Greek astronomer and scholar, born in Cyrene. He became chief librarian at Alexandria, and is remembered for the first scientific calculation of the Earth's circumference, which was correct to within 80 km/50 mi.
Eratosthenes (Greek Ἐρατοσθένης) (276 BC - 194 BC) was a Hellenistic mathematician, geographer and astronomer. He is noted for devising a system of latitude and longitude, and for being the first known to have calculated the circumference of the Earth.
Life
Eratosthenes was born in Cyrene (in modern-day Libya), but worked and died in Alexandria capital of Ptolemaic Egypt. Eratosthenes studied at Alexandria and for some years in Athens.
He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies with having calculated the Earth's circumference around 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt).
Measurement of the Earth
Eratosthenes knew that on the summer solstice at local noon in the town of Syene on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7.2° south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 7.2/360 of the total circumference of the Earth. The distance between the cities was known from caravan travellings to be about 5000 stadia: approximately 800 km. The exact size of the stadion he used is no longer known (the common Attic stadion was about 185 m), but it is generally believed that the circumference calculated by Eratosthenes corresponds to 39,690 km . The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is not precisely on the Tropic of Cancer, is not directly south of Alexandria, and the Sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, angles could only be measured to within about a quarter of a degree, and overland distance measurements were even less reliable. So the accuracy of the result of Eratosthenes' calculation is surprising: the circumference of the Earth around the poles is now measured at 40,008 km.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards.
Other work
Eratosthenes' other contributions include:
The Sieve of Eratosthenes as a way of finding prime numbers. Possibly, the measurement of the Sun-Earth distance, now called the astronomical unit and of the distance to the Moon (see below).The fragmentary collection of Hellenistic sky-myths called Catasterismi (Katasterismoi) was attributed to Eratosthenes;
The mysterious astronomical distances
Eusebius of Caesarea in his Praeparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of stadia myriads 400 and 80000") and the distance to the moon to be 780,000 stadia. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. It is true that the distance Eusebius quotes for the moon is much too low (about 144,000 km) and Eratosthenes should have been able to do much better than this since he knew the size of the earth and Aristarchos of Samos had already found the ratio of the moon's distance to the size of the earth. But if what Eusebius wrote was pure fiction, then it is difficult to explain the fact that, using the Greek stadium of 185 metres, the figure of 804 million stadia that he quotes for the distance to the sun comes to 149 million kilometres.
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