This text describes the methods of calculating ancient calendars, which are quite technical and intricate. Let's explain it sentence by sentence in modern colloquial language.
First, it talks about how to calculate the lengths of day and night. "Based on the distance the moon travels, multiply it by the number of nighttime hours of the closest solar term, and then divide by 200 to get the daytime duration (mingfen); subtract this value from the moon's travel distance to determine the nighttime duration (hunfen)."
The meaning is to calculate the daytime and nighttime durations based on the moon's movement and the number of night hours during the recent solar term. "Convert the lengths of day and night into units, multiply the total units by the daytime and nighttime durations, and add the units for midnight to determine the units for daytime and nighttime. If the remainder exceeds half, round it up; otherwise, discard it."
Next, it discusses how to calculate the "day" in the calendar. "The moon's movement is tracked by four tables and three paths, and by dividing the moon's speed by these values, you can determine the calendar day."
"The number of weeks multiplied by the synodic month gives the synodic division; the total units multiplied by the synodic number, with the remainder divided by the synodic month, gives the retrograde calculation; based on the moon's cycle, calculate the degrees added each day, then divide by the synodic month to find the difference rate."
This section explains that by multiplying the number of weeks by the synodic month (which refers to the moon's full cycle), and then dividing by the number of synodic months, one can obtain the synodic division; multiplying the total units by the synodic number, and dividing the remainder by the synodic month gives the retrograde calculation; finally, calculate the degrees added each day, then divide by the synodic month to find the difference rate.
Next is the profit and loss rate table of the lunar-solar calendar, which can be quite complex. It lists the daily increases and decreases for the lunar-solar calendar, specifically indicating that adjustments need to be made based on the date. Some days require a reduction in value, while others require an increase. The table lists the specific daily increases and decreases. "Reduce one and increase seventeen on the first day" means to reduce one on the first day and increase seventeen, and so on. The explanation in parentheses clarifies some special cases, such as "if the reduction is insufficient, it should be treated as an increase," meaning that if the result of the reduction is insufficient, it should be reversed and treated as an increase. "Remaining value" and "differential" represent some remainders and fine adjustments in the calculations.
Finally, it explains how to determine whether it is the lunar calendar or the solar calendar based on the calculation results. "Subtract the accumulated months from the starting point, and multiply the remaining by the lunar-solar fraction and the differential respectively. If the differential reaches a certain threshold, it is added to the lunar-solar fraction. If the lunar-solar fraction reaches the total weeks, it is subtracted from the week count. The remaining value, if less than the calendar cycle, is the solar calendar; if it is equal to or exceeds the calendar cycle, it is classified as the lunar calendar." This means that the accumulated number of combined months is subtracted from the accumulated number of the starting point (where the starting point refers to the beginning of a calendar), and the remaining values are multiplied by the lunar-solar fraction and the differential. If the differential reaches a certain threshold, it is added to the lunar-solar fraction; if the lunar-solar fraction reaches the total weeks, the week count is subtracted. Finally, if the remainder is less than the calendar cycle, it is the solar calendar; if it is equal to or exceeds the calendar cycle, it is the lunar calendar. "All remaining values are like the monthly cycle yielding one day, excluding the calculation, the desired month is combined with the lunar-solar calendar, with not all values being day remainders. Add two days; the day remainder is two thousand five hundred eighty, and the differential is nine hundred fourteen. Using this method to calculate days, subtract thirteen when complete and divide the remainder into fractions of days. The lunar and solar calendars ultimately interconvert, with the entry into the calendar happening before the remaining value, and the latter remaining after, indicating the midpoint of the monthly cycle." This passage summarizes the calculation method and explains the meaning of the final results, as well as the interconversion relationship between the lunar and solar calendars. Overall, this text outlines a very complex ancient calendar calculation system that involves a lot of astronomical and mathematical knowledge.
First, let’s explain this ancient text, which outlines a complex method for calculating calendars. This text describes an algorithm for calendar calculation, involving many technical terms such as "day remainder," "small fraction," "combined number," "profit and loss rate," etc., which all require an understanding of the calendar knowledge of that time to comprehend. We will translate it sentence by sentence into modern vernacular, aiming for clarity and ease of understanding.
First, calculate all the time differences (speed and duration), expressed in smaller units of time, and represent the surplus and deficit using Yin-Yang surplus. Adjust the number of days based on the surplus and deficit situation. Then, multiply the adjusted number of days by the profit and loss rate (a correction coefficient). For example, the number of days in a month is fixed; use this method to calculate the overtime constant (adjusted number of days).
Next, multiply the difference rate by the small remainder of the new moon day (the first day of each lunar month), calculating a value similarly to calculus. Then subtract this value from the remaining days in the calendar. If it is not enough, add the number of days in a month and then subtract. If there is still one day short, subtract an additional day. Then add the fractional part to this result, and use the sum to approximate the differential, yielding small units of time, thus obtaining the calendar data for midnight on the new moon day.
To calculate the next day, simply add one day. If the day surplus is 31, the small units of time are also 31. If the small units of time exceed the total, subtract a month's days and add one day. If the calendar calculation reaches the end and the day surplus is full, subtract it to get the starting point of the calendar. If the day surplus is not full, retain it and add 2720; if the small units of time are 31, this gives the starting point of the next calendar.
Multiply the total number of days by the midnight surplus and remainder of the late-early calendar. If the remainder fills half a cycle, it is used to represent small units of time. Adjust the Yin-Yang surplus based on the surplus and deficit situation. Then multiply the adjusted number of days by the profit and loss rate to obtain the midnight constant.
Multiply the profit and loss rate by the number of water clocks at night during the recent solar terms (ancient timing devices); 200 water clocks equal one day's bright time. Subtract this value from the profit and loss rate to obtain the dim time, using the midnight value to determine the times of brightness and darkness.
Add the overtime number and dim constant together, then divide by 12 to get the degrees. One-third of the remainder indicates a deficiency, while a value of less than one minute signifies strength, and two deficiencies indicate weakness. This result represents the degrees the moon has moved away from the ecliptic. For the solar calendar, subtract the extreme from the calendar data at the ecliptic where the added day is located; for the lunar calendar, add it to get the degrees the moon has moved away from the extreme. Strength is positive, weakness is negative; same names add, different names subtract. When subtracting, same names cancel, different names add; there are no opposites—two strengths add to one deficiency and subtract one weakness.
From the year of the Metal Ox in the Yuan Dynasty to the year of the Metal Dog in the eleventh year of Jian'an, a total of 7378 years have passed.
己丑, 戊寅, 丁卯, 丙辰, 乙巳, 甲午, 癸未, 壬申, 辛酉, 庚戌, 己亥, 戊子, 丁丑, 丙寅
Five Elements: Wood (Year Star), Fire (Mars), Earth (Filling Star), Metal (Venus), Water (Chen Star). Calculate the weekly and daily rates using the degrees and celestial positions of their daily movements. Multiply the chapter age by the weekly rate to obtain the monthly calculation method, multiply the chapter month by the daily rate to get the month point, and divide the month point by the monthly calculation method to obtain the month number. Multiply the total number of days by the monthly calculation method to obtain the daily calculation method. Multiply the Dipper by the weekly rate to get the Dipper. (The daily calculation method is obtained by multiplying the record method by the weekly rate, so it is also multiplied by the minute here).
The method for calculating the calendar described in this text is quite complex, involving a wealth of astronomical and mathematical knowledge, and it is difficult for us to completely restore its calculation process now. It reflects the outstanding achievements of the ancient Chinese people in the field of astronomical calendar.
First, we need to understand what these numbers signify. This text discusses calculating the positions of planets using ancient algorithms, which can seem quite complicated. "Five Stars" refers to the five planets of metal, wood, water, fire, and earth. "Shuo" refers to the first day of the lunar calendar. "Da Yu," "Xiao Yu," "degrees," "degree residue," and so on, are intermediate results generated in the calculation process, the specific meanings of which we will not delve into, as long as we recognize that they are used for calculating planetary positions. "Ji Yue," "Zhang Run," "Zhang Yue," "Sui Zhong," and so on should all be constants related to the calendar. "Tong Fa," "Ri Fa," "Hui Shu," "Zhou Tian," and "Dou Fen" are also some fixed parameters. The numbers after Jupiter, Mars, and Saturn represent their respective calculation parameters.
Now, let's break it down into simpler language, sentence by sentence:
1. First, calculate the "Da Yu" and "Xiao Yu" values for the planets. (The calculation method is as follows: multiply "Tong Fa" by the month, and then divide by "Ri Fa"; the quotient is "Da Yu," and the remainder is "Xiao Yu." Then subtract 60 from "Da Yu.")
2. Then calculate the "Ru Yue Ri" and "Ri Yu" values for the planets. (The calculation method is: multiply "Tong Fa" by "Yue Yu," multiply "He Yue Fa" by "Shuo Xiao Yu," add these two results together, simplify if necessary, and finally divide by the "Ri Du Fa"; the result will yield "Ru Yue Ri" and "Ri Yu.")
3. Finally, calculate the "degree" and "remainder" of the planet. (The calculation method is: subtract the excess to get the "remainder," then multiply the "orbital period" by the "remainder," and then simplify using the "solar degree method," resulting in the "degree," with the remainder being the "remainder." If it exceeds the "orbital period," subtract the "orbital period" and the "Doufen" (斗分).)
4. The total number of months in the calendar year is 7285.
5. The total number of leap months is 7.
6. The total number of chapters (months) is 235.
7. There are 12 months in a year.
8. The common method is 43026.
9. The solar method is 1457.
10. The total number of cycles is 47.
11. The orbital period is 215130.
12. The Doufen is 145.
13. The following are the parameters for Jupiter: the orbital period is 6722, the solar rate is 7341, the total number of lunar months is 13, the lunar remainder is 64810, the combined lunar method is 127718, and the solar degree method is 3959258.
14. Jupiter's large lunar remainder is 23, small lunar remainder is 1370, the day of the new moon is 15, and the solar remainder is 3484646. The lunar virtual fraction is 150, Doufen is 974690, the degree is 33, and the remainder is 2509956.
15. The following are the parameters for Mars: the orbital period is 3447, the solar rate is 7271, the total number of lunar months is 26, the lunar remainder is 25627, the combined lunar method is 64733, and the solar degree method is 2006723.
16. Mars's large lunar remainder is 47, small lunar remainder is 1157, the day of the new moon is 12, and the solar remainder is 973113. The lunar virtual fraction is 300, Doufen is 494115, the degree is 48, and the remainder is 1991760.
17. The following are the parameters for Saturn: the orbital period is 3529, the solar rate is 3653, the total number of lunar months is 12, the lunar remainder is 53843, the combined lunar method is 6751, and the solar degree method is 278581.
18. Saturn's large lunar remainder is 54, small lunar remainder is 534, and the day of the new moon is 24.
This passage describes the methods used by ancient astronomers to calculate the positions of planets. Although it seems complex, it is actually a series of mathematical operations to determine the position of planets in the sky. These numbers and formulas reflect the ancient astronomers' observations and understanding of the universe, as well as their excellent mathematical calculation skills. Unfortunately, we no longer use this method; modern astronomical calculations have become more accurate and convenient.
Wow, these numbers are a lot to take in! Let me break it down for you in simpler terms.
Firstly, this first paragraph discusses the calculation results, various remainders and fractional values, such as "the remainder for the day of 166,272" and "the fraction for the new moon of 923," which are intermediate results in astronomical calculations. We don't need to get too caught up in the specific meanings; after all, it's just a bunch of numbers. "The Doufen of 511,750," "the angle of 12 degrees," and "the degree remainder of 1,733,148" are the same; they are all data from the calculation process. "Gold: the orbital period of 9,022, the daily orbital rate of 7,213, the combined lunar count of 9, and the lunar remainder of 152,293..." These numbers are also similar intermediate calculation results, related to the operational patterns of the "Gold" star. Later, there are terms like "combined lunar method," "daily degree method," "new moon large remainder," "new moon small remainder," "entry lunar day," etc.; all are technical terms in astronomical calculations, and we just need to know they are data from the calculation process.
Next, this section continues to list calculation results, similar to the previous ones, consisting of various remainders and fractional values, such as "the remainder for the day of 56,954," "the fraction for the new moon of 328," and "the Doufen of 1,308,190," etc. These numbers represent the operational law calculation results of the "Water" star. "Water: the orbital period of 11,561, the daily orbital rate of 1,834, the combined lunar count of 1, and the lunar remainder of 211,331..." Later, there are also "combined lunar method," "daily degree method," "new moon large remainder," "new moon small remainder," "entry lunar day," along with a long string of numbers, all of which are data from the calculation process. Finally, there are "the remainder for the day of 6,419,967," "the fraction for the new moon of 684," "the Doufen of 1,676,345," "the angle of 57 degrees," and "the degree remainder of 6,419,967."
The final paragraph begins to explain the calculation method. "Take the Shangyuan of the desired year, multiply by the cycle rate; if the result is exactly an integer multiple of the daily rate, it is called Jihe; if it is not an integer multiple, the remainder is called Heyu." This means that multiplying the Shangyuan of the year you want to calculate by the cycle rate, if the result is an integer multiple of the daily rate, it is called Jihe; if not, the remainder is Heyu. "Divide by the cycle rate; if the result is 1, it is the previous year; if it is 2, it is the year before the previous year; if there is no result, it is the current year." This means that when you divide the Jihe by the cycle rate, if the result is 1, it is calculated as the previous year; if it is 2, it is calculated as two years ago; if it does not divide evenly, it is calculated as the current year. "Subtract the cycle rate from the Heyu to obtain the degree." This means that you subtract the cycle rate from the Heyu to obtain the degree. "The accumulation of gold and water; if the result is an odd number, it is referred to as 'morning'; if it is an even number, it is called 'evening'." This means that the accumulation of gold and water, if it is an odd number, is referred to as 'morning'; if it is an even number, it is called 'evening'. "Multiply the accumulation of the number of months and the remainder of the month; the full month law starts from the month; if it is not an integer multiple, the remainder is the new month remainder." This means that you multiply the number of months and the remainder of the month by the accumulation; if the result is an integer multiple of the full month law, it represents the month; if it is not an integer multiple, the remainder is the new month remainder. "Subtract the accumulated month from the accumulated month; the remainder is the entry month. Multiply by the leap month; the full chapter month gets one leap; subtract from the entry month; subtract from the middle of the year; calculate according to the Tianzheng method, which also applies to the month. If it is at the leap intersection, use the new moon." This paragraph explains how to calculate the month and leap month, using many professional terms, which may be difficult to understand. In simple terms, it determines the month and leap month based on the calculation results. "Multiply the month remainder by the common method; multiply the full month law by the small remainder, and round off the number of meetings. If the result is an integer multiple of the full day law, it is the entry date of the star in the month. If it does not yield an integer multiple, it becomes the day remainder; calculate according to the new moon." This explains how to calculate the entry date of the star in the month, which is the specific date of a planet in a certain month. "Multiply the degree by the cycle day; if the full day law gets one degree, if it does not yield an integer multiple, it becomes the remainder; calculate the degree from the front five of the ox." This explains how to calculate degrees. "Seek the star conjunction." The last sentence means that the above outlines the method for determining the star conjunction.
In summary, this text describes the calculation methods for the rules of planetary motion in ancient astronomical calendars, involving a large number of technical terms and complex calculation processes, which can indeed be quite difficult for modern people to understand. Overall, it describes a complex mathematical model used to predict the positions of planets.
Let's calculate the days by first adding the months together, and also adding any surplus months. If the total is exactly one month, it indicates that there is no intercalary month that year; if it is not a full year, then carry over the excess to the next year; if the next year also completes, carry it over to the following year. For Venus and Mercury, if they appear in the morning, add them to the evening, and if they appear in the evening, add them to the morning.
Next, calculate the size of the new moon day (the first day of each lunar month) and the excess days, and add them together. If the total equals one month, then add 29 days (for a short month) or 30 days (for a long month), deducting the days of the short month from the long month. The calculation method is the same as before.
Then calculate the new moon days and the excess days, adding them together. If the excess days total one day, count it; if the excess days on the first day of the lunar month are insufficient, subtract one day; if the excess days exceed 29, subtract 29 days, and if not enough, subtract 30 days, leaving the remainder for the next month.
Finally, add the degrees together, and also add the excess degrees; if the degrees amount to one day, count it as one degree.
Here is the motion of Jupiter:
Jupiter: Concealed for 32 days and 3,484,646 minutes; appeared for 366 days; concealed running 5 degrees, 2,509,956 minutes; appeared running 40 degrees. (Retrograde 12 degrees, actual running 28 degrees.)
Mars: Concealed for 143 days and 973,113 minutes; appeared for 636 days; concealed running 110 degrees, 478,998 minutes; appeared running 320 degrees. (Retrograde 17 degrees, actual running 303 degrees.)
Saturn: Concealed for 33 days and 166,272 minutes; appeared for 345 days; concealed running 3 degrees, 1,733,148 minutes; appeared running 15 degrees. (Retrograde 6 degrees, actual running 9 degrees.)
Venus: Concealed in the east for 82 days and 113,908 minutes; appeared in the west for 246 days. (Retrograde 6 degrees, actual running 240 degrees.) Concealed in the morning running 100 degrees, 113,908 minutes; appeared in the east. (The solar position matches that of the west, concealed for 10 days and retrograde 8 degrees.)
Mercury: In the morning, it is concealed in the east for 33 days, 612,505 minutes; it appears in the west for 32 days. (Retrograde motion 1 degree, actual motion 31 degrees.) Concealed motion 65 degrees, 612,505 minutes; appears in the east. (The solar degree is the same as the west, concealed for 18 days, retrograde 14 degrees.)
First, let's talk about how to calculate the motion of planets. First, calculate the degrees the planet moves each day, then add the daily degree difference between it and the sun. If this difference equals the degree of one day, it indicates that the conjunction period between the planet and the sun has arrived, and as calculated before, we can know when the planet can be seen. Then, multiply the number of increments the planet moves (denominator) by the degrees it appears, and for the remaining part, divide by one day's degree. If it cannot be divided evenly, treat it as a whole day if it exceeds half. Next, sum the degrees the planet moves each day; if the total equals the number of increments it moves, it is considered to have completed a full orbit. The calculation methods for direct and retrograde motion are different and should be based on the planet's current increments (denominator). For the remaining part, based on previous calculations, if it is retrograde, it should be subtracted. If it cannot be divided evenly, use a unit for division, using the planet's increments (denominator) as a ratio, thus allowing the calculation of the increase or decrease in the degrees of the planet's motion, with mutual correction before and after. In summary, terms like “full,” “about,” and “complete” are used to achieve precise division results; while “go,” “reach,” and “divide” are all aimed at obtaining the final division results.
Next, let's look at the motion of Jupiter. Jupiter aligns with the sun in the morning, then goes retrograde, followed by direct motion, running for 16 days at 1,742,323 minutes, with the planet moving 2,323,467 minutes. At this time, Jupiter appears in the east, lagging behind the sun. During direct motion, it moves quickly, covering 11 minutes out of 58 daily, which translates to 11 degrees in 58 days. Then continuing direct motion, the speed slows down, moving 9 minutes daily, which results in 9 degrees in 58 days. Then it stops moving and resumes after 25 days. In retrograde, it moves 1 minute out of 7 daily, covering 12 degrees in 84 days. It stops moving again, and after 25 days resumes direct motion, moving 9 minutes out of 58 daily, which results in 9 degrees in 58 days. The direct motion speed is fast again, moving 11 minutes daily, covering 11 degrees in 58 days. At this time, Jupiter appears in front of the sun, setting in the west in the evening. After 16 days of running 1,742,323 minutes, with the planet moving 2,323,467 minutes, it aligns with the sun again. A complete cycle lasts 398 days, during which it runs for 3,484,646 minutes, covering a distance of 43 degrees and 2,509,956 minutes.
When the sun rises in the morning, Mars and the sun align, and then Mars becomes obscured. Next, it starts moving forward for a total of 71 days, covering a distance of 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes. Then, it becomes visible in the east behind the sun. During its forward motion, it travels 23 minutes and 14 seconds daily, covering 112 degrees in 184 days. Its speed then decreases, moving 23 minutes and 12 seconds each day, covering 48 degrees in 92 days. It then remains stationary for 11 days. Subsequently, it begins its retrograde motion, traversing 62 minutes and 17 seconds each day, moving back 17 degrees in 62 days. It stops for another 11 days, then resumes its forward motion, covering 12 minutes each day, covering 48 degrees in 92 days. Afterwards, the forward speed increases, covering 14 minutes each day, traversing 112 degrees in 184 days. At this point, it passes in front of the sun and becomes visible in the west during the evening. Over the course of this entire cycle, the total duration is 779 days and 973,113 minutes, covering 414 degrees and 478,998 minutes.
As for Saturn, it also aligns with the sun in the morning before becoming obscured. It then moves forward for 16 days, covering a distance of 1,122,426.5 minutes, equivalent to 1 degree and 1,995,864.5 minutes. Then, in the morning, it can be seen in the east, behind the sun. While moving forward, it covers 35 minutes and 3 seconds each day, covering 7.5 degrees in 87.5 days. It stops for 34 days. It then starts moving backward, covering 17 minutes and 1 second each day, moving back 6 degrees in 102 days. After an additional 34 days, it resumes its forward motion, covering 3 minutes each day, covering 7.5 degrees in 87 days. At this point, it passes in front of the sun and becomes visible in the west during the evening. Over the course of this entire cycle, the total duration is 378 days and 166,272 minutes, traversing 12 degrees and 1,733,148 minutes.
Venus, when it conjuncts the sun in the morning, first "submerges," which means it retrogrades. Over five days, it will move back four degrees, and then it can be seen in the east in the morning; at this point, it is positioned behind the sun. Continuing to retrograde, it retrogrades three-fifths of a degree each day, totaling six degrees over ten days. Next comes "stationary," meaning it remains still for eight days. Then it begins to "rotate," which means it moves forward, but at a slower speed, covering three thirty-sixths of a degree each day, totaling thirty-three degrees over the course of forty-six days. After that, the speed increases to one degree and fifteen ninety-firsts each day, totaling one hundred six degrees over the course of ninety-one days. The speed continues to increase, moving one degree and twenty-two ninety-firsts each day, totaling one hundred thirteen degrees over the course of ninety-one days, at which point it has moved back behind the sun again, which can be seen in the east in the morning. Finally, moving forward, it covers one fifty-six thousand nine hundred fifty-fourth of a complete circle in forty-one days, while the planet also travels fifty degrees one fifty-six thousand nine hundred fifty-fourth of a complete circle, ultimately meeting the sun again. The cycle for one conjunction is two hundred ninety-two days and one fifty-six thousand nine hundred fifty-fourth of a complete circle, and the planet's movement follows this pattern.
In the evening, when Venus conjuncts the sun, it first "submerges," this time moving forward. It covers one fifty-six thousand nine hundred fifty-fourth of a complete circle in forty-one days, while the planet travels fifty degrees one fifty-six thousand nine hundred fifty-fourth of a complete circle, and it can be seen in the west during the evening; at this point, it is in front of the sun. Then it continues to move forward, with increasing speed, moving one degree and twenty-two ninety-firsts each day, totaling one hundred thirteen degrees over the course of ninety-one days. The speed then starts to decrease, moving one degree and fifteen hundredths each day, totaling one hundred six degrees over the course of ninety-one days, and then continues to move forward. The speed decreases, moving three thirty-sixths of a degree each day, totaling thirty-three degrees over the course of forty-six days. Next comes "stationary," remaining still for eight days. Then it "rotates," this time retrograding, retrograding three-fifths of a degree daily, which totals six degrees over ten days. At this point, it has moved in front of the sun, and can be seen in the west in the evening, continuing to retrograde, with increasing speed, moving back four degrees in five days, ultimately meeting the sun again. The two conjunctions complete one cycle, spanning five hundred eighty-four days and eleven thousand three hundred ninety-eight hundredths of a complete circle, and the planet's movement follows this pattern as well.
Mercury, when it meets the sun in the morning, first "伏" (lies low), which means retrograde. It retreats seven degrees after a period of nine days, and then in the morning, it can be seen in the east, positioned behind the sun. Continuing to retrograde, the speed increases, retreating one degree after one day. It then "pauses" for two days. Then it "turns," which means direct motion, at a slower speed, moving eight-ninths of a degree each day, covering eight degrees in nine days. The speed increases, moving one and a quarter degrees each day, covering twenty-five degrees in twenty days, at which point it is once more behind the sun and visible in the eastern sky in the morning. Finally, it moves direct, traversing 641,009,067 parts of a circle in sixteen days, with the planet moving thirty-two degrees 641,009,067 parts of a circle, ultimately meeting the sun. The cycle of one conjunction is fifty-seven days 641,009,067 parts of a circle, and the planet's movement follows this pattern.
Speaking of Mercury, when it appears at the same time as the sun, it is called a "conjunction." The patterns of Mercury's movement are as follows: sometimes it moves quickly, covering three hundred twenty-six degrees forty-one minutes nine hundred sixty-seven seconds in sixteen days (this is precise to the second!), at which point it can be seen in the evening sky to the west, positioned ahead of the sun. When moving quickly, it covers one and a quarter degrees in one day, completing twenty-five degrees in twenty days.
Sometimes it moves slowly, covering only seven-eighths of a degree in one day, taking nine days to cover eight degrees. Sometimes it simply comes to a halt for two days. Even more astonishing is that it can retrograde! It can retreat one degree in a day, at which point it can be seen in the evening sky to the west, positioned ahead of the sun. During retrograde, its speed is also slow, taking nine days to retreat seven degrees, and then it "conjoins" with the sun again.
From one "conjunction" to the next, taking into account all its movement phases, it takes a total of one hundred fifteen days six hundred one million two thousand five hundred five seconds, and this constitutes the complete cycle of Mercury's movement.
