A tropical year is set at 365.24 148 1 (today's measurement is 365.2425438+09878), which is the most accurate data until Yang Zhongfu made a unified calendar in the fifth year of Qingyuan, Ningzong, Southern Song Dynasty (A.D. 1 199).
The new leap week of 39 1 year (144 leap) is more accurate than the leap week of 19 year (7 leap) adopted in the previous calendar.
The fixed intersection days are 27.2 1223 days (currently estimated as 27.2 1222 days). Accurate measurement of the number of months and days at the intersection makes it possible to accurately predict solar and lunar eclipses. Zu Chongzhi calculated the time of the four eclipses in the 23 years from the 13th year of Yuanjia (AD 436) to the 3rd year of Daming (AD 459) with Da Ming Li, and the results were completely in line with the reality.
It is concluded that Jupiter overtakes the sun once every 84 years, that is, the period of revolution of Jupiter is 1 1.858 years (currently measured as 1 1.862 years).
A more accurate five-star rendezvous period is given, in which the rendezvous period of mercury and Jupiter is also close to the modern value.
A method of determining the winter solstice time by measuring the length of the noon sun shadow with a standard table is put forward.
To commemorate this great ancient scientist, people named a crater on the back of the moon as Zu Chongzhi crater, and the asteroid 1888 as Zu Chongzhi asteroid.
Due to the needs of animal husbandry and agricultural production, the working people in ancient China discovered the basic laws of the movement of the sun and the moon through long-term observation. They set the period from the first full moon or lack of moon to the second full moon or lack of moon as one month, each month is a little more than twenty-nine days, and twelve months is called a year. This method of calculating the year is called the lunar calendar.
They also observed that it takes 365 days 1/4 days from the first winter solstice to the second winter solstice (in fact, the earth goes around the sun once), so it is also called a year. Calendars calculated in this way are usually called solar calendars. However, the number of days in the lunar year and the solar year is not exactly equal. According to the lunar calendar, a year is 354 days; According to the solar calendar, a year should be 365 days, 5 hours, 48 minutes and 46 seconds. The lunar calendar is more than eleven days shorter than the solar calendar. In order to make the dates of the two calendars consistent, we must find ways to adjust the dates of the lunar year.
For this problem, our ancestors found a solution long ago, that is, adopting the method of "leap moon". Arrange a leap year in several years, and add a leap month to each leap year. Leap year every year, there are thirteen months in a year. Because of this leap year method, the lunar year and the solar year are more consistent.
China ancient calendar experts have always used 19 years as the unit to calculate leap years, which is called "one chapter", and each chapter has seven leap years. In other words, after nineteen years, seven years is thirteen months. This leap method has been used for more than 1000 years, but it is not thorough and accurate enough.
In 4 12 A.D., Zhao Zuo of Beiliang wrote Yuan Li, which broke the limitation of the annual chapter and stipulated that 22 1 leap month should be inserted in the middle of 600 years. Unfortunately, Zhao Xu's reform did not attract people's attention at that time. For example, He Chengtian, a famous calendar mathematician, still used the ancient method of 19 years and seven periods when he made Li Yuanjia in 443 AD.
Based on Zhao Cuo's advanced theory and his own observation, Zu Chongzhi thinks that there are too many jumps in 19 years, one day less every 200 years, while the leap number of 22 1 in Zhao Cuo's 600 years is too thin and not very accurate. So he proposed a new leap method of 39 1 year 144 leap. This leap method was the most advanced at that time.
According to the principle of physics, when a rigid body rotates, the direction and speed of rotation should be the same if it is completely free from external forces; If it is affected by external force, its rotation speed will change periodically. The earth is a rigid body with uneven surface and irregular shape, which is often influenced by the gravity of other planets in its operation, so the rotation speed always changes periodically and cannot be absolutely consistent.
Therefore, it is impossible to completely return to last winter when the sun went around once a year (actually, the earth went around the sun once a week), and there will always be subtle differences. According to the accurate calculation of astronomers, the difference of one year is about 50.2 seconds, and it goes backwards every 7 1 year and 8 months. This phenomenon is called precession.
With the gradual development of astronomy, ancient Chinese scientists gradually discovered the precession phenomenon. Deng Ping in the Western Han Dynasty, Liu Xin and Jia Kui in the Eastern Han Dynasty all observed the phenomenon of winter moving to the future, but they did not explicitly point out the existence of precession. It was not until the early years of the Eastern Jin Dynasty that astronomers began to affirm the existence of precession and advocated the introduction of precession into the calendar for the first time. He put forward the first data of precession, and calculated that the winter solstice will recede every 50 years. Later, in the early years of the Southern Song Dynasty, He Chengtian thought that precession was once in a hundred years, but he did not apply it in his Yuan Jiali Calendar.
Zu Chongzhi inherited the scientific research achievements of predecessors, not only confirmed the existence of precession, but also calculated precession once every forty-five years and eleven months, and applied precession in his Da Liming. Because the astronomical historical materials he relied on were not accurate enough, the data he proposed could not be very accurate. Nevertheless, Zu Chongzhi's application of precession to the calendar is a pioneering work in astronomical history, which opens a new page for the improvement of China's calendar. After the Sui Dynasty, precession was valued by many historians, such as Daye calendar and Huangji calendar in the Sui Dynasty.
The so-called intersection month is the time when the moon passes through the intersection of the ecliptic and the white road twice in a row. The ecliptic refers to the orbit of the sun as seen by the earth people, and the ecliptic refers to the orbit of the moon as seen by the earth people. You can calculate the number of days in intersecting months. The number of intersecting months measured by Zu Chongzhi is 27.2 1223, which is much more accurate than that measured by astronomers in the past and very similar to that measured by modern astronomers. With the astronomical level at that time, it was remarkable that Zu Chongzhi could get such accurate figures.
Since both eclipses occur near the intersection of the ecliptic and the ecliptic, it is more accurate to calculate the time of the eclipse after calculating the number of days of the intersection. In his Ming Li, Zu Chongzhi calculated the time of the solar eclipse with the intersection month, which is more accurate than in the past and very close to the actual time of the solar eclipse.
Based on the above research results, Zu Chongzhi finally succeeded in making the most scientific and progressive calendar at that time-Daming Calendar. This is the genius of Zu Chongzhi's scientific research and his most outstanding contribution to the astronomical calendar.
In addition, Zu Chongzhi also observed and calculated the orbits of the five planets-wood, water, fire, gold and earth-in the sky and the time required for one cycle. Scientists in ancient China calculated that Jupiter (known as the year-old star in ancient times) runs once every twelve years. When Liu Xin wrote "San Li" in the Western Han Dynasty, he found that Jupiter had been running for less than twelve years. Zu Chongzhi went further and calculated that Jupiter's orbital time was 1 1.858 years. Modern scientists estimate that the period of Jupiter is about 1 1.862 years. The result calculated by Zu Chongzhi is only 0.04 years away from this figure.
In addition, Zu Chongzhi calculated that the time of Mercury's orbit is 1 15.88 days, which is completely consistent with the two decimal places determined by modern astronomers. He calculated that the time for Venus to orbit was 583.93 days, which was only 0.0 1 day away from the figure determined by modern scientists.
In 462 AD (the sixth year of Song Daming), Zu Chongzhi presented the carefully compiled Da Liming to the court for promulgation and implementation. Emperor Xiaowu of Song ordered officials familiar with the calendar to discuss the advantages and disadvantages of this calendar. During the discussion, Zu Chongzhi was opposed by conservative forces represented by Dai Faxing. Dai Faxing is a trusted minister of Emperor Xiaowu of Song Dynasty, and he has great power. Because he took the lead in opposing the new calendar, all the officials in the imperial court, big and small, echoed it, and everyone was not in favor of changing the calendar.
Zu Chongzhi always insisted on his correct opinion and had a heated argument with Dai Faxing. This debate about the advantages and disadvantages of the new calendar actually reflected the sharp struggle between science and anti-science, progress and conservatism at that time.
Dai Faxing wrote to the emperor first, and performed miracles of ancient sages and sages from ancient books to suppress Zu Chongzhi. He said that during the winter solstice, the sun was always in a certain position, which was decided by ancient sages and could never be changed. He said that Zu Chongzhi thought that the winter solstice moved every year, slandering the sky and violating the Bible. This is a heinous act. He also said that the prevailing calendar of 19 was formulated by ancient sages and must not be changed. He even called Zu Chongzhi a humble and ordinary person who was not qualified to talk about reforming the calendar.
Zu Chongzhi showed no fear of attacks by powerful forces. He wrote a famous rebuttal article. According to the ancient literature and the records of observing the sun at that time, he proved that the winter solstice changed. He pointed out: the facts are clear. How can we believe in the past and doubt the present? He also listed in detail the changes of shadow length around noon from the winter solstice for many years, and accurately calculated the date and time of the winter solstice, which showed that the seventh leap in the nineteenth year was very inaccurate. He asked: The old calendar is not allowed. Should it be used forever and never reformed? Anyone who wants to say that Li Ming is not good should produce conclusive evidence. If there is evidence, I am willing to suffer.
At that time, Dai Faxing could not point out the shortcomings of the new calendar, so he argued about the speed of the day, the length of the shadow, the speed of the month and so on. Zu Chongzhi refuted them one by one. Under the refutation of Zu Chongzhi's righteous words, Dai Faxing had nothing to answer, but said rudely, "No matter how good the new calendar is, it can't be used."
Zu Chongzhi was not intimidated by Dai Faxing's outrageous attitude, but said firmly, "Never trust the ancients blindly. Since the shortcomings of the old calendar have been discovered and the new calendar has many advantages, it should be replaced with a new one. "
In this big debate, many ministers were convinced by Zu Chongzhi's incisive and thorough theory, but they were afraid of the power of Dai Faxing and dared not speak for Zu Chongzhi. Finally, a minister named Chao Shangzhi came out to support Zu Chongzhi. He said, "Daming Calendar" is the result of Zu Chongzhi's years of research. According to the records in Daming Calendar, the four eclipses in the 13th year of Yuanjia (436), 14th year, 28th year and 3rd year of Daming (459) are all accurate, and the results calculated with the old calendar have great errors. Since Daming Calendar has been proved to be better, it should be adopted.
As a result, Defarge was speechless. Zu Chongzhi won the final victory. In the ninth year of Daming (465), Emperor Xiaowu of the Song Dynasty decided to switch to a new calendar. Who knows that Emperor Xiaowu died in the eighth year of Daming, and then the ruling clique had an accident, so the matter of changing the calendar was put on hold. It was not until the ninth year of Liang Chaotian's imprisonment (5 10) that the new calendar was officially adopted, but by then Zu Chongzhi had died for ten years.
Zu Chongzhi also wrote five volumes of composition, which is a wonderful mathematical work and highly praised by people. In the mathematics discipline of government-run schools in the Tang Dynasty, students were required to study "composition" for four years; When the government holds a math exam, it often comes up with composition questions. Later, this book spread to Korea and Japan. Unfortunately, in the middle of the Northern Song Dynasty, this precious book was lost.
Seal script is a masterpiece of Zu Chongzhi's and his son's mathematical research achievements. This book is so profound that "scholars can't study its profundity, so they ignore it." Seal script was included in Ten Arithmetic Classics in the Tang Dynasty, and became a textbook of imperial academy in the Tang Dynasty. It took four years to learn seal script at that time, which shows the difficulty of seal script. Seal script was once spread to Korea, but it was lost in the Northern Song Dynasty.
Zu Chongzhi's research on pi has positive practical significance and adapted to the needs of production practice at that time. He personally studied weights and measures and revised the ancient calculation of volume with the latest pi results.
In ancient times, there was a measuring instrument called "kettle", which was generally one foot deep and cylindrical. What is the volume of this measuring device? To find this value, you need to use pi. Zu Chongzhi worked out the exact value with his research. He also pointed out that Zu Chongzhi's achievements in the field of mathematics were only one aspect of China's achievements in ancient mathematics.
In fact, before14th century, China was one of the countries with the most advanced mathematics in the world. For example, Pythagorean theorem in geometry was discussed in China's early mathematical monograph "The Book of Changes" (written in the 2nd century BC). Another important mathematical monograph, Nine Chapters of Arithmetic, was written in 1 century, and put forward the concept of negative number and the law of addition and subtraction of positive and negative numbers for the first time in the history of mathematics in the world. In the 3rd century/kloc-,China had the solution of the decagonal equation, but it was not until the 6th century/kloc-that Europe put forward the solution of the cubic equation.
Zu Chongzhi was a great mathematician and astronomer in ancient China. Among the astronomical calendars, his Da Ming Calendar was the most accurate one at that time. In mathematics, he calculated pi accurately to six decimal places and achieved the best results in the world at that time.
Zu Chongzhi is admired not only by the people of China, but also by the scientific community all over the world. 1960, after studying the photos on the back of the moon, Soviet scientists named the valley above it with the names of some of the most contributing scientists in the world, and one of them was named "Zu Chongzhi Crater".
1964165438+1October 9th In order to commemorate Zu Chongzhi's great contribution to China and the world's science and culture, the Purple Mountain Observatory named the asteroid with the international permanent number 1888 discovered in1964 as "Zu Chongzhi Star".