First, let's break down this ancient astronomical calculation method into modern terms. This text mainly discusses how to calculate the timing of planetary conjunctions (when planets and the moon align in the sky). It employs some special algorithms, such as the "lunar conjunction method" and the "solar degree method," which are experiential formulas summarized by ancient astronomers.
The first paragraph talks about calculating the date of planetary and lunar conjunctions. It uses some intricate calculation techniques, such as using "lunar remainder" and "new moon remainder" to adjust the calculation results. Specifically, it involves adding different data together and then determining the final date based on the "solar degree method." If the calculation result does not meet the "solar degree method," it indicates that a few more days need to be calculated from the New Moon (the first day of the lunar calendar).
The second paragraph discusses how to calculate the degrees of planets. It calculates the degrees of planets by multiplying the full circle (360 degrees) by the degrees and minutes, and then determines the specific position of the planet based on the "solar degree method." If the calculation results in a remainder, the "Five Ascensions of the Ox" method is used to handle it. This section mainly explains how to determine the position of planets on the ecliptic.
Next, the third paragraph begins to explain how to calculate the cycle of planetary conjunctions. It states that the number of months is added to the lunar remainder, and if the result exceeds a month's cycle, one month is subtracted, resulting in the conjunction time for the next year or subsequent years. The calculation methods for Venus and Mercury are slightly different, needing to consider the morning star and evening star situations.
The fourth paragraph continues to explain the details of calculating planetary conjunctions. It mentions adding the remainder associated with the New Moon and the conjunction remainder, and then based on different situations, adding 29 or 773, ultimately obtaining a corrected conjunction date.
The fifth paragraph further refines the calculation method, which involves adding the day of entry into the month to the solar remainder, and then determining the final date based on the "solar degree method." If the calculation results in a remainder, adjustments need to be made according to the size of the remainder.
The sixth paragraph is a simple addition operation, which adds the degrees to the degree remainder and then determines the final degree based on the "solar degree method."
The seventh paragraph to the last paragraph provides specific data for Jupiter, Mars, Saturn, Venus, and Mercury, including their invisible days (days when the planets are behind the sun and not visible), visible days (days when the planets are in front of the sun and visible), degrees of invisibility (degrees of movement within invisible days), and degrees of visibility (degrees of movement within visible days). These data include specific days and degrees, as well as some correction values, such as the degrees of retrograde motion (when the planet's movement is opposite to its usual direction). It should be noted that the content in parentheses is a correction explanation for the original data; for example, "subtract twelve degrees for retrograde motion and add twenty-eight degrees for visibility" means that after subtracting the retrograde motion degrees from the original degrees, the final movement degrees are obtained.
In summary, this passage describes a rather complex ancient astronomical calculation method, which requires a deep understanding of ancient astronomical terms and calculation methods to fully comprehend.
First, let's calculate the movement of the sun. Calculate the degrees the sun moves each day, then add the daily movement of the stars. If it exceeds a full day's worth, subtract that amount, and the remaining degrees represent the stars' daily movement relative to the sun. Then, multiply the daily movement of the stars by the degrees they appear, then divide by one day's degrees. If it doesn't divide evenly, any excess over half a day counts as a full day. Add the calculated degrees to the sun's daily movement degrees. If the degrees exceed its cycle, subtract a full cycle. The cycles differ for direct and retrograde calculations. Multiply its current cycle by the previous degrees, then divide by the previous cycle to get its current degrees. Continue calculating the remaining degrees, subtracting if calculating retrograde motion. If the calculated degrees are less than a full cycle, divide by the cycle's total degrees, then adjust the degrees based on the cycle, ensuring coordination between past and future adjustments. In summary, terms like "waxing," "waning," and "full" help determine accurate divisors, while "subtract," "add," and "divide" are used for precise calculations.
Next, let's talk about Jupiter. Jupiter rises in the morning with the sun and then disappears. Based on its apparent motion, it travels a total of 1,742,323 minutes over the course of sixteen days. Jupiter moves 2 degrees and 323,467 minutes, then appears in the east, behind the sun. During direct motion, it moves quickly, covering 11 out of 58 minutes each day, which totals 11 degrees in 58 days. During retrograde motion, its speed decreases, moving at a rate of 1/7 of a minute each day, retreating 12 degrees after 84 days. Then it stays stationary for 25 days. After that, it resumes direct motion, moving 9 out of 58 minutes each day, covering 9 degrees in 58 days. During direct motion, it moves quickly again, covering 11 minutes each day, which totals 11 degrees in 58 days, appearing in front of the sun and hiding in the west in the evening. It travels a total of 1,742,323 minutes in sixteen days, moving 2 degrees and 323,467 minutes, before aligning with the sun. A complete cycle lasts a total of 398 days and 3,484,646 minutes, with Jupiter moving 43 degrees and 250,956 minutes.
When the sun rises in the morning, Mars aligns with the sun and then hides. Next, it starts moving direct, lasting 71 days, covering a total of 1,489,868 minutes, which is 55 degrees and 242,860.5 minutes. Then, you can see it in the east in the morning, behind the sun. During direct motion, Mars moves 14 out of 23 minutes each day, covering 112 degrees in 184 days. The speed during direct motion slows down a bit, moving 12 out of 23 minutes each day, covering 48 degrees in 92 days. Then it stops, remaining stationary for 11 days. After that, it starts moving retrograde, moving 17 out of 62 minutes each day, retreating 17 degrees after 62 days. It stops again for 11 days, then resumes direct motion, moving 12 minutes each day, covering 48 degrees in 92 days. The speed during direct motion increases again, moving 14 minutes each day, covering 112 degrees in 184 days, reaching in front of the sun, and can be seen in the west in the evening. After 71 days, it travels a total of 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes, before aligning with the sun once more. The entire cycle lasts a total of 779 days and 973,113 minutes, covering a total of 414 degrees and 478,998 minutes.
Saturn is similar; in the morning when the sun rises, it aligns with the sun and then becomes less visible. Next, it begins to move forward for 16 days, traveling 1,122,426.5 minutes, which is 1 degree and 1,995,864.5 minutes of arc. Then, you can see it in the eastern sky in the morning, behind the sun. While moving forward, Saturn travels 3/35 of a degree each day and covers 7.5 degrees in 87.5 days. Then it stops for 34 days without moving. Then it begins to retrograde, moving 1/17 of a degree each day, and after 102 days, it retreats 6 degrees. Another 34 days later, it begins to move forward again, traveling 3 minutes each day, covering 7.5 degrees in 87 days. At this point, it has moved in front of the sun and can be seen in the western sky at night. After 16 days, it travels another 1 degree and 1,995,864.5 minutes of arc and aligns with the sun again. Over the entire cycle, it totals 378 days and 166,272 minutes, covering 12 degrees and 1,733,148 minutes.
As for Venus, when it appears with the sun in the morning, it first slowly recedes, retrograding, and after five days, it retreats 4 degrees, making it visible in the eastern sky behind the sun. While retrograding, it moves 3/5 of a degree each day, retreating 6 degrees in 10 days. Then it will remain stationary for 8 days without moving. Next, it begins to move forward slowly, traveling 33/46 of a degree each day, covering 33 degrees in 46 days before it begins to move forward. Its speed increases further, moving 15/91 of a degree each day, covering 160 degrees in 91 days. Then, its forward speed increases even more, moving 22/91 of a degree each day, covering 113 degrees in 91 days, at which point it is behind the sun, appearing in the eastern sky in the morning. It continues to move forward smoothly, covering 1/56,954 of a full orbit in 41 days, and the planet also moves 50 degrees and 1/56,954 of a full orbit before it aligns with the sun again. This alignment takes a total of 292 days and 1/56,954 of a full orbit, with the planet following the same trajectory.
When Venus appears with the Sun in the evening, it first moves direct (伏), traveling one fifty-six thousand nine hundred fifty-fourth of a revolution in forty-one days, while the planet also moves one fifty degrees and five hundred sixty-nine thousand nine hundred fifty-fourth of a revolution, making it visible in the western sky, positioned ahead of the Sun. Then it moves direct (顺), speeding up (疾), traveling two twenty-seconds of a degree each day, and one hundred thirteen degrees in ninety-one days. After that, the speed decreases (迟), moving one degree and fifteen minutes each day, and one hundred six degrees in ninety-one days, before it resumes its direct motion. The speed slows down (迟), covering thirty-three degrees over forty-six days, and then it will stop (留) for eight days without moving. Next, it enters retrograde motion (旋), moving three-fifths of a degree each day, retreating six degrees after ten days, at which point it is positioned ahead of the Sun and appears in the western sky in the evening. In retrograde (逆), the speed increases (疾), retreating four degrees after five days, and then it meets the Sun again. Two conjunctions are counted as one cycle, totaling five hundred eighty-four days and one hundred thirteen thousand nine hundred eight one-fifth of a revolution, and the planet follows the same trajectory.
As for Mercury, when it appears with the Sun in the morning, it first slowly retreats (伏), going retrograde, retreating seven degrees after nine days, making it visible in the eastern sky, positioned behind the Sun. Then the retrograde speed increases (更逆，疾), retreating one degree each day. After that, it will stop (留) for two days without moving. Next, it begins to move forward (旋), moving at a slow pace (迟), covering eight degrees over nine days at a rate of eight ninths of a degree, before it begins to move forward. The speed increases (疾), moving one and a quarter degrees each day, and twenty-five degrees in twenty days, at which point it is behind the Sun and appears in the eastern sky in the morning. It continues to move forward (顺), covering one six hundred forty-one million nine thousand sixty-seven thousandths of a revolution in sixteen days, while the planet also moves thirty-two degrees six hundred forty-one million nine thousand sixty-seven thousandths of a revolution, then it meets the Sun again. One conjunction spans fifty-seven days and six hundred forty-one million nine thousand sixty-seven thousandths of a revolution, and the planet follows the same trajectory.
It is said that Mercury, when it sets alongside the sun, seems to hide away. Sometimes it moves in a direct trajectory, traversing 32 degrees over the course of 16 days, and can be seen in the western sky during the evening, positioned in front of the sun. When moving forward, it travels a quarter of a degree each day, and 25 degrees in 20 days. However, there are times when it slows down, covering only 7/8 of a degree each day, taking 9 days to cover 8 degrees. At times, it even comes to a complete stop for two days. Even more astonishingly, it can move in reverse! It can still be seen in the western sky during the evening, positioned in front of the sun. When moving backwards, it is slow, taking 9 days to retreat 7 degrees, eventually rejoining the sun. From one conjunction with the sun to the next, this entire cycle lasts a total of 115 days and about 6.125 days, and Mercury's orbit follows this pattern.
