Guo Shoujing and His Shoushi Calendar

     Ancient Chinese had long led the world in making calendars. Legends said the Yellow Emperor, or ancestor of the Chinese nation, worked out the first calendar in ancient China. Shang Shu, or Documents of Ancient Times, a book said to be compiled by Confucius, says that in the times of Emperor Yao a year was divided into 366 days and an additional month was established to decide the four seasons. In the Spring and Autumn Period Chinese astronomers were the first in the world

The number of days was the same as that of the Julian calendar, but the Roman counterpart came 500 years later than the Chinese one. In 104 BC, Emperor Wudi of the Han Dynasty promulgated the Taichu calendar, which set the tropical I year at 365 385/1539 days and the lunar month at 29 43/81 days, and established for the first time the Twenty-four Solar Terms in the calendar. For more than 1,000 years after the Taichu calendar, 70-odd other calendars were formulated in ancient China. The well- known ones among them include the Linde calendar compiled by Li Chunfeng in the Tang Dynasty and the Dayan Calandar by the Monk Yixing, but most of them were in use not for long. The only exception was the Shoushi calendar worked out by Guo Shoujing (1231-1316) in the Yuan Dynasty, which was used for more than 360 years. This calendar thus became the best representative of ancient Chinese calendars.

    In 1276 Kublai Khan, the first emperor of the Yuan Dynasty, assigned the task of compiling a new calendar to astronomer Guo Shoujing, so that his new empire would have a unified calendar from north to south and the errors in previous calendars could be corrected. Guo was a scientist with exceptional talent and dedication. On taking over the task, Guo said, "A good calendar must be based on observations, and observations depends on good devices." He went to examine the hun yi (armillary sphere), the only instrument at the observatory of the capital Dadu (now Beijing), and found that the North Star of it was set at 35 degrees, which was the latitude of Kaifeng, where the hun yi was made. This meant that the instrument had not been adjusted when it was transported to Dadu from Kaifeng. And for all those years of wars, the instrument had fallen into disrepair and could no longer be used. Guo thus made it a priority to develop new devices. With three years of strenuous efforts, he worked out 12 astronomical devices, which were far better in functions and accuracy than previous ones. He also made a number of portable instruments to be used in field studies outside Dadu.

    As part of the calendar project, Guo presided over a nationwide program of astronomical observations. He selected 27 sites for astronomical observation throughout the country, which covered a wide area from latitude 15¡ã North to latitude 65¡ãNorth and from longitude 128¡ãEast to longitude 102¡ã East. Items of observation included the length of shadow of the gnomon, the angle of the North Star from the ground surface, and the beginning times of day and night on the vernal equinox and the autumnal equinox. All the records of the angle of the North Star from the ground had an average error of only 0.35. Guo also examined nearly 900 years of astronomical records from 462 to 1278 - and selected six figures from the records for calculating the duration of the tropical year. Guo's result was 365.2425 days, which was the same as that of the Gregorian calendar, the calendar now widely used in the world, but came three centuries earlier. Pierre Simon de Laplace (1749-1827), a noted French astronomer, acknowledged that in the mid-13th century Guo made the most accurate surveys of the length of shadow of the gnomon.

     Guo Shoujing and other astronomers worked for four years and completed the calendar in 1280. They made numerous calculations converting the data of the ecliptic coordinate and the equatorial coordinate systems, and used twice interpolations to solve the variations in the speed of the sun's movement, which affected the accuracy of the calendar. The calendar was unprecedented in accuracy. It adopted the winter solstice of the year 1280, the ninth year of the Yuan Dynasty, as the epoch, the point of reference for the calendar, and established the duration of a tropical year at 365.2425 days, and that of a lunar month at 29.530593 days. The error between the duration of its tropical year and that of the revolution of the earth around the sun was only 26 seconds. The calendar was named Shoushi, meaning measuring time for the public.

     The Shoushi calendar was soon spread to Japan and Korea, and adopted in the two countries. In recent years astronomers in the United States, Japan and other countries had a renewed interest in this calendar, and they organized translation of this work and in-depth study of it. This calendar has established its place in the history of world astronomy. To honor Guo, a crater on the Moon is named Guo Shoujing Crater, and a planetoid discovered in 1964 named Guo Shoujing Planetoid.