The Summer Solstice Occurs this Saturday, June 20th, at 22:44 pm, marking the beginning of this season in the northern hemisphere. The sun on this solstice day will be as high in the sky as possible and, upon its meridian passage, it will reach a maximum height of 75° in Lisbon.
The summer solstice is linked to the first experimental determination of the length of a terrestrial meridian, made around two thousand years ago by the Greek mathematician and geographer Eratosthenes of Cyrene (now the Libyan city of Shahhat).
Eratosthenes, who was born in Cyrene (c. 276 BC) and died in Alexandria (c. 194 BC) – “director” of the famous library of that city – was the first mathematician of antiquity to calculate the Earth's circumference (meridian length).
With his feet firmly on the ground, he calculated the Earth's circumference from an observation that intrigued him. He found that, at noon on June 21 (summer solstice), the sun's rays were perpendicular to the surface, fully illuminating the bottom of a well in Siena (now the Egyptian city of Aswan or Aswan).
But he found that the same was not observed, at the same time and day, in the city of Alexandria.
From this observation, and assuming that the Earth was spherical (which has been confirmed several times by astronauts from space), that the sun's rays that illuminated the two cities were parallel, Eratosthenes planned the following experiment: measuring the angle of the shadow formed by stakes of the same size, in those two cities, on the same June 21st, at noon.
In Siena, the shadow was nil. In Alexandria it recorded an angle of 7,2. He thus concluded that the length of an arc with 7,2 degrees was equal to the distance between those two places. He divided this value by 360, which is, as Eratosthenes knew, the inside angle of any circle, and got a value equal to 50.
Thus, he deduced that the length of the terrestrial meridian was equal to 50 times the distance from Siena to Alexandria. Based on the help he requested from the local king, he measured the distance between the two cities: 5 thousand stadia (Greek measure equal to 125 steps).
In this way, he arrived at the value of 250 stades for the length of the Earth's circumference. Now, depending on the value we attribute to a “Greek stadium” (from what I found there is no consensus on the subject), this is equivalent to a value between 39.700 kilometers and 46.600 kilometers.
Today we know that the value of a terrestrial meridian is approximately equal to 40.003 kilometers. The approximation achieved by Eratosthenes is amazing.
Note that he only used mathematical knowledge and acumen to do this. The same mathematical knowledge (some trigonometry and geometry) is, even today, sufficient to calculate the position of a vehicle, by GPS, and measure distances, despite the need for “some” technology that Eratosthenes would not have dreamed of…
Author Antonio Piedade
© 2020 – Science in the Regional Press / Ciência Viva
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