The secrets of our planet and the cosmos have always been dancing between the curiosity and doubt of humans who, from their first moments, have tried to clear up the origin of the cosmos at any cost. Currently we have high technology that allows us to know important data about our Earth and even beyond the distant horizons of the Solar System. However, 2 thousand years ago, the tools were limited but this did not stop Eratosthenes, he managed to calculate the circumference of the Earth with great precision, however, the question is how did he achieve it?
However, thousands of years ago these calculations were very complex to perform. This is why it is very surprising that Eratosthenes in Ancient Greece, just over two thousand years ago, managed to calculate the circumference of the Earth with only 6% error. The key was in the first instance curiosity and also the scientific method, that is, the logic of reasoning to arrive at the data.
Eratosthenes directed the Library of Alexandria and here his curiosity arose after reading a piece of information that he called his. The data mentioned the city of Siena, located in the south of Egypt. According to the book that came into the hands of Eratosthenes, in Siena the shadows disappeared at noon on the summer equinox. That is, if a stick is placed completely vertically, it would not cast a shadow just after noon on the indicated date.
Carl’s story explains very clearly the Greek scientist’s reasoning to reach a solution.
“Eratosthenes then wondered why it was that at the same instant a staff cast no shadow in Syena while in Alexandria, a great distance to the north, it cast a pronounced shadow.”
The Greek’s curiosity manifested itself in extremely surprising actions, leading him to hire an assistant to measure the distance between Alexandria and Syena. Of course, back then there were no measurement methods as exact as those now. Despite this, since the assistant calculated the distance in , the measurement showed that the distance was 800 kilometers.
Eratosthenes added one more piece of information to his equation, but the logical reasoning that would lead him to solve the problem was still missing. Sagan himself explained that:
“Eratosthenes understood that the only possible answer is that the Earth’s surface is curved. And not only this: the greater the curvature, the greater the difference between the lengths of the shadows. The Sun is so far away that its rays are parallel when they reach the Earth. Sticks placed at different angles to the Sun’s rays cast shadows of different lengths.
Once the Greek scientist developed this logic, he imagined a way to hypothetically relate the suits in both cities. To do this, he imagined that if the sticks were extended towards the center of the Earth, there would come a moment when they would touch each other, right at the center of the planet. The angle formed by both sticks would be about 7°. This last piece of information was enough to establish a trigonometric problem with a rule of three, with enough parts to solve it.
“Seven degrees is approximately one-fiftieth of the 360 degrees contained in the entire circumference of the Earth. Eratosthenes knew that the distance between Alexandria and Syena was about 800 kilometers, because he hired a man to measure it in steps. Eight hundred kilometers times 50 gives 40,000 kilometers: this must therefore be the circumference of the Earth.
2 thousand years after his great feat, scientists were able to verify that the curious Eratosthenes was right. Thanks to advanced technology we now know exactly that the circumference of the Earth measures 40,091 kilometers.