Speaking of ancient calculations and calendars, it was quite complex. First, they used "the surplus of calendar days at midnight" multiplied by the "loss and gain rate," similar to dividing the total number of days by a specific number; the remainder is the base number of "night midnight gain and shrink." Then, based on the length of a year ("complete solar year"), they calculated the "minutes" and "degrees," multiplied these numbers, added the remainder, and made continuous adjustments, ultimately obtaining the accurate "fixed degree."
Next, they used "the surplus of calendar days at midnight" multiplied by "column decline" to obtain a new remainder in order to calculate the daily length changes. Then, they used "week cycle" multiplied by "column decline" to obtain a constant used to correct errors in the calendar, ensuring that the calendar could be used in the long term.
During the calculation process, they would adjust the "minutes" according to changes in daily length. If the "minutes" were too high or too low, it affected the calculation of seasonal markers throughout the year. They would multiply the minutes and remainder by the number of days, then add the result to the "fixed degree at midnight" to get the value for the next day. If the calculated result did not match the actual number of Sundays, complex adjustments were needed, such as subtracting 1338, adding 837, or dividing by 899 as needed; in short, it was quite troublesome to calculate.
They adjusted the "loss and gain rate" using "variable decline" to correct the "night midnight gain and shrink." If the calculated result was insufficient, adjustments would be made in reverse.
To calculate more accurate twilight and dawn moments, they used the "minutes" of the moon's orbit multiplied by the "nighttime duration" of the solar terms, then divided by 200 to get the "bright minutes." They then subtracted the "bright minutes" from the "minutes" of the moon's orbit to get the "twilight minutes." Finally, they multiplied the number of days by the "minutes" and then added the "fixed degree at midnight" to get the "twilight dawn fixed degree." If the remainder exceeded half, it was kept; otherwise, it was discarded.
Calculating the calendar also involved factoring in the lunar cycle. They used four tables to record the moon's orbit, and through complex calculations, they eventually obtained the daily length. They multiplied the number of days by the conjunction of the new moon and full moon to calculate the "conjunction minute," then multiplied the conjunction by the number of days to get the "retreat minute," ultimately calculating the daily length changes.
The following are specific examples, presented in table format for clarity:
Lunar-Solar Calendar Decline Loss and Gain Rate Multiplication Factors
Day One Decrease Gain Seventeen Beginning
Day Two (limited remainder of one thousand two hundred and ninety units, with a minor difference of four hundred fifty-seven units.) This is the previous limit
Decrease Gain Sixteen Seventeen
Day Three Decrease Gain Fifteen Thirty-three
Day Four Decrease Gain Twelve Forty-eight
On the fifth day, subtract four, add eight, resulting in sixty.
On the sixth day, subtract three, add four, resulting in sixty-eight.
On the seventh day, subtract three (if this subtraction is insufficient, then treat the shortfall as an addition; for example, if one should subtract three but cannot, then just add one instead).
Add one, resulting in seventy-two.
On the eighth day, add four, subtract two, resulting in seventy-three.
(If the month exceeds halfway, and has passed the extreme point, then it should be subtracted.)
On the ninth day, add four, subtract six, resulting in seventy-one.
This passage describes the complex calculation process of ancient calendar systems, showing that ancient people put in tremendous effort to establish accurate calendars.
Ten days, add three days, subtract ten days, equals sixty-five.
Eleven days, add two days, subtract thirteen days, equals fifty-five.
Twelve days, add one day, subtract fifteen days, equals forty-two.
Thirteen days, (the limit is 3,912, the variation is 1,752.) This is the deadline.
Add one day (initial calculation of the calendar), subtract sixteen days, equals twenty-seven.
Calculate by days (5,203), subtract sixteen from the lesser addition, equals eleven.
Using the lesser law, the result is four hundred seventy-three.
The calendar cycle is one hundred seventy-five thousand six hundred five.
The difference rate is one thousand nine hundred eighty-six.
The new moon conjunction is eighteen thousand three hundred twenty-eight.
The variation is nine hundred fourteen.
The differential law is two thousand two hundred nine.
Subtract the accumulated months of the new moon conjunction from the previous year, then multiply the new moon conjunction and the variation by this difference. If the variation is full, deduct it from the conjunction; if the conjunction is full, subtract the number of days in a week. The remaining portion that does not complete the calendar cycle is the value that is assigned to the solar calendar; if it is full, subtract it, and the remaining part is the value that enters the lunar calendar. The rest are calculated as one day according to the monthly cycle; this is an extra calculation. The sought month conjunction enters the calendar, and the remainder of less than a day is the day remainder.
Adding two days, the day remainder is two thousand five hundred eighty, the variation is nine hundred fourteen. Calculating into days according to the method, subtract thirteen if it reaches thirteen; the remainder is calculated in days. The lunar and solar calendars alternate in this way, entering the calendar time. The remainder before the deadline is the front limit remainder; the remainder after the deadline is the back limit remainder, as the month runs to the middle position.
Calculate the increase and decrease in the lunar calendar separately, by multiplying the conjunction number with the small fraction to get the differential. If the surplus from the increase and decrease combined with the yin-yang day remainder is insufficient, adjust the number of days accordingly. Multiply the determined day remainder by the profit and loss rate, which corresponds to one in the monthly cycle, and use the combined profit and loss number as the constant for additional time.
Multiply the difference rate by the new moon's small remainder, which is similar to the differential method to obtain one, and use it to subtract from the lunar calendar day remainder. If it is insufficient, add the monthly cycle, subtract that, and then subtract one more day. Add the fraction of the day to it, using the conjunction number to simplify the differential to the small fraction; this marks the entry into the lunar calendar at midnight of the new moon.
To find the next day, add one day; the day remainder is thirty-one, and the small fraction is thirty-one. The small fraction, similar to the conjunction number, is deducted from the remainder. When the remainder fills up the monthly cycle, subtract it, and add one day; the lunar calendar calculation is complete. When the remainder fills the fraction of the day, subtract it; this marks the entry into the initial lunar calendar. If it doesn't fill the fraction of the day, retain it and add the remainder of two thousand seven hundred and two to the small fraction of thirty-one, which is the entry into the next lunar calendar cycle.
Multiply the total by the increase and decrease in the lunar calendar at midnight, along with the remainder; when the remainder fills up to half a week, it becomes a small fraction. Use the increase and decrease to adjust the yin-yang day remainder. If the surplus of the day remainder is insufficient, adjust the number of days using the monthly cycle accordingly. Multiply the profit and loss rate by the nearby solar terms' night leak; one two-hundredth indicates brightness, then use the profit and loss midnight figure as the dim-bright constant.
This text discusses ancient astronomical calculations, which can be quite overwhelming, so let’s take it one sentence at a time.
The first paragraph talks about calculating the moon's distance from the ecliptic. "If the added time is determined by whether it is day or night, divide by twelve as degrees; the remainder divided by three and one is counted as less, while a remainder greater than or equal to one is strong; two 'less' together are counted as weak. The final result is the degree of the moon away from the ecliptic." This paragraph explains the method of calculating the degree of the moon's distance from the poles in the solar and lunar calendars, using addition and subtraction, adding and subtracting positive and negative numbers, adding the same sign, and subtracting the opposite sign, where two "strong" offset one "less" and one "weak."
The second paragraph discusses the time span. "Since the first year of Jichou in Shangyuan until the eleventh year of Bingxu in Jian'an, the total amounts to 7,378 years." The terms Jichou, Wuyin, etc., are era names and do not require translation.
The third paragraph explains the calculation method. "Five elements: wood, year star; fire, Mars; earth, Saturn; gold, Venus; water, Dragon star. Each corresponds to the daily motion and the degree of the sky, representing the weekly rate and daily rate. Multiply the annual figures by the weekly rate for the monthly calculation. Multiply the monthly figures by the day for the month. If the division is accurate, this represents the month. Multiply the total by the monthly method to derive the daily degree. Multiply the Dipper by the weekly rate for the Dipper. (The daily degree method is multiplied by the weekly rate with the record method, so it is multiplied by the minute.)" This paragraph discusses using the orbital periods and daily degrees of the five elements (Jupiter, Mars, Saturn, Venus, Mercury) to calculate, which includes various technical terms like weekly rate, daily rate, monthly method, and monthly division.
The fourth to sixth paragraphs are specific calculation steps and results, involving "Five Stars New Moon Big Remainder, Small Remainder", "Five Stars Enter Month Day, Day Remainder", "Five Stars Degrees, Degree Remainder", and a series of calculation formulas and parameters, such as "Recorded Month, 7285; Leap Month, 7; Chapter Month, 235; Year Middle, 12; Common Method, 43026..." and so on. These are specific numerical values, and we only need to know that this is a series of complex calculations to ultimately obtain the operational data regarding the Five Stars. These numbers and formulas do not provide much help in understanding the summary of the story, so I will not translate them sentence by sentence.
In conclusion, this passage describes an extremely complex ancient calendar calculation method, involving knowledge of astronomy, mathematics, and other fields. Its precision is astonishing. Although we may not fully understand the calculation process, we can appreciate the depth of ancient research into astronomical calendars.
First, let's take a look at these numbers. What do they represent? It feels like the results of some astronomical calculations, recording various orbital periods, daily rates, remainders, and so on. I don't understand the specifics, so let's read them in order and see if we can figure something out.
The degree is thirty-three, the degree remainder is 2509956. Fire: Orbital period 3407, daily rate 7271. Combined month number 26, month remainder 25627. Combined Month Method 64733, daily degree law 2006723. New Moon big remainder 47, New Moon small remainder 1157. Enter month day 12, day remainder 97313. New Moon virtual division 300, Dipper division 49415.
Next, we'll continue. The degree is forty-eight, the degree remainder is 1991706. Earth: Orbital period 3529, daily rate 3653. Combined month number 12, month remainder 53843. Combined Month Method 67051, daily degree law 2078581. New Moon big remainder 54, New Moon small remainder 534. Enter month day 24, day remainder 166272. New Moon virtual division 923, Dipper division 51175.
These are another set of numbers, which feels quite similar to the previous set. The degree is twelve, and the remainder of the degree is one million seven hundred thirty-one thousand four hundred forty-eight. For metal: the Zhou rate is nine thousand two hundred twenty-two, and the Ri rate is seven thousand two hundred thirteen. The total number of combined months is nine, with a month remainder of one hundred fifty-two thousand two hundred ninety-three. The combined month method is one hundred seventy-one thousand four hundred eighteen, and the daily degree method is five hundred thirty-one thousand three hundred fifty-eight. The Shuo Da surplus is twenty-five, and the Shuo Xiao surplus is one thousand one hundred twenty-nine. The entry day of the month is twenty-seven, with a remainder of fifty-six thousand nine hundred fifty-four. The Shuo virtual division is three hundred twenty-eight, and the Dou division is one million eight thousand one hundred ninety.
Finally, these are the last set of numbers. The degree is two hundred ninety-two, and the degree remainder is fifty-six thousand nine hundred fifty-four. For water: the Zhou rate is eleven thousand five hundred sixty-one, and the Ri rate is one thousand eight hundred thirty-four. The combined month number is one, with a month remainder of two hundred eleven thousand three hundred thirty-one. The combined month method is twenty-one thousand nine hundred fifty-nine, and the daily degree method is six hundred eighty-nine thousand four hundred twenty-nine. The Shuo Da surplus is twenty-nine, and the Shuo Xiao surplus is seven hundred seventy-three. The entry day of the month is twenty-eight, with a day remainder of six hundred forty-one thousand nine hundred sixty-seven. The Shuo virtual division is six hundred eighty-four.
Overall, these numbers are densely packed and can be quite overwhelming. It feels like ancient astronomical calendar calculations, with each number having its own meaning, but unfortunately, I can't understand them. It would be great to have some context to explain them.
First, let's calculate; the total comes to one million six hundred seventy-six thousand three hundred forty-five. The degree is fifty-seven, and the degree remainder is six hundred forty-one thousand nine hundred sixty-seven.
Then, multiply the values from the first year by the Zhou rate to get an integer, which we call "accumulated product," and the remaining is the "combined remainder." Then divide the "accumulated product" by the Zhou rate; if the result is 1, it is the star combination of the previous year; if it is 2, it is the star combination of the previous two years; if nothing is obtained, it is the star combination of the current year. Subtract the Zhou rate from the "combined remainder" to get the degree. For Venus and Mercury, if the accumulated product is odd, it indicates morning; if even, it indicates evening.
Next, multiply the number of months and the remaining months by "accumulated months." If the result is a multiple of the combined months, then that is the month, and the rest is the remaining months. Subtract the calendar months from the accumulated months, and the remaining is the entered months. Then multiply by the chapter leap; if the result is a multiple of the chapter months, subtract one leap month, and then subtract from the total year. This is the combined month not included in the Tianzheng calculation. If it is in a leap year, use the new moon to control.
Use the common method to multiply the remaining months, multiply the new moon by the combined month method, and then divide by the total count of months. If the result is a multiple of the daily method, then that is the star combination entry month day. If it is not an integer, the remainder is the remaining days, recorded outside of the new moon calculation.
Multiply the week by the degree; if the result is a multiple of the daily method, then that is one degree, and the remainder is noted in the first five days before the ox. The above is the method of seeking star combinations.
Next, add up the number of months and also add up the remaining months. If the result is a multiple of the combined months, then that is one month. If it does not complete a year, then it is added to the current year. If it is complete, then subtract. If there is a leap month, it must be included in the calculation, and the remaining is the value for the following year; after another full year, it is the value for the following two years. Venus and Mercury: morning plus morning equals evening, evening plus evening equals morning.
Add the new moon's remainder to the total months' remainder. If the result exceeds one month, then add another large remainder of twenty-nine, small remainder of seven hundred and seventy-three, and subtract from the large remainder using the full daily method, as before.
Add the entered month day and the day remaining, then add the combined entry month day and the remainder. If the remainder is a multiple of the daily method, then that is one day. If the previous combined new moon is full of fractional parts, subtract one day; if the later small remainder exceeds seven hundred and seventy-three, subtract twenty-nine days; if not full, subtract thirty days. The remaining is the entry month day for the later combination.
Finally, add up the degrees, and also add up the remainder of the degrees. If the result is a multiple of the daily method, then that is one degree.
Jupiter: Retrograde motion lasts thirty-two days, with a total of three hundred and forty-eight million four thousand six hundred and forty-six minutes; direct motion lasts three hundred and sixty-six days; retrograde for five degrees amounts to two hundred and fifty million nine thousand nine hundred and fifty-six minutes; direct motion covers forty degrees. (Except for retrograde by twelve degrees, stationary motion by twenty-eight degrees.)
Mars: It has been in retrograde motion for one hundred forty-three days, totaling nine hundred seventy-three thousand one hundred thirteen minutes; it has been in direct motion for six hundred thirty-six days; it has moved one hundred ten degrees below the horizon, totaling four hundred seventy-eight thousand nine hundred ninety-eight minutes; it has moved three hundred twenty degrees. (Excluding a retrograde motion of seventeen degrees, it has moved three hundred three degrees.)
Saturn: It has been in retrograde motion for thirty-three days, totaling one hundred sixty-six thousand two hundred seventy-two minutes; it has been in direct motion for three hundred forty-five days.
This passage describes ancient astronomical calculation methods, recording the movement patterns of the three celestial bodies: Venus, Mercury, and Jupiter. Let's interpret it sentence by sentence in contemporary language.
First, "In retrograde motion for three degrees. One hundred seventy-three thousand three hundred forty-eight minutes." This means that this celestial body has traveled three degrees below the horizon, totaling one hundred seventy-three thousand three hundred forty-eight "minutes." The "degrees" and "minutes" here are units used in ancient astronomical calculations, similar to divisions of angles.
"In direct motion for fifteen degrees. (Excluding a retrograde motion of six degrees, it has moved nine degrees.)" This celestial body has moved fifteen degrees along the horizon, but excluding the retrograde motion of six degrees, it has actually moved nine degrees. Retrograde means the celestial body is moving in the opposite direction to its usual path.
"Venus: In retrograde motion in the east for eighty-two days. Eleven thousand three hundred ninety-eight minutes." Venus has been below the eastern horizon for eighty-two days, totaling eleven thousand three hundred ninety-eight "minutes."
"In the west. Two hundred forty-six days. (Excluding a retrograde motion of six degrees, it has effectively moved two hundred forty-six degrees.)" Venus appears in the west along the horizon for two hundred forty-six days. Similarly, after accounting for a retrograde motion of six degrees, it has effectively moved two hundred forty-six degrees.
"In retrograde motion for one hundred degrees. Eleven thousand three hundred ninety-eight minutes." Venus has been below the eastern horizon for one hundred degrees, totaling eleven thousand three hundred ninety-eight "minutes."
"Appearing in the east. (The daily motion is like in the west. Below the horizon for ten days, and it has retreated eight degrees.)" Venus appears in the east, and its movement pattern is similar to when it is in the west. It has been below the horizon for ten days and has retreated eight degrees.
"Mercury: In retrograde motion for thirty-three days. With a total of six million twelve thousand five hundred five minutes." Mercury has been below the eastern horizon for thirty-three days, with a total of six million twelve thousand five hundred five minutes.
"Look to the west. Thirty-two days. (Except for one retrograde, it moved thirty-two degrees.)" Mercury appeared in the west and lasted for thirty-two days. After deducting one retrograde, it actually moved thirty-two degrees.
"Moved sixty-five degrees below the horizon. Six million one hundred twenty-five thousand five arcminutes." Mercury moved sixty-five degrees below the horizon, totaling six million one hundred twenty-five thousand five arcminutes.
"Look to the east. Its daily movement is similar to that observed in the west, was below the horizon for eighteen days, retreated fourteen degrees." Mercury appeared in the east, with a movement pattern similar to that in the west. It was below the horizon for eighteen days, then retreated fourteen degrees.
The following segment describes the calculation method, which is rather technical, so we will try to explain it in layman's terms:
"By taking the daily movement and remainder, adding the combined daily movement of the star, the remainder equals one when the total daily movement is reached. Proceeding as before, the star's appearance time and angle are calculated. Multiply the visible angle by the denominator used in the star's movement calculations, and the remainder equals one when divided by the daily movement. If the division is not exact, one is also obtained above half of the daily movement; adding the movement to the division, when the division is complete, one degree is obtained. The retrograde and direct movements have different denominators, so the division is based on the current movement's denominator. Subtract if retrograde, leave if not complete, divide by the fraction, using the movement as a ratio, with variations in gain and loss, adjusting before and after. All references to fullness and completion are seeking the actual division; removing and dividing refer to achieving the complete division." This passage describes a complex algorithm for calculating the time and angle of a celestial body's appearance based on its movement pattern, involving many technical terms. In simple terms, it involves a series of division and addition operations, combining the celestial body's movements in degrees and arcminutes to ultimately calculate the time and position of its appearance.
"Wood: The morning aligns with the sun, prostrating and smoothly. On the sixteenth day, one hundred seventy-four million two hundred thirty-two thousand three hundred twenty-three minutes, the planet moves two degrees and three hundred twenty-three million four thousand six hundred seven minutes, and the morning is seen in the east after the sun. Smooth, fast, the sun moves eleven-fifty-eighths of a degree, and over fifty-eight days, it moves eleven degrees. Smooth again, slow, the sun moves nine minutes, and over fifty-eight days, it moves nine degrees. Stop for twenty-five days without movement, then rotate. Retrograde, the planet moves one-seventh of a degree, and over eighty-four days, it retreats twelve degrees. Stop again for twenty-five days, then smooth, the sun moves fifty-eight minutes out of nine, and over fifty-eight days, it moves nine degrees. Smooth, fast, the sun moves eleven minutes, and over fifty-eight days, it moves eleven degrees, and the evening sets in the west after the sun. On the sixteenth day, one hundred seventy-four million two hundred thirty-two thousand three hundred twenty-three minutes, the planet moves two degrees and three hundred twenty-three million four thousand six hundred seven minutes, and aligns with the sun. In total, over three hundred ninety-eight days, the planet travels forty-three degrees and two hundred fifty-nine million nine hundred fifty-six minutes." Jupiter's movement is more complex; its relative position with the sun changes, sometimes moving fast, sometimes slow, and even appearing retrograde. This passage details Jupiter's speed, direction, and duration at different stages, as well as its cycle of conjunction with the sun. In summary, it describes Jupiter's movement within one cycle (three hundred ninety-eight days), including its angles and distance traveled.
In the morning, the sun and Mars met, and Mars went into hiding. Then it started moving in direct motion, traveled for 71 days, covering a total of 1489868 units (original text did not specify units, kept as is), and the position of the planet also shifted by 55 degrees 1242860.5 units (original text did not specify units, kept as is). After that, people could see Mars in the east in the morning, behind the sun. While moving in direct motion, Mars traveled 23/14 minutes per day, covering 112 degrees in 184 days. Then it slowed down, only moving 23/12 minutes per day, covering 48 degrees in 92 days. It then stopped for 11 days. Then it began its retrograde motion, covering 17 degrees in 62 days at a rate of 17/62 minutes per day. It stopped for 11 days again, then started moving forward, covering 48 degrees in 92 days at a rate of 12/1 minutes per day. Its forward speed then increased, covering 112 degrees in 184 days at a rate of 14/1 minutes per day. At this point, it moved in front of the sun and could be observed in the western sky at night. After another 71 days, covering 1489868 units (original text did not specify units, kept as is), the position of the planet shifted by 55 degrees 1242860.5 units (original text did not specify units, kept as is), and it finally met the sun again. The entire cycle spanned a total of 779 days and 97313 units (original text did not specify units, kept as is), with the planet's position changing by a total of 414 degrees 478998 units (original text did not specify units, kept as is).
In the morning, when the sun and Saturn meet, Saturn goes into hiding. Then it starts to move forward for 16 days, a total of 1122426.5 units (original text did not specify the unit, keeping the original text), and the position of the planet also moves 1 degree and 1995864.5 units (also keeping the original text). After that, people can see Saturn in the east in the morning, behind the sun. While moving forward, Saturn moves 3/35 of a degree each day, traversing 7.5 degrees over 87.5 days. It then remains stationary for 34 days. After that, it starts moving backward, moving 1/17 of a degree each day, retracting 6 degrees over 102 days. After another 34 days, it starts moving forward again, moving 1/3 of a degree each day, moving 7.5 degrees in 87 days. At this point, it has moved in front of the sun, and is visible in the west at night. After another 16 days, it covers 1122426.5 units (original text did not specify the unit, keeping the original text), and the position of the planet also moves 1 degree and 1995864.5 units (also keeping the original text), and finally, it meets the sun again. Over the entire cycle, the entire cycle lasts 378 days and 166272 units (original text did not specify the unit, keeping the original text), and the position of the planet moves a total of 12 degrees and 1733148 units (also keeping the original text).
As for Venus, when it meets the sun in the morning, it first goes into hiding, then moves backward, retracting 4 degrees over 5 days, and then it can be seen in the east in the morning, behind the sun. Continuing to move backward, it moves 3/5 of a degree each day, retracting 6 degrees over 10 days. It then remains stationary for 8 days. Then it turns to move forward slowly, moving 33/46 of a degree each day, moving 33 degrees in 46 days to move forward. Its speed increases, moving 15/91 of a degree each day, moving 160 degrees in 91 days. Speeding up again, it moves 22/91 of a degree each day, moving 113 degrees in 91 days; at this point, it is positioned behind the sun, appearing in the east in the morning. Moving forward for 41 days, traversing 1/954 of a complete orbit, the planet also moves 50 degrees, covering 1/954 of a complete orbit, and then meets the sun again. One meeting is a total of 292 days and 1/954 of a complete orbit, and the planet follows the same pattern.
When Venus meets the sun in the evening, it first "hides," then moves forward. It travels 1/56,954 of a circle in 41 days, and the planet also travels 50 degrees, which is 1/56,954 of a circle. Then, in the evening, it can be seen in the western sky, positioned in front of the sun. It continues to move forward, increasing its speed to 91/22 degrees per day, covering 113 degrees over 91 days before continuing its forward motion. Its speed decreases, moving at 15/1 degrees per day, covering 160 degrees in 91 days, and then continues forward. The speed slows down, moving at 46/33 degrees per day, covering 33 degrees in 46 days. Then it comes to a stop, remaining stationary for 8 days. Then it reverses direction, traveling 5/3 degrees per day, retreating 6 degrees in 10 days; at this point, it is positioned in front of the sun, becoming visible in the west during the evening. It "hides," moves backward, and speeds up, retreating 4 degrees in 5 days, and then it meets the sun once more. Two conjunctions are counted as one complete cycle, totaling 584 days and 1/11,398 of a circle, and the planet is the same.
When Mercury meets the sun in the morning, it first "hides," then moves backward, retreating 7 degrees in 9 days; then it becomes visible in the east, positioned behind the sun. It continues to move backward, accelerating to retreat 1 degree each day. It then pauses, remaining stationary for 2 days. Then it turns and moves forward, moving at a slower pace of 9/8 degrees per day, covering 8 degrees in 9 days. As it speeds up, it moves at a rate of 1 1/4 degrees per day, covering 25 degrees in 20 days; then it is behind the sun, appearing in the east in the morning. It "hides." It moves forward for 16 days, covering 1/641,967 of a circle, and the planet also travels 32 degrees 1/641,967 of a circle, and then it meets the sun once more. This single conjunction totals 57 days and 1/641,967 of a circle, and the planet is the same.
Speaking of Mercury, when it gets close to the Sun, it seems to disappear, and then it starts to move forward along its orbit. After sixteen days, it has traveled thirty-two degrees and one six-million four hundred nineteen thousand six hundred seventy-seventh of a degree. At this time, you can see it in the west in the evening, as it is positioned in front of the Sun. It moves quite quickly, covering one and a quarter degrees each day, which means it takes twenty days to cover twenty-five degrees. Sometimes it slows down, moving only seven-eighths of a degree in a day, which means it takes nine days to cover eight degrees. There are even times when it stops altogether, pausing for two days. Even more astonishingly, it can even move in reverse! It can move backward one degree in a day, still in front of the Sun, but by evening, it hides in the west. When it moves backward, it also slows down, taking nine days to move backward seven degrees, and then it aligns with the Sun again. From when it aligns with the Sun to the next time it aligns again, the entire cycle lasts 115 days and one six-million two thousand five hundred fifty-fifth of a day. The other movements of Mercury are quite similar.
In summary, Mercury's movement patterns are quite complex, sometimes fast, sometimes slow, sometimes moving forward, sometimes backward, and the cycle is quite long, taking over a hundred days to complete one orbit. The ancient observations are incredibly meticulous, accurately recording even such small angular changes, which is nothing short of astonishing!
