There Earth has a well -known form to date, that of a geoidthat is, a solid similar to one Bitterzoluta sphere. When we try to represent it in a mappamondo, however, we should draw it as an ellipissoid, that is, a huge three -dimensional oval with an equatorial circumference of 40,075 km and polar circumference of 39,942 km. These dimensions nowadays are easy to establish even extremely precisely thanks to the satellites. But what not everyone knows is that already in 240 BC the mathematician, philosopher and astronomer Eratostene di Cirene managed to demonstrate that the earth is spherical to measure its circumference with an witty experiment using only a stick (called “Gnomone”), oneshadow And the knowledge of geometry! Its measurements, already then they had a mistake of only a few hundred kilometers. But how is it possible?
Let’s see in this article as the experiment that made his business possible, as simple as it is brilliant possible.
Who is Eratostene: the man who studied the size of the earth
Eratostene di Cireneborn around 276 BC in the current Libya, was a mathematical, poet, historical, philosopher, astronomer And geographerconsidered among the most brilliant scholars of his time. It was a librarian of the Library of Alexandria of Egyptthe largest center of ancient knowledge, where he had access to knowledge from all over the world and collaborated with Archimedes. The need to know precisely the measure of the terrestrial meridian probably was born from the need for make geographical maps and above all nautical of the world then known, to facilitate trade and navigation. The results of this extremely accurate study on the measurement of terrestrial dimensions were collected in the work “On the measure of the earth”, Unfortunately I go leak. The story that has come down to us is the Simplified and popular version reported by CleansGreek astronomer and mathematician.
How the measurement with the stick and its shadow took place: the Etatostene experiment
In the writings that have reached us, Cleomedes tells that, to structure his experiment, Eratostene started from three hires:
- First of all, at the time it was known that the Earth era spherical – Not an ellipsoid as we know today, for that was to arrive Isaac Newton – because Aristotle had already shown it in the 4th century BC;
- Then, he knew that a Tienetoday’s Egyptian city Assuan, the sun manages to illuminate the bottom of very deep wells around Mezzogiorno of the summer solstice. At that moment, in fact, the Sun It is exactly at the Zenitthat is, it is perfectly vertical. Consequently, a stick planted vertically On a flat ground – such as those of the sundials, the gnomons – He would not have projected any shadow;
- Finally, according to his knowledge, Alexandria of Egypt It was on the same meridian Of Tiene to 5000 stadiums – the unit of measurement of the time, equal to 157.5 m – distance. Assume that they were on the same meridian guaranteed that the South in the two cities was simultaneously and there were no “time zone” problems.
The results of the experiment: the length of the earth’s circumference is about 40 000 km
Etatostene began by measuring how long theshadow of stick of a meridiana in Alexandria of Egypt exactly a Mezzogiorno of the summer solstice. Using this measurement and the properties of rectangles triangles, he obtained that thecalendar angle to Alexandria was of 7 degrees and 12 first. Since the sun is so far as to be able to consider its parallel rays, also thecorner between the center of the earth, Alessandria and Siene – the one indicated in yellow, α, in the figure above – size 7 degrees and 12 first. At this point, Etatostene realized that she could use this measure to estimate the length of the circumference. As 7 degrees and 12 first correspond exactly to 1/50 of a turn angle (360 °), also the distance between Siene and Alessandria he had to correspond to 1/50 of the earth’s circumference. Etatostene therefore multiplied the distance Between Tiene And Alexandria, equal to 5000 stadiums, for 50, obtaining the length of the terrestrial circumference of 250,000 stadiumsabout 39.375 km. This measurement represents the most successful and famous among those made in antiquity.
Subsequent writings also report the result 252,000 stadiumsvalue probably chosen because much more comfortable to deal. 252,000, in fact, is divisible by all natural numbers from 1 to 10.
Errors in measurement: Eratostene’s inaccuracies
This method, incredibly simple and ingenious, does not reach the exact result because it contains some inaccuracies. First of all, as we know, the Earth it is not perfectly spherical, but looks more like a ellipsid. Then, the Distance between Siene and Alessandriaestimated at 5000 stadiums, had probably been calculated on the basis of travel days necessary to travel it rather than from an exact measurement, therefore resulting approximate. Also, today we know that the two cities they are not found on the same meridian And that, therefore, the South of the summer solstice does not happen simultaneously. In the end, Siene is located 72 km away from the tropic cancerso the moment of the Zenit is not exactly at noon, as it would be if it were in the tropic.
Despite this, the result obtained is surprisingly Neighbor to that real And it is incredible to see how it managed to get it with very simple tools and great intuitions.
To learn more we made an ad hoc video on the subject:
