When the earthâ€™s circumference was calculated by ancient Greek it was calculated very accurately. That time the calculations and assumptions were based on Aristotleâ€™s idea that the earth was round which was later found out to oblate spheroid i.e. Earth bulges at the equator. Eratosthenes calculated with -2.4% to +0.8%.
Eratosthenes calculations of earthâ€™s circumference
Eratosthenes was born around 276 B.C., in present day Libya. He studied in Athen. Eratosthenes has done many famous works, the one which stands out is the calculation of the circumference of the earth. The data which he recorded is now not available exactly, but his method has been written down by many other writers.
Eratosthenes had heard about this well in Syene (now, Egypt) has a property that â€œOn summer solstice which occurs about 21 June every year, the sun illuminates the whole well, without any shadow, showing that the sun is directly above the well. After hearing about that Eratosthenes who was at that time in Alexandria, took a stick and casted its shadow on the ground and then measured the angle between the stick and the shadow which was found to be around 7.2 degrees.
He then realized that to calculate the size of the earth he first had to know the distance between Alexandria and Syene. At that time measuring such a large distance was not an easy task. One way was to wait for a caravan to travel that distance and then calculate, but caravan uses camels and animals, but he knew he can’t trust animals for this distance. So, he contacted professional surveyors who got the result.
An arc is a continuous piece of a circle. Eratosthenes assumed thatÂ SyeneÂ and Alexandria formed an arc on earth and the angle so calculated 7.2Â° and thus calculated the circumference of the earth.
Eratosthenes after calculating the angle and the arc length calculated the circumference of the earth which was about 250,000 stadia. The exact value of stadia is not known, some scientists assume it to be 500 feet some 600 feet,Â it is assumed that the value is somewhere between these two values. The result calculated by Eratosthenes calculated the circumference of the earth about 24,000 miles to 29,000 miles. Currently it is found to be around 24,900miles.
Eratosthenes had made some assumptions which were that the sun is very far away so the rays that came to earth are parallel secondlyÂ SyeneÂ is onÂ theÂ tropic of cancer which later was found to be false. And thirdly thatÂ SyeneÂ and Alexandria are on the same meridian,Â which was also found to be not true. But these assumptions were quite accurate in measurement of the earthâ€™s circumference. His basic method was very sound.
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