First, we need to understand what this is about. This is a method for calculating the orbits of celestial bodies using ancient algorithms, which may seem quite complex. The first sentence means that when calculating, we first need to calculate the basic degrees, then add the remaining degrees until we complete a full day, which gives us the final degree. This is similar to how we use decimals today, except that in ancient times, fractions were used.
Next, there are the orbital situations of Jupiter, Mars, Saturn, Venus, and Mercury, which list their "伏" (hidden) and "见" (visible) days and degrees respectively. "伏" refers to when a planet reaches a certain position, while "见" refers to when a planet appears at a certain position. For instance, Jupiter is hidden for 32 days, totaling 3,484,646 minutes; it is visible for 366 days, with 5 degrees of hidden motion, and has 2,509,956 minutes; it appears for 40 degrees, but we must subtract 12 degrees for retrograde motion, resulting in a final 28 degrees. The other planets have similar calculation methods, just with different values. This part of the data looks dense, but it actually records the specific times and angles of planetary movements.
The following section is even more complex, explaining how to calculate the movements of planets. The gist is that we first sum the degrees of the planet's movement and any remaining degrees, then add that to the remaining degrees of the sun. If the total equals a full day, we get a complete cycle. Then, we multiply the denominator of the planet's movement by the degrees at which the planet appears. If the result divided by the remainder of the day method is not enough to be half or more, we take one, and then add the result to the degrees of the planet's movement. If it fills the denominator, we add one degree. The methods for calculating retrograde and direct motion differ and must be adjusted based on the specific circumstances. Finally, it mentions "盈约满" (full approximation) and "去及除" (removal and division), which refer to different calculation methods, with the ultimate goal of obtaining precise values. In summary, this part discusses the details of the calculation methods, which are quite technical and require a solid understanding of mathematics to grasp. It's similar to how we calculate using formulas today, but the ancient formulas were more intricate and depended heavily on manual calculations.
Overall, this text describes an ancient astronomical calculation method, which centers on accurately calculating the orbits of planets. Although it appears complex, it reflects the ancient astronomers' in-depth study of the laws of the universe and their exquisite calculation skills.
In the morning, the Sun and Jupiter appear simultaneously, with Jupiter hiding and then beginning its prograde motion. After 16 days, equivalent to 1,742,323 minutes, Jupiter has moved 2 degrees and 323,467 minutes, and then appears in the east after the Sun. The prograde motion speed is fast, moving 11 degrees over 58 days. Then the prograde motion speed slows down, moving 9 degrees over 58 days. Jupiter then halts its motion and resumes after 25 days. During retrograde motion, it retreats 1/7 of a degree daily, retreating 12 degrees in 84 days. After another stop of 25 days, it resumes prograde motion, moving 9 degrees over 58 days. The prograde motion speeds up again, moving 11 degrees over 58 days, at which point it is in front of the Sun, setting in the western sky at dusk. After 16 days, equivalent to 1,742,323 minutes, Jupiter has moved 2 degrees and 323,467 minutes, appearing simultaneously with the Sun again. One cycle concludes, lasting a total of 398 days, equivalent to 3,484,646 minutes, with Jupiter moving 43 degrees and 2,509,956 minutes.
In the morning, the Sun and Mars appear simultaneously, with Mars hiding and then beginning its prograde motion. After 71 days, equivalent to 1,489,868 minutes, Mars has moved 55 degrees and 428,860.5 minutes, appearing in the east after the Sun. During prograde motion, it moves 14/23 of a degree daily, moving 112 degrees in 184 days. Then the prograde motion speed slows down, moving 12/23 of a degree daily, or 48 degrees in 92 days. Mars then stops moving for 11 days. It then enters retrograde motion, retreating 17/62 of a degree daily, retreating 17 degrees in 62 days. After another 11-day stop, it resumes prograde motion, moving 12 degrees over 92 days. The prograde motion speeds up again, moving 14 degrees over 184 days, at which point it is in front of the Sun, setting in the western sky at dusk. After 71 days, equivalent to 1,489,868 minutes, Mars has moved 55 degrees and 428,860.5 minutes, appearing simultaneously with the Sun again. One cycle concludes, lasting a total of 779 days, equivalent to 973,113 minutes, with Mars moving 414 degrees and 478,998 minutes.
In the morning, when the sun and Saturn come together, Saturn becomes obscured. Saturn moves forward, covering 1,120,426.5 arc minutes in 16 days, while the planet covers 1,995,864.5 arc minutes in one degree. Then, in the morning, Saturn is visible in the east, positioned behind the sun. During the forward movement, Saturn moves 35 arc minutes per day, covering 7.5 degrees in 87.5 days. It remains stationary for 34 days. It then moves in retrograde, covering 1/17 of a degree each day and retreating 6 degrees in 102 days. After another 34 days of direct motion, covering 1/3 of a degree per day and 7.5 degrees in 87 days, Saturn is now positioned in front of the sun, becoming obscured in the west during the evening. It covers 1,120,426.5 arc minutes in 16 days, while the planet covers 1,995,864.5 arc minutes in one degree, then they come together with the sun again. In one cycle, a total of 378 days and 16 days and 672 minutes have passed, and the planet has moved 12 degrees, 1,733,148 arc minutes.
In the morning, when the sun and Venus come together, Venus becomes obscured. Venus moves in retrograde, retreating 4 degrees over 5 days, then in the morning, Venus is visible in the east, positioned behind the sun. During the backward movement, Venus moves 3/5 of a degree per day, retreating 6 degrees in 10 days. It remains stationary for 8 days. It then moves forward slowly, covering 33 degrees over 46 days at a daily rate of 33/46 degrees. When moving at a faster pace, it covers approximately 1.91 degrees each day, moving 160 degrees in 91 days. It then continues moving forward at a faster speed, covering 2.22 degrees per day, moving 113 degrees in 91 days, now positioned behind the sun and obscured in the east during the morning. Moving forward, it covers 56,954 arc minutes in 41 days, moving 50 degrees and 56,954 arc minutes, then comes together with the sun again. In one conjunction, a total of 292 days and 56,954 arc minutes have passed, which is approximately 39 days, and the planet is the same.
In the evening, when the sun and Venus align, Venus is obscured. Venus moves forward, covering a total of 41 days and 56,954 minutes, traversing 50 degrees and 59 minutes. Then, in the evening, Venus appears in the western sky, positioned in front of the sun. While moving forward, it travels quickly, advancing 1 degree and 91 minutes each day, covering 113 degrees in 91 days. Then it continues moving forward, slowing down, advancing 1 degree and 15 minutes each day, covering 160 degrees over 91 days. When moving slowly, it progresses 33 degrees over 46 days, averaging 46 minutes of movement each day. Then, it remains stationary for 8 days. Following that, it begins its retrograde motion, receding 6 degrees over 10 days, becoming visible in the western sky in front of the sun in the evening. While moving backward, it travels quickly, retreating 4 degrees in 5 days, and then it aligns with the sun again. After two alignment cycles, totaling 584 days and 113,908 minutes, Venus's position remains unchanged.
In the morning, Mercury rises in the east at the same time as the sun. Then Mercury begins its retrograde motion, retreating 7 degrees after 9 days, becoming visible in the eastern sky behind the sun in the morning. Then Mercury continues to move backward, speeding up, retreating 1 degree each day. Then it stops for 2 days. After that, it starts moving forward, at a slower speed, advancing 8 degrees in 9 days, traversing 8/9 of the sun's apparent movement each day. Speeding up, it advances 1 degree and 1/4 each day, moving 25 degrees in 20 days, still behind the sun. In the morning, Mercury rises in the east, then continues its forward motion, traversing 32 degrees over 16 days and 641,967 minutes. Finally, it aligns with the sun again, requiring a total of 57 days and 641,967 minutes for this alignment, with Mercury covering the same degrees and time.
In the evening, Mercury and the Sun appear simultaneously. Then Mercury begins to move in direct motion, at a relatively slow speed, traveling thirty-two degrees and six hundred forty-one thousand nine hundred sixty-seven minutes in sixteen days and six hundred forty-one thousand nine hundred sixty-seven minutes, and then it can be seen in the western sky in front of the Sun at night. The speed increases, moving one and a quarter degrees each day, covering twenty-five degrees in twenty days, still in direct motion. The speed slows down, moving at eight-ninths of the Sun's speed each day, covering eight degrees in nine days. Then it comes to a stop for two days. After that, it begins its retrograde motion, retreating one degree per day, appearing in the western sky in front of the Sun at night. The retrograde motion slows down, retreating seven degrees in nine days, and ultimately it conjoins with the Sun again. From the first conjunction to the end of the second conjunction, it took a total of one hundred fifteen days and six hundred one thousand two hundred fifty-five minutes, with Mercury traveling the same distance and duration.
