety-nine thousand seven hundred six." This section is similar to the previous one, about the calculation results of Mars.
"Earth: Orbital period, three thousand five hundred twenty-nine; daily orbital rate, three thousand six hundred fifty-three; total number of days, twelve; remaining days, fifty-three thousand eight hundred forty-three; total lunar calculation, sixty-seven thousand fifty-one; daily calculation method, two hundred seventy-eight thousand five hundred eighty-one; major lunar remainder, fifty-four; minor lunar remainder, five hundred thirty-four; entry month day, twenty-four; daily remainder, one hundred sixty-six thousand two hundred seventy-two; lunar virtual division, nine hundred twenty-three; Dou division, fifty-one thousand one hundred seventy-five; degree number, twelve; degree remainder, one hundred seventy-three thousand one hundred forty-eight." This is about the calculation results of Saturn, with the same recording format as Jupiter and Mars.
"Metal: Orbital period, nine thousand twenty-two; daily orbital rate, seven thousand two hundred thirteen; total number of days, nine." This is about the calculation results of Venus, which only includes partial data.
In summary, this text is a record of ancient astronomical calculations, filled with various astronomical parameters and methods, which is very helpful for our understanding of ancient astronomical calendar knowledge. However, to fully understand its meaning, more in-depth research is needed. Behind these numbers lies the exploration and understanding of the laws of the universe by ancient astronomers.
One month later, the value is 152,293.
According to the combined lunar method, the result is 171,418.
Using the daily degree method, the result is 5,313,958.
The large remainder for the new moon is 25.
The small remainder for the new moon is 1,129.
The day of the month when it begins (入月日) is 27.
The daily remainder is 56,954.
The virtual new moon division is 328.
The Doufen (斗分) is 1,308,190.
The degree is 292.
The degree remainder is 56,954.
Water: The circumference (周率) is 11,561.
The daily rate (日率) is 1,834.
The combined lunar number is 1.
One month later, the value is 211,331.
According to the combined lunar method, the result is 219,659.
Using the daily degree method, the result is 6,809,429.
The large remainder for the new moon is 29.
The small remainder for the new moon is 773.
The day of the month when it begins (入月日) is 28.
The daily remainder is 6,410,967.
The virtual new moon division is 684.
The Doufen (斗分) is 1,676,345.
The degree is 57.
The degree remainder is 6,410,967.
First, input the data for the Upper Yuan (上元) for the year you wish to calculate. Multiply it by the circumference. If it can be evenly divided by the daily rate to get 1, it is called the accumulated combination; the portion that cannot be evenly divided is referred to as the combined remainder. Divide the accumulated combination by the circumference; if it can be evenly divided to get 1, then it is a star combination in previous years; if it can be evenly divided to get 2, then it is a star combination in the previous two years; if it cannot be evenly divided, then it is combined in the current year. Subtract the combined remainder from the circumference; the result is the degree division. For the accumulated combination of gold and water, odd numbers indicate morning, while even numbers indicate evening.
Multiply the number of months and the remainder of months by their product; if the result can be divided evenly by the total months method, then the month is obtained, and the leftover is the remainder of months. Subtract the accumulated months from the counted months to get the entering counted months. Then multiply by the leap month adjustment; if it can be divided evenly by the leap month, a leap month is obtained, which is then subtracted from the entering counted months, and the remaining part is subtracted from the year. This represents the total months calculated outside of the Tianzheng method. If it is during the transition of the leap month, adjust using the new moon.
Apply the general method to the remainder of months and the total months method to the new moon, then divide by the total number of meetings. If the result can be divided evenly by the daily method, this indicates the day of the month for the star conjunction; the remaining part is the remaining day, which is outside the new moon calculation.
Multiply the number of weeks by the number of days; if the result can be divided evenly by the daily method, then it is one degree, and the remaining part is the remainder, counted starting from the beginning of the cycle.
The above is the method for calculating the star conjunction. Add the months together and the remainders together; if it can be divided evenly by the total months method to get a month, then it means in this year. If it cannot be divided evenly, determine the relevant year; if it can be divided, then subtract, considering the leap month. The remaining is the next year; divide again, and then it is the next two years. When gold and water are added in the morning, it becomes evening; when added in the evening, it becomes morning.
First of all, let's calculate the size of the remainder of the moon. Add up the size remainder of the new moon; if it exceeds one month, add either twenty-nine (for large remainder) or seven hundred seventy-three (for small remainder). If the small remainder is full, then the calculation follows the same method as previously described.
Next, calculate the day of the entering month and the remaining day. Add up the day of the entering month and the remaining day; if the remainder is enough for a day, then add a day. If the small remainder was exactly filled with virtual minutes during the conjunction, then subtract one day; if the small remainder exceeds seven hundred seventy-three, then subtract twenty-nine days; if it does not exceed, then subtract thirty days. The remainder is calculated based on the day of the entering month for the subsequent conjunction.
Finally, sum the degrees and their remainders; if it is enough for one day of degrees, then add one degree.
Here are the operating data of Jupiter, Mars, Saturn, Venus, and Mercury:
Jupiter: Duration of hiding: 32 days, 3484646 minutes; Duration of appearance: 366 days; Duration of hiding operation: 5 degrees, 2509956 minutes; Duration of appearance operation: 40 degrees. Retrograde: 12 degrees; Actual operation: 28 degrees.
Mars: Duration of hiding: 143 days, 973113 minutes; Duration of appearance: 636 days; Duration of hiding operation: 110 degrees, 478998 minutes; Duration of appearance operation: 320 degrees. Retrograde: 17 degrees; Actual operation: 303 degrees.
Saturn: remains for 33 days, 166,272 minutes; appears for 345 days; lurks for 3 degrees, 1,733,148 minutes; then appears and travels 15 degrees. (Retrograde movement of 6 degrees, actual movement of 9 degrees.)
Venus: remains in the east in the morning for 82 days, 113,908 minutes; appears in the west for 246 days. (Retrograde movement of 6 degrees, actual movement of 240 degrees.) Lurks for 100 degrees in the morning, 113,908 minutes; then appears in the east. (The daily and western movements are the same; it remains for 10 days, retrograde 8 degrees.)
Mercury: remains in the morning for 33 days, 612,505 minutes; appears in the west for 32 days. (Retrograde movement of 1 degree, actual movement of 31 degrees.) Lurks for 65 degrees, 612,505 minutes; then appears in the east. (The daily and western movements are the same; it remains for 18 days, retrograde 14 degrees.)
First of all, let's calculate the relationship between daily and stellar degrees. Subtract the stellar degrees from the daily degrees, then add back the remainder to the stellar degrees. If the remainder is exactly equal to the daily degrees, then the calculation is correct, and the position of the celestial body is found. Next, multiply the speed of the celestial body (denominator) by the observed angle (in degrees). Handle the remainder using the same method as with daily degrees. If it cannot be divided evenly, treat the remainder as one if it exceeds half of the divisor. Add this result to the degrees of the celestial body, and if it reaches the denominator, increase by one degree. The calculation methods for direct and retrograde movements are different. Use the current speed (denominator) multiplied by the previous remainder, then divide by the previous speed. Get the current degrees. Subtract for retrograde and add for direct movement if there was a previous remainder. If the degrees are not enough, use division, taking speed as a reference, continuously adjusting the degrees and correcting back and forth. In summary, phrases like "fulfillment of obligations" are used to ensure precise division results; "go and divide it," "take the complete division" are all used to obtain the final accurate result.
The situation with Jupiter is as follows: Jupiter appears in the morning alongside the sun, then gradually falls behind, moving forward. After 16 days, its position is 1,742,323 minutes in time, and Jupiter has moved 2,323,467 minutes, which is just over 2 degrees. At this point, it appears to the east of the sun, lagging behind. When moving forward quickly, it covers 11 minutes for every 58 minutes each day, covering a total of 11 degrees over 58 days; when moving forward slowly, it travels 9 minutes each day, covering 9 degrees in 58 days. If Jupiter stays still, it remains motionless for 25 days; when moving in reverse, it retreats 7 minutes out of 58 each day, retreating a total of 12 degrees over 84 days; then it remains still for another 25 days before moving forward again, traveling 9 minutes for every 58 minutes each day, covering 9 degrees in 58 days. When moving forward quickly, it travels 11 minutes each day, covering 11 degrees in 58 days; at this point, it aligns with the sun once more. Over one cycle, it totals 398 days, amounting to 3,484,646 minutes, and Jupiter has moved a total of 43 degrees and 2,509,956 minutes.
In the morning, Mars appears simultaneously with the sun, then Mars appears to "crouch" and begins to move forward. It moves forward for 71 days, covering 1,489,868 minutes, which is 55 degrees and 242,860.5 minutes. Then, we can see Mars in the eastern sky in the morning, behind the sun. While moving forward, Mars travels 14 minutes out of 23 each day, covering a total of 112 degrees over 184 days. It continues moving forward, but the speed slows down, traveling 12 minutes out of 23 each day, covering 48 degrees in 92 days. Then it remains stationary for 11 days. Next, it moves in reverse, traveling 17 minutes out of 62 each day, retreating a total of 17 degrees over 62 days. It stops for another 11 days and then resumes its forward motion, traveling 12 minutes each day, covering 48 degrees in 92 days. It moves forward again, increasing speed, traveling 14 minutes each day, covering a total of 112 degrees over 184 days, at which point it moves in front of the sun and can be seen in the evening sky to the west. After another 71 days, it covers 1,489,868 minutes, which is 55 degrees and 242,860.5 minutes, and it appears simultaneously with the sun again. Overall, the entire cycle lasts 779 days and 973,113 minutes, during which it covers a total of 414 degrees and 478,998 minutes.
As for Saturn, it also appears simultaneously with the sun in the morning, then "goes into a stationary phase" and begins to move forward. It moves forward for 16 days, covering 1,122,426.5 minutes, which is equivalent to 1 degree and 1,995,864.5 minutes. Then we can see Saturn in the eastern morning sky, behind the sun. While moving forward, Saturn travels 3/35 of a degree daily, covering 7.5 degrees in 87.5 days. It then remains stationary for 34 days. After that, it moves backward at a rate of 1/17 of a degree per day, retreating 6 degrees in 102 days. After another 34 days, it resumes its forward motion, covering 3 minutes each day, and 7.5 degrees in 87 days. At this point, it has moved in front of the sun, making it visible in the western sky at night. After another 16 days, it covers 1,122,426.5 minutes, which is again 1 degree and 1,995,864.5 minutes, and it appears simultaneously with the sun again. Over the entire cycle, it takes a total of 378 days and 166,272 minutes, covering 12 degrees and 1,733,148 minutes.
As for Venus, when it conjoins with the sun in the morning, it first enters a stationary phase, meaning it moves backward, retreating 4 degrees in 5 days, making it visible in the eastern sky behind the sun. It then continues to move backward, covering 3/5 of a degree per day, retreating 6 degrees in 10 days. After that, it "stays," pausing for 8 days. Then it begins to move forward at a slower speed, covering 33 degrees in 46 days, or 3/46 of a degree per day. The speed increases, covering 15/91 of a degree per day, or 160 degrees in 91 days. The speed increases further, covering 22/91 of a degree per day, or 113 degrees in 91 days. At this point, it is behind the sun, appearing in the eastern sky in the morning. Finally, it moves forward, covering 1/56,954 of a full circle over 41 days, while Venus also covers 50 degrees and 1/56,954 of a full circle, before conjoining with the sun again. In total, the conjunction takes 292 days and 1/56,954 of a full circle, with Venus following a similar trajectory.
When Venus meets the Sun in the evening, it first "hides", this time it goes in the same direction, completing 41 days to traverse one fifty-six-thousand-nine-hundred-fifty-fourth of a full orbit. The planet moves fifty degrees and one fifty-six-thousand-nine-hundred-fifty-fourth of a full orbit, and in the evening, it can be seen in the west, positioned in front of the Sun. Then it continues in the same direction, speeding up, moving one degree and ninety-one twenty-second degrees per day, completing one hundred and thirteen degrees in ninety-one days. The speed then begins to slow down, moving one degree and fifteen minutes per day, completing one hundred and six degrees in ninety-one days, and then continues in the same direction. The speed slows down again, moving forty-six minutes and thirty-three seconds per day, completing thirty-three degrees in forty-six days. Then it "pauses" for eight days. "Rotate", this time it goes in the opposite direction, moving five-thirds of a degree each day, retreating six degrees in ten days; at this point, it is positioned in front of the Sun and can be seen in the west during the evening. It continues moving in the opposite direction, speeding up to retreat four degrees in five days, and then meets the Sun again. The two conjunctions total five hundred eighty-four days and one one hundred thirty-nine thousand nine hundred eighth of a full orbit; the planet follows the same orbital path.
As for Mercury, when it meets the Sun in the morning, it first "hides", meaning it moves in the opposite direction, retreating seven degrees in nine days, then it can be seen in the east in the morning, behind the Sun. It continues moving in the opposite direction, speeding up to retreat one degree each day. It "pauses" for two days. Then it "rotates", which means going in the same direction, at a relatively slow speed, moving one and an eighth degrees per day, completing eight degrees in nine days. Speeding up, it moves one and a quarter degrees each day, completing twenty-five degrees in twenty days; at this time, it is behind the Sun, appearing in the east in the morning. Then it moves in the same direction, traversing sixty-four million nine thousand sixty-sevenths of a full orbit in sixteen days; the planet walks thirty-two degrees sixty-four million nine thousand sixty-sevenths of a full orbit, and then meets the Sun again. The total duration of one conjunction is fifty-seven days and sixty-four million nine thousand sixty-sevenths of a full orbit; the planet follows the same orbital path.
Well, what on earth is this about? Let me break it down for you, sentence by sentence.
The first sentence, "Mercury: evening and sun together, lurking, moving forward," means that Mercury sets with the sun, and then it lurks, starting to move forward. The terms "lurking" and "moving forward" refer to the state of Mercury's movement, which will be explained shortly. Next, "On the sixteenth day, six hundred forty-one minutes, the planet moves thirty-two degrees, and in the evening, you can see it in the west, in front of the sun," translates to: approximately sixteen days and some extra time, Mercury will move about 32 degrees, and in the evening, you will be able to see it in the west, in front of the sun. The time and angle mentioned here are in ancient measurement units, so we don't need to be overly precise about the specific values. "Moving forward, fast, moving one and a quarter degrees in a day, moving twenty-five degrees in twenty days," means that if Mercury is moving forward (which is to say, moving from west to east like the sun), it moves very quickly, covering one and a quarter degrees in a day, and in twenty days, it can cover twenty-five degrees. "Slow, moving eight-ninths of a degree in a day, moving eight degrees in nine days," this indicates that if Mercury's forward speed slows down, it only moves eight-ninths of a degree in a day, taking nine days to cover eight degrees. "Staying, not moving for two days," which means that Mercury sometimes "stays," meaning it comes to a stop for about two days. "Turning, retrograde, retreating one degree in a day, in front of the sun, evening lurking in the west," this indicates Mercury beginning to move retrograde, meaning it appears to be moving backward, retreating one degree in a day, still in front of the sun, and in the evening, you can see it in the west, then it lurks again. "Retrograde, slow, retreating seven degrees in nine days, aligning with the sun," during retrograde, it moves slowly, retreating seven degrees in nine days, and finally sets with the sun again. The last sentence, "In total, from one conjunction of Mercury and the sun to the next, one hundred fifteen days and six hundred one million two thousand five hundred five minutes, the planets exhibit similar behavior," means that the entire cycle from one conjunction of Mercury and the sun to the next is about one hundred fifteen days and some extra time, and other planets exhibit similar behavior. In summary, this passage describes the trajectory and cycle of Mercury's movement, using ancient astronomical expressions, which are very professional and quite complex.
