Everything about Eratosthenes totally explained
Eratosthenes of Cyrene (
Greek Ἐρατοσθένης; 276 BCE - 194 BCE) was a
Greek mathematician,
poet,
athlete,
geographer and
astronomer. His contemporaries nicknamed him
"beta" (Greek for "number two") because he supposedly proved himself to be the second in the ancient
Mediterranean region in many fields. He is noted for devising a system of
latitude and
longitude, and for being the first known person to have calculated the
circumference of the Earth. He also created a
map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
Life
Eratosthenes was born in
Cyrene (in modern-day
Libya). He was the chief librarian of the
Great Library of Alexandria and died in the capital of
Ptolemaic Egypt. He never married.
Eratosthenes studied in Alexandria and claimed to have also studied for some years in
Athens. In 236 BC he was appointed by
Ptolemy III Euergetes I as librarian of the
Alexandrian library, succeeding the first librarian,
Apollonius of Rhodes, in that post
(External Link
). He made several important contributions to
mathematics and
science, and was a good friend to
Archimedes. Around 255 BC he invented the
armillary sphere, which was widely used until the invention of the
orrery in the
18th century.
In 194 BC Eratosthenes became blind and, supposedly, a year later he starved himself to death.
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 knowledge of the angle of
elevation of the
Sun at noon on the summer solstice in Alexandria and in the
Elephantine Island near
Syene (now
Aswan, Egypt).
Eratosthenes' measurement of the Earth's circumference
Eratosthenes knew that on the
summer solstice at local noon in the Ancient Egyptian city of
Swenet (known in Greek as 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 1/50 of a full circle (7°12') 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 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000
stadia (about 500 geographical or nautical miles). He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, for example 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.
Although Eratosthenes' method was well founded, the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene isn't precisely on the Tropic of Cancer, isn't 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, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. So the accuracy of Eratosthenes' size of the earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. His method was used by
Posidonius about 150 years later.
The mysterious astronomical distances
Eusebius of Caesarea in his
Preparatio 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 80,000") 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. H. Gifford), or as 804,000,000 stadia (edition of
Edouard des Places, dated 1974-1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad.
This testimony of Eusebius is dismissed by the scholarly
Dictionary of Scientific Biography. 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
Aristarchus 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's difficult to explain the fact that, using the Greek, or Olympic, stadium of 185 metres, the figure of 804 million stadia that he quotes for the distance to the Sun comes to 149 million kilometres. The difference between this and the modern accepted value is less than 1%.
Works
Named after Eratosthenes
Sieve of Eratosthenes
Eratosthenes crater on the Moon
Eratosthenian period in the lunar geologic timescale
Eratosthenes Seamount in the eastern Mediterranean Sea
Jules Eratosthenes Brown (fictional character from the Back to the Future franchise)Further Information
Get more info on 'Eratosthenes'.
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