Let's first talk about the winter solstice. The large remainder is 2356, and the small remainder is 927. Adding 27 to the large remainder and 927 to the small remainder yields the date of the winter solstice. Next, for the start of spring, adding 18 to the large remainder and 618 to the small remainder gives us the date of the start of spring, which signifies the dominance of the wood element. Adding 73 to the large remainder and 116 to the small remainder returns us to the period of earth element dominance. Earth produces fire, and the metal and water can be calculated according to this pattern.
Next, multiplying the small remainder by 12 gives us a "chen" (a time period). Starting from the midnight hour, the dates for the new moon, first quarter, and full moon should be calculated separately. Multiplying the small remainder by 100 gives us a quarter of an hour; if it's less than one-tenth, we express it as a fraction. Referring to the recent solar terms, we start counting from midnight. If the night is not finished, we refer to the most recent time.
During the calculation, there will be advances and retreats; advances add and retreats subtract, resulting in the outcome. The difference between advances and retreats begins at two degrees, decreasing by four degrees each time, with the amount halved each time. After three times, it is tripled, stopping when the difference reaches three, and after five degrees, it returns to the initial state.
The moon's speed fluctuates but follows consistent patterns. Combining various numbers from the heavens and the earth, multiplying them according to the remainder's pattern until the result is one gives us the portion that exceeds one cycle. Dividing the number of weeks by the number of lunar cycles gives us the number of days in the calendar. The speed of the moon's movement has a diminishing trend, which is a trend. Summing the diminishing amounts provides the profit and loss rate. If there is a profit, we add; if there is a loss, we subtract, resulting in the accumulation of gains and losses. Multiplying the number of half a small cycle by the general method until the result is one, then subtracting it from the number of cycles in the calendar, gives us the fraction of the new moon's movement.
Here are the specific data:
- Daily rotation degrees and minutes, column of decline, profit and loss rate, accumulation, lunar movement minutes:
- Day One: Fourteen degrees and ten minutes, one retreat, profit of twenty-two, initial profit of two hundred seventy-six.
- Day Two: Fourteen degrees and nine minutes, two retreats, profit of twenty-one, profit of twenty-two, two hundred seventy-five.
- Day Three: Fourteen degrees and seven minutes, three retreats, profit of nineteen, profit of forty-three, two hundred seventy-three.
- Day Four: Fourteen degrees and four minutes, four retreats, profit of sixteen, profit of sixty-two, two hundred seventy.
- Day Five: Fourteen degrees, four retreats, profit of twelve, profit of seventy-eight, two hundred sixty-six.
- Day Six: Thirteen degrees and fifteen minutes, four retreats, profit of eight, profit of ninety, two hundred sixty-two.
On the 7th, at thirteen degrees eleven minutes, subtract four, then add four, resulting in a surplus of ninety-eight. The total is two hundred fifty-eight.
On the 8th, at thirteen degrees seven minutes, subtract four, then subtract two, resulting in a surplus of one hundred two. The total is two hundred fifty-four.
On the 9th, at thirteen degrees three minutes, subtract four, then add two, resulting in a surplus of one hundred two. The total is two hundred fifty.
On the 10th, at twelve degrees eighteen minutes, subtract three, then add eight, resulting in a surplus of ninety-eight. The total is two hundred forty-six.
On the 11th, at twelve degrees fifteen minutes, add four, then subtract eleven, resulting in a surplus of ninety, with a total of two hundred forty-three.
On the 12th, the moon is at twelve degrees eleven minutes. Subtract three, then add, then subtract fifteen, resulting in a surplus of seventy-nine. The total is two hundred thirty-nine.
On the 13th, the moon is at twelve degrees eight minutes. Subtract two, then add, then subtract eighteen, resulting in a surplus of sixty-four. The total is two hundred thirty-six.
On the 14th, the moon is at twelve degrees six minutes. Subtract one, then add, then subtract twenty, resulting in a surplus of forty-six. The total is two hundred thirty-four.
On the 15th, the moon is at twelve degrees five minutes. Add one, then subtract, then subtract twenty-one, resulting in a surplus of twenty-six. The total is two hundred thirty-three.
On the 16th, the moon is at twelve degrees six minutes. Add two, then subtract, then subtract twenty (Note: If the number to subtract is insufficient, add five instead as surplus). The surplus is five, subtract the initial number. The total is two hundred thirty-four.
On the 17th, the moon is at twelve degrees eight minutes. Add three, then subtract, resulting in a surplus of eighteen. Subtract fifteen. The total is two hundred thirty-six.
On the 18th, the moon is at twelve degrees eleven minutes. Add four, then subtract, resulting in a surplus of fifteen. Subtract twenty-three. The total is two hundred thirty-nine.
On the 19th, the moon is at twelve degrees fifteen minutes. Add three, then subtract, resulting in a surplus of eleven and a total of two hundred forty-three.
On the 20th, the moon is at twelve degrees eighteen minutes. Add four, then subtract, resulting in a surplus of eight and a total of two hundred forty-six.
On the 21st, the moon is at thirteen degrees three minutes. Add four, then subtract sixty-seven, resulting in a total of two hundred fifty.
On the 22nd, the moon is at thirteen degrees seven minutes. Add four, then add four, then subtract seventy-one. The total is two hundred fifty-four.
On the 23rd, the moon is at thirteen degrees eleven minutes. Add four, then add four, then subtract seventy-one. The total is two hundred fifty-eight.
On the 24th, the moon is positioned at 13 degrees and 15 minutes. Add four, then subtract sixty-seven; the total is two hundred sixty-two.
On the 25th, the moon is at 14 degrees. Add four, then subtract fifty-nine; the total is two hundred sixty-six.
On the 26th, the moon is at 14 degrees and 4 minutes. Add three, then subtract forty-seven; the total is two hundred seventy.
On the 27th, the moon is at 14 degrees and 7 minutes. This is a special case: add three, then add three large cycles, subtract nineteen, and reduce by thirty-one; the total is two hundred seventy-three.
On Sunday, the moon is at 14 degrees and 9 minutes. Add less, then subtract twelve; the total is two hundred seventy-five.
Next are some astronomical data: Sunday minutes value, three thousand three hundred thirty-three; Sunday void, two thousand six hundred sixty-six; Sunday law, five thousand nine hundred sixty-nine; total week, one hundred eighty-five thousand thirty-nine; historical week, one hundred sixty-four thousand four hundred sixty-six; minor law, one thousand one hundred one; new moon large minutes, ten thousand one hundred eighty-one; small minutes, twenty-five; half a week, one hundred twenty-seven.
The last paragraph is an explanation of the calculation method: use the previously mentioned lunar accumulation to multiply by the new moon large minutes; if the small minutes total thirty-one, subtract this from the large minutes. If the large minutes reach historical week, subtract that as well. The remainder is then divided by Sunday law; the quotient is one day, and the remainder is the day remainder. The remainder of the day must be calculated separately to ultimately obtain the result of the new moon entering the calendar.
The first month adds one day, totaling 5832 days, with a remainder of 25 minutes.
Next, calculate the waxing gibbous, adding seven days to each, totaling 2283 days, with a remainder of 29.5 minutes. Convert the remainder into days according to regulations; if it reaches 27 days, subtract 27 days, and calculate the remaining according to weeks. If not enough to subtract, subtract one day and add a week void number.
Use the accumulated value of the calendar's gains and losses, multiplying the weeks by it as the base number. Then multiply the total number by the remainder of the days, and then multiply by the gain and loss rate to adjust the base number; this is the additional time gain and loss. Subtract the lunar movement minutes from one year, multiply by half the number of weeks as the difference, and use it to divide, obtaining the remainder of the gain and loss, just like calculating the gain and loss of days. The new moon adjusts the time in the days before and after. The large remainder of the waxing gibbous is utilized to determine the small remainder.
Multiply the year by the surplus and deficit ratio, divide by the difference, and the resulting full number indicates the magnitude of the surplus and deficit. Adjust the position of the sun and moon on the day using the surplus and deficit; if insufficient, adjust the degrees with the calendar to determine the position and degrees of the sun and moon.
Multiply half of the number of weeks by the remainder from the new moon, divide by the total, then subtract the remainder of the calendar days. If the remainder is not enough, subtract the number of weeks again, then subtract one day. Subtracting will give the number of weeks plus its fraction, which is the time of entering the calendar at midnight.
Calculate the second day; go back one day; if the day count remainder is 27, subtract one week; if less than one week, add the virtual number of weeks to the remainder. This remainder corresponds to the entry into the calendar on the second day.
Multiply the remainder of entering the calendar at midnight by the surplus and deficit rate; if it can be divided by the number of weeks, the remaining part is the remainder. Use it to adjust the accumulated value of the surplus and deficit; if the remainder cannot be used for adjustment, divide by the total as the adjustment value. This is the surplus and deficit at midnight. A full year is considered one degree, while anything less is considered a minute. Multiply the total by the fraction and remainder; the remainder is treated as the number of weeks for the fraction. If the fraction is full according to the calendar, treat it as degrees, adding the surplus and subtracting the deficit from the degrees and remainder at midnight to determine the degrees.
Multiply the remainder of entering the calendar by the rate of decline; if it can be divided by the number of weeks, the remaining part is the remainder. This allows you to track daily changes and declines.
Multiply the virtual number of weeks by the rate of decline; if it can be divided by the number of weeks, you get a constant. At the end of the calendar, add it to the change and decline; subtract if the rate of decline is full, converting it to the change and decline of the next calendar.
Adjust the daily change score of the calendar with the change and decline; if the score is insufficient, it is the number of degrees entering and leaving in a year. Multiply the total by the fraction and remainder, adding the degrees determined at night every day, which is the second day. At the end of the calendar, if it is less than a week, subtract 138, then multiply by the total. If it constitutes a full week, add the remainder of 837, then add the small fraction of 899, add the change and decline of the next calendar, and calculate as before.
Subtract or add the surplus and deficit rate from the change and decline to get the change surplus and deficit rate, then use it to adjust the surplus and deficit at midnight. At the end of the calendar, if the surplus and deficit is insufficient, reverse the earlier subtraction, enter the next calendar, and the added or subtracted remainder is the same as the numbers above.
This text describes an ancient method of calendar calculation, which is very specialized. Let's explain it sentence by sentence in modern spoken language.
First paragraph: First, based on the moon's movements each month and the solar terms, calculate the lengths of day and night each day ("mingfen" and "hunfen"). The calculation method is: first calculate the length of daylight each day, then calculate the length of nighttime each day, and use a unit called "du" to represent this, finally adding them together to determine the specific times for day and night. Any excess amount, if it exceeds half, is carried over, and if it's less than half, it's discarded.
Second paragraph: Then, it explains how to calculate the number of days in the calendar based on the moon's lunar cycle ("Yuejing Sibiao, Churuzhandao, Jiaocuo Fentian" refers to the complexity of the moon's trajectory). The calculation method is: divide the moon's speed by a constant to get the number of days in the calendar. Additionally, it mentions the concept of "Shuowanghe," which refers to the conjunction of the new moon (the first day of the lunar month) and the full moon (the fifteenth day of the lunar month) used to calculate the length of a month. Through a series of calculations, we ultimately obtain the daily increments and a value referred to as "chali."
Third to fourteenth paragraphs: This section lists a table that details the "gain and loss rate" of the lunar-solar calendar—essentially the daily adjustments needed. The table shows the values that need to be reduced or increased each day, as well as the cumulative values. It mentions "qianxian" and "houxian," along with some minor correction values ("weifen"). The calculation methods for these values are quite complex, involving many intermediate steps and parameters, such as "shaodafa," "lizhous," "chali," "shuoheshu," etc., which will not be explained one by one here.
Final paragraph: Finally, it describes how to determine the specific calendar date based on the calculation results. The method is: compare the calculated value with a reference value called "Shangyuan," and then based on the result, combine "shuoheshu" and "weifen" in the calculations to ultimately determine whether it is the solar calendar or the lunar calendar. During the calculation process, if any value exceeds a certain threshold, corresponding adjustments need to be made. Lastly, it emphasizes the importance of calculation accuracy, noting that there may be some minor errors. In summary, this is a very complex calendar calculation process that requires a lot of mathematical calculations and astronomical knowledge.
First, let's translate these steps of ancient astronomical calculations into modern spoken language step by step.
This text describes an algorithm for calculating a calendar, which involves many fine-tuning adjustments and calculations. First, various factors affecting the calendar must be considered, such as the passage of time, surpluses and deficits, etc., which are represented by terms like "differential," "surpluses and deficits," and so on. Then, through complex multiplication and division operations, the daily surpluses and deficits are determined, ultimately resulting in a relatively accurate calendar. Specifically, it first calculates the daily surplus or deficit, then uses these surpluses or deficits to adjust the calendar, ensuring that the calendar aligns with actual astronomical phenomena. It's like a finely-tuned gear system, where each step is interconnected and indispensable.
Next, it continues to explain how to calculate the next date. It adds the leftover time from the previous day and some minor correction values, and if it exceeds a month's length, it deducts a month. This part of the calculation is indeed very complex, involving many intermediate variables and steps, requiring repeated addition, subtraction, multiplication, and division to arrive at the final result. It's like playing a complex mathematical game that requires very meticulous calculations to obtain the correct answer. Finally, it arrives at a new date and continues this process to calculate future dates.
This text also describes how to calculate longer time periods, such as a year or even longer. It accumulates the daily surpluses and deficits and then adjusts them with certain coefficients to ultimately obtain a more precise calendar. This is like a process of continuously building up errors and then correcting them, ensuring that the calendar maintains accuracy over a long time. This part of the calculation is also very complex, requiring a deep understanding of astronomical knowledge to comprehend.
Finally, this text introduces how to calculate certain astronomical phenomena, such as the obliquity of the ecliptic (the angle between the plane of the Earth's orbit and the plane of the celestial equator), etc. It uses some astronomical constants and formulas to obtain the values of these astronomical phenomena through complex calculations. This part involves advanced astronomical knowledge, requiring a certain professional background to understand. The entire calculation process is like a massive mathematical model that cleverly combines various astronomical phenomena and calendar calculations, leading to a fairly accurate calendar system.
Finally, this passage mentions that from the Ji Chou year of the Shangyuan era to the Bing Xu year of the Jian'an era, a total of 7378 years have been accumulated. It then lists the stem-branch calendar years during this period and explains the relationship between the Five Elements and the Five Stars, as well as how to use this data to calculate astronomical parameters such as the weekly cycle and daily cycle. This section summarizes the fundamental data and methods behind the entire calendar system, providing a solid foundation for its establishment. This passage showcases the ingenuity of ancient astronomical calendar calculations, as well as the remarkable intellect and craftsmanship of ancient astronomers.
First, we need to understand what these numbers represent. This passage discusses the calculation of planetary movements using ancient methods, which looks quite complex. In simple terms, it calculates the specific positions of Jupiter, Mars, and Saturn in a particular month. Parameters like "weekly cycle," "daily cycle," and "synodic month" are used in the calculation process. Terms such as "major lunar excess," "minor lunar excess," "entry day of the month," "day excess," "degrees," and "degree excess" represent the final calculated results that indicate the positions of the planets. Terms like "lunar calendar," "intercalary month," "lunar chapter," and "mid-year" may refer to some parameters related to the calendar.
Next, let's break it down step by step. "The major and minor excess of the five stars. (Multiply the number of months using the common method, divide by the number of days; the quotient is the major excess, and the remainder is the minor excess. Subtract sixty from the major excess if it exceeds sixty.)" This sentence means: calculate the major and minor excess of the five stars (Jupiter, Mars, Saturn, etc.) on the new moon day (first day of the lunar month). The calculation method is to multiply the number of months using the common method, then divide by the number of days; the quotient is the major excess, and the remainder is the minor excess. If the major excess exceeds sixty, subtract sixty. This section covers purely ancient astronomical calculation methods, and we don’t need to get into the specifics of the algorithms. "The entry day of the five stars into the month, and the day excess. (Multiply each by the common method of the month excess, multiply by the minor excess of the synodic month, add them together, round the total, divide by the day degree method, then all are obtained.)" This sentence is about calculating the date when the five stars enter a certain month and the remaining days. The calculation method is very complex, involving calculations of parameters such as the common method, month excess, synodic month method, minor excess of the new moon, rounding the total, and the day degree method, so we also do not need to delve into the specific steps.
"Degrees and remainders of the five planets. (This involves subtracting to find the degree remainder, multiplying by a cycle, and using specific methods to approximate the values.)" This sentence is to calculate the degrees and degree remainders of the five planets. The calculation method is still very complex, involving parameters such as "cycle," "daily degree method," and "Dipper fraction." In simple terms, it is to calculate the position of the planets on the ecliptic and the remaining degrees. Similarly, we do not need to understand the specific calculation process.
Next is a series of parameter values, such as "record month, 7285," "chapter leap, 7," "chapter month, 235," and so on. These numbers are various constants needed to calculate the position of the planets, and we only need to know that they are necessary conditions for the calculation. The parameters and results for Jupiter, Mars, and Saturn are provided, such as Jupiter's "cycle rate, 6722," "daily rate, 7341," "synodic month, 13," "month remainder value, 64801," and so on, as well as the final calculated values: "large remainder at new moon, 23," "small remainder at new moon, 1307," "entry month day, 15," "daily remainder, 3484646," "degree, 33," "degree remainder, 2509956." These results are derived from the complex calculations mentioned earlier, and we only need to know that they represent the positional information of the planets at specific times. The parameters and calculation results of Mars and Saturn are similar. In short, this passage describes an ancient astronomical calculation system, the complexity of which is extraordinary. We only need to understand its general meaning and do not need to delve into the specific calculation methods.
Wow, all these numbers are really overwhelming! Let's break it down sentence by sentence and put it into simpler terms.
First paragraph:
"Degree remainder" is 166272; for Venus: week rate is 9022, daily rate is 7213, synodic month is 9, month remainder value is 152293, synodic month method is 171418, and daily degree method is 5313958. The large remainder at new moon is 25, the small remainder at new moon is 1129, and the entry month day is 27. Next, there are new data: daily remainder is 56954, new moon virtual fraction is 328, Dipper fraction is 1308190, degree is 292, and degree remainder is 56954.
Second paragraph:
In terms of Venus, the week rate is 11,561, the daily cycle is 1,834, the total number of months is 1, the remaining days in the month are 211,331, the combined lunar formula is 219,659, and the daily lunar method is 6,809,429. The major remainder is 29 days, the minor remainder is 773, and the entry date for the month is the 28th. The remaining days are 6,419,967, the virtual remainder is 684, the Dipper remainder is 1,676,345, the degree is 57, and the degree remainder is 6,419,967. This section is just numbers, which can be confusing to read, almost like doing accounting.
Next is the explanation of the calculation method. First, multiply the data of the year you want to calculate by the week rate, then divide the result by the daily cycle. If this indicates that it is evenly divisible, then the calculation is correct, and the remainder is the combined remainder. Divide the week rate by the combined remainder to obtain the year. For the conjunction of Venus and Mercury, odd numbers indicate morning appearances, while even numbers indicate evening appearances. Multiply both the number of months and the remaining days by this product; if this is evenly divisible by the combined lunar formula, you determine the month, and the remainder is the remaining days in the month. Then use the chapter method to multiply by the remainder; if this is evenly divisible by the chapter formula, it indicates there is a leap month. Subtract the leap month, and what remains is the combined month outside of the accurate calculation. If a leap month transition is encountered, use the new moon to adjust.
Multiply the common method by the remaining days of the month, multiply the combined lunar formula by the minor remainder, then simplify using the combined number. If the result can be divided evenly by the daily lunar method, you get the entry date of the month. If it cannot be divided evenly, the remainder represents the remaining days. Finally, multiply the week days by the degree fraction. If it can be divided evenly by the daily lunar method, you get one degree, and the remainder is the remainder. Use the method of the first five oxen to ascertain the degree. This explanation of the calculation method includes many technical terms that may be challenging to comprehend. In summary, this text describes a complex calendar calculation method involving a large amount of astronomical data and computational steps.
Finally, the original text quotes: **Seeking the conjunction of stars.**
Let's first talk about how to calculate the month. Add the days of this month to the remaining days of the previous month. If it adds up to a full month, it's straightforward; if it doesn't add up to a year, calculate according to this year, subtract when it's full, add a leap month, and leave the remaining days for the next year; if it's full for another month, leave it for the year after next. For Venus and Mercury, if they appear in the morning, add them up until evening; if they appear in the evening, add them up until morning.
Next is to calculate the size of the new moon (first day of the lunar month). Add the remaining days of the new moon of this month to the remaining days of the new moon of the previous month. If it adds up to a month, add another twenty-nine days (large month) or seven hundred and seventy-three minutes (small month). The remaining days of the small month are calculated according to the remaining days of the large month, using the same method as before.
To determine the specific date of the new moon each month, add the date of the new moon for the month to the remaining days. If the total equals a full day, it counts as one day. If the remaining days from the previous month's new moon are enough to cover this month's new moon, subtract one day from the count; if the remaining days of this month exceed seven hundred seventy-three minutes, subtract twenty-nine days; if not enough, subtract thirty days, and carry over the remaining days to the next month, which will be the new moon of the following month.
The calculation for angles is similar: add the angle to the remaining angle, and if it totals a full day's angle, it counts as one degree.
Below are the orbital data for Jupiter:
Jupiter:
Retrograde for thirty-two days and three million four hundred eighty-four thousand six hundred forty-six minutes.
Prograde for three hundred sixty-six days.
Retrograde five degrees and two million nine thousand nine hundred fifty-six minutes.
Prograde forty degrees. (After moving retrograde by twelve degrees, the actual movement is twenty-eight degrees.)
Mars's orbital data:
Mars: Retrograde for one hundred forty-three days and ninety-seven thousand three hundred thirteen minutes.
Prograde for six hundred thirty-six days.
Retrograde one hundred ten degrees and forty-seven thousand eight hundred ninety-eight minutes.
Prograde three hundred twenty degrees. (After moving retrograde by seventeen degrees, the actual movement is three hundred three degrees.)
Saturn's orbital data:
Saturn: Retrograde for thirty-three days and sixteen thousand six hundred seventy-two minutes.
Prograde for three hundred forty-five days.
Retrograde three degrees and one hundred seventy-three thousand one hundred forty-eight minutes.
Prograde fifteen degrees. (After moving retrograde by six degrees, the actual movement is nine degrees.)
Venus's orbital data:
Venus: Retrograde in the east in the morning for eighty-two days and eleven thousand three hundred ninety-eight minutes.
Is visible in the west for two hundred forty-six days. (After moving retrograde by six degrees, the actual movement is two hundred forty-six degrees.)
Retrograde in the morning for one hundred days and eleven thousand three hundred ninety-eight minutes.
Is visible in the east. (The daily degree is the same as in the west. Retrograde for ten days, retrograde eight degrees.)
Mercury's orbital data:
Mercury: Retrograde in the east in the morning for thirty-three days and six million twelve thousand five hundred five minutes.
Is visible in the west for thirty-two days. (After moving retrograde by one degree, the actual movement is thirty-two degrees.)
Retrograde sixty-five degrees and six million twelve thousand five hundred five minutes.
Is visible in the east. (The daily degree is the same as in the west, retrograde for eighteen days, retrograde fourteen degrees.)
First, let's first calculate the movements of the sun and the planets. First, calculate how many degrees the sun moves each day, then add the number of degrees the planets move each day. If the total exceeds the sun's daily movement in degrees, divide the excess by the number of degrees the sun moves each day to find a quotient. This quotient, similar to calculating an entire horoscope, can then help determine the degrees at which the planets appear next to the sun. Next, multiply the planet's movement denominator by the "degrees at which the planet appears next to the sun," and then divide the remaining portion by the number of degrees the sun moves each day. If it doesn't divide evenly and exceeds half, treat it as one. Then, add this result to the degrees the planet moves, and if the degrees reach the denominator, add one degree. The methods for direct and retrograde motions differ. Multiply the current denominator by the previous degree and divide by the previous denominator to obtain the current degree. For retrograde motion, subtract the remaining degrees from before. If the calculated degrees are insufficient, use the division method with the movement's denominator as a proportion; the degrees will increase or decrease, influencing one another. In summary, terms like "excess," "approximate," and "full" are used to find accurate quotients, while terms like "subtract," "reach," and "divide" help find complete quotients.
Next, let's talk about Jupiter. Jupiter appears in the morning with the sun, and then "hides" (or disappears). When moving forward, it travels 1,742,323 minutes of travel every sixteen days, covering 323,467 minutes every two degrees, then appears in the east in the morning, behind the sun. When moving quickly, it covers 11/58 of a degree each day, totaling 11 degrees over 58 days; when moving slowly, it moves 9 minutes daily, amounting to 9 degrees over 58 days. When it is stationary, it remains still for 25 days before starting to move again. During retrograde motion, it moves 1/7 of a degree each day, and after 84 days, it retreats 12 degrees. Then it stays stationary for 25 days before starting to move forward again, traveling 9/58 of a degree daily, amounting to 9 degrees over 58 days. When moving quickly, it travels 11 minutes each day, totaling 11 degrees over 58 days; during this phase, it is positioned in front of the sun and sets in the west by evening. After sixteen days, it reappears alongside the sun, covering 1,742,323 minutes every sixteen days, with the planet moving 323,467 minutes every two degrees. Over the course of this entire cycle, which lasts 398 days, it travels a total of 348,446 minutes, with the planet shifting a total of 43 degrees, or 250,956 minutes.
In the morning when the sun rises, Mars aligns with the sun, and then Mars goes out of view. Next, it begins to move forward for a total of 71 days, traveling 1,489,868 minutes, which means the planet has moved 55 degrees and 242,860.5 arc minutes. Then at sunrise, we can see it in the east, behind the sun. During its forward motion, it moves 14 minutes out of every 23 minutes each day, covering 112 degrees in 184 days. Then its forward speed slows down, moving 12 minutes out of every 23 minutes each day, covering 48 degrees in 92 days. After that, it remains stationary for a total of 11 days. Then it begins to move backward, traveling 17 minutes out of every 62 minutes each day, retreating 17 degrees in 62 days. After another 11 days, it begins moving forward again, traveling 12 minutes each day, covering 48 degrees in 92 days. Its forward speed then increases, moving 14 minutes each day, covering 112 degrees in 184 days, at which point it has moved ahead of the sun, and in the evening, we can see it going out of view in the west. After 71 days, it has traveled 1,489,868 minutes, and the planet has moved 55 degrees and 242,860.5 arc minutes, after which it aligns with the sun again. Over the entire cycle, it totals 779 days, traveling 973,113 minutes, and the planet has moved 414 degrees and 478,998 arc minutes.
In the morning when the sun rises, Saturn aligns with the sun, and then Saturn goes out of view. Next, it begins to move forward for a total of 16 days, traveling 1,122,426.5 minutes, which means the planet has moved 1 degree and 1,995,864.5 arc minutes. Then at sunrise, we can see it in the east, behind the sun. During its forward motion, it moves 3 minutes out of every 35 minutes each day, covering 7.5 degrees in 87.5 days. Then it stops for a total of 34 days. After that, it begins to move backward, traveling 1 minute out of every 17 minutes each day, retreating 6 degrees in 102 days. After another 34 days, it begins moving forward again, traveling 3 minutes each day, covering 7.5 degrees in 87 days. At this point, it has moved ahead of the sun, and in the evening, we can see it going out of view in the west. After 16 days, it has traveled 1,122,426.5 minutes, and the planet has moved 1 degree and 1,995,864.5 arc minutes, after which it aligns with the sun again. Over the entire cycle, it totals 378 days, traveling 166,272 minutes, and the planet has moved 12 degrees and 1,733,148 arc minutes.
Venus, when it meets the sun in the morning, will first "go into retrograde," moving back four degrees over five days. Then, in the morning, it can be seen in the east, positioned behind the sun. As it continues retrograding, it moves three-fifths of a degree daily, retreating six degrees in ten days. Then it will "pause," remaining stationary for eight days. Next, it will "rotate," starting to move forward at a slower speed, moving thirty-three forty-sixths of a degree each day, traveling thirty-three degrees in forty-six days. Afterward, the speed increases to one degree and ninety-one-fifteenths each day, moving one hundred and six degrees in ninety-one days. Speeding up again, it moves one degree and ninety-one twenty-seconds each day, traveling one hundred and thirteen degrees in ninety-one days. At this point, it is positioned behind the sun, appearing in the east during the morning. Finally, moving forward, it travels fifty-six thousand nine hundred fifty-fourths of a circle in forty-one days, while the planet also travels fifty degrees and fifty-six thousand nine hundred fifty-fourths of a circle, then meets the sun again. One conjunction totals two hundred ninety-two days and fifty-six thousand nine hundred fifty-fourths of a circle; the planet follows this pattern as well.
When Venus meets the sun in the evening, it first "retreats," but this time it moves forward, traveling fifty degrees and fifty-six thousand nine hundred fifty-fourths of a circle in forty-one days, and can be seen in the west in the evening, in front of the sun. Then it continues to move forward, speeding up, moving one degree and ninety-one twenty-seconds each day, traveling one hundred and thirteen degrees in ninety-one days. Then the speed slows down, moving one degree and fifteen-hundredths each day, traveling one hundred and six degrees in ninety-one days, before starting to move forward again, with the speed slowing down to thirty-three forty-sixths of a degree each day, moving thirty-three degrees in forty-six days. It will "pause," remaining stationary for eight days. Then it will "rotate," starting to retrograde, moving five-thirds of a degree each day, retreating six degrees in ten days, at this point appearing in the west in the evening. "Retreat," retrograde, speeding up, moving back four degrees in five days, and then it meets the sun again. Two conjunctions are counted as one complete cycle, totaling five hundred eighty-four days and one hundred thirty-nine thousand eight hundredths of a circle; the planet also follows this pattern.
Mercury, when it meets the sun in the morning, first "dips", retrogrades, and retreats seven degrees over nine days. Then, in the morning, it can be seen in the east, positioned behind the sun. Continuing to retrograde, the speed increases, retreating one degree per day. It "pauses" for two days without moving. Then it "turns", starting to move forward more slowly, covering just under one degree each day, or eight degrees over nine days. Then the speed increases to one and a quarter degrees per day, covering twenty-five degrees in twenty days. At this point, it is still behind the sun and can be seen in the east in the morning. Finally, moving forward, it covers 641,000,067 parts of a circle in sixteen days, while the planet also moves thirty-two degrees and 641,000,067 parts of a circle, then meets the sun again. In total, it takes fifty-seven days for 641,000,067 parts of a circle; the planet follows this pattern.
When it comes to Mercury, it seems to dip behind the sun, then it runs along its orbit. Specifically, in sixteen days it can run thirty-two degrees and 641,000,066 parts of a degree; at this point, you can see it appearing in the west, ahead of the sun. When it moves quickly, it can cover one degree and fifteen minutes in a day, or twenty-five degrees in twenty days. When it moves slowly, it can only cover seven-eighths of a degree in a day, or eight degrees in nine days. If it stops, it remains still for two days. Sometimes it even moves backward, retreating one degree each day; at this point, you can still see it appearing in the west, ahead of the sun. When it moves backward, it is slow as well, taking nine days to retreat seven degrees, and finally meets the sun again. This back and forth, including the entire cycle of it meeting the sun twice, takes a total of one hundred and fifteen days and five hundred and five parts of a day; this outlines the pattern of Mercury's movement.
Mercury, during its conjunction with the Sun, has a speed that varies, and can even move backwards. It is truly miraculous! It can travel just over 32 degrees in sixteen days, 25 degrees in twenty days, just 8 degrees in nine days, and can even remain completely still for two days! Even stranger, it can move backwards, retracting 7 degrees in nine days before returning to the Sun. The entire cycle lasts 115 days and 6 hours, and this conjunction of Mercury and the Sun repeats in this manner.
