Thanks to the enormous advances in technology in the last years, we have been able to send satellites to orbit, and measure in a precise way the circumference of the Earth. However, thousands of years ago, this option wasn’t possible, and the form the Earth had wasn’t even known. It is to Eratosthenes that we attribute the first measure of the circumference of the Earth.
The measurement of a shadow
Studying the papyrus from Alexandria’s library, Eratosthenes read that in the midday of summer’s solstice (the current 21 of June) the Sun’s rays at the city of Syene arrive vertically to the ground, so they don’t produce any shadow on the objects.
Then, Eratosthenes waited for the next summer solstice to arrive, to prove if the same effect took place in his city, Alexandria. However, he observed that the same didn’t happen. On the contrary, he calculated that the objects provoked a shadow of 7.2 degrees. Knowing this, he reasoned that if the Sun’s rays were parallel the ones with the others, and that, at the same time of the day, an object in Alexandria made a shadow and an object in Syene not, this meant that the Earth has a curved surface, and, consequently, it is a sphere (this is illustrated in the following image).
From here, and keeping in mind that the two cities are found in the same meridian (there is only a 3% difference between the longitude of the one and the other), we only needed to know the distance between the two cities. With this data, he would be able to calculate the circumference of the Earth.
Calculating the circumference of the Earth
Eratosthenes sent some of his assistants and some camel drivers that he hired, to measure the distance (in the straightest way possible) between the two cities. This way, he discovered that the distance between the two cities in a straight line was 5 000 stadia (a unit of measurement used in that epoch).
Knowing this, he found himself in the conditions of calculating the circumference of the Earth: as the difference between the shadows of Alexandria and Syene is 7.2 degrees, this means that the two cities are separated by 7.2 degrees of the 360 degrees of the whole circumference. 7.2 degrees is the fiftieth part of the 360 degrees, and if a fiftieth of the terrestrial circumference corresponds to 5 000 stadia, the total circumference of the Earth will be 50 × 5 000 = 250 000 stadia.
It has always been supposed that Eratosthenes used the measure of the Egyptian stadium (in each state the measures were different), which corresponds to 156.9 metres, to calculate the circumference of the Earth. This gives a circumference of 39 225 kilometres. Keeping in mind that the real circumference is 40 008 kilometres, we can affirm that Eratosthenes (with the scarce resources of the epoch) obtained a result with excellent accuracy: less than a 2% error.