This article takes us more than 2000 years back in the past, in Greece.

Ancient Greece was a unique place, because science was one of the most important segments of their everyday life. Greek scientists were very successful, many of their discoveries were groundbreaking and humanity needed centuries to embrace and understand their ideas. Working without any equipment or tools, mostly self-educated ancient scientist are not getting today as much recognition as they deserve.

One of the forgotten and one of the greatest is Eratosthenes of Cyrene. He was born in 276 BC and he had unusually long life for that period. Although, exact year of his death is not known, some people estimate that he was more than 80 when he passed.

He entered the history as a successful astronomer, but he was also geographer, mathematician and even music theorist.

But, what has he done so important to stand out from others, and to earn a place among immortals?

Before him,  Aristarchus of Samos, another amazing  person, using extremely simple experiments and basic math, proved that Earth revolves around the Sun, and calculated radius of the Sun, the Moon, and distances between Earth and celestial bodies. 

His results were

• The Moon is 22 times smaller than Earth
• Distance between the Moon and Earth is  equal to 81 Earth's radii
• The Sun is 312 times bigger than Earth
• Distance between the Sun and Earth is equal to 150 Earth's radii

We can say that these results were pretty accurate if you take into account all difficulties he had at that time. If you are not familiar with Aristarchus or his works, you can take a look at this article: https://steemit.com/science/@laniakea1/great-people-you-have-never-heard-of-2-aristarchus-of-samos

If you notice, previous results are expressed in units of Earth's radius, so they still did not have proper image of real dimensions and distances. Earth's radius could be 1000 km, or 10000000 km...

Eratosthenes was dedicated to solve this problem, and he managed to find, almost perfectly exact, value of Earth's radius and circumference, and then using Aristarchus' results to measure accurately how big the Universe is. Things are getting even more interesting if I say that he was using only one deep water well and one wooden stick. 

The Experiment

The image above is of vital importance for understanding the basic concept  of this experiment. Don't get scared, it's really simple.

So, let's go to southern Egypt, city of Aswan, where the experiment started. In this city very deep well was located, which was famous across Egypt because you could see the reflection of the Sun in the well only once a year. Ancient Egyptians were not aware of the fact that city of Aswan lies exactly on 23.5 degrees north, which corresponds with north returnee. This means, that the Sun  will be in it's zenith (the highest point in the sky, or let's say, exactly above our heads) only once a year, during the longest day, summer solstice, or first day of the summer. On the opposite side of the planet, on a south returnee, the Sun will be in zenith during the shortest day of the year, first day of the winter. For any other place northern than north returnee, or southern than south returnee, the Sun will never reach zenith. This was really important fact for the destiny of the experiment. Although Eratosthenes was not aware of mechanics of the Sun's movement  he has used proper logic patterns to get correct solution. Let's go back to the well, the well was very deep, and that's why you could see the Sun's reflection in the well only when the Sun was in zenith.

In the image above, Aswan is denoted with S. North from Aswan is city of Alexandria. As I mentioned before, because Alexandria is north from Aswan, the Sun will never reach zenith for a observer in Alexandria. Alexandria is denoted with A.

The difference between zenith, and maximum height the Sun can reach in Alexandria is denoted with Z in the image above. Because Aristarchus proved that the Sun is much bigger than Earth, and that the distance between Earth and the Sun is huge, Eratosthenes assumed that lines SG and AF (lines that connect Aswan and Alexandria, respectively, to the center of the Sun) are almost parallel, because the angle between those two lines is insignificantly small. This approximation is good to use, because our final result will not differ to much from the reality. This assumption also means that angle α is equal to the angle Z. Angle α is actually the angle between lines that connects Aswan and Alexandria to the center of Earth, in other words these lines represent Earth's radii.

If he could measure the angle Z, and the distance between Aswan and Alexandria, he could find the exact value of Earth's circumference, becaues Earth's circumference would be the same number of times bigger than the distance Aswan-Alexandria, as full angle of 360 degrees than the angle Z. The distance between two cities was well known and properly measured, and it was 5000 stadion (stadion is ancient unit of length). 

And now, there is the wooden stick to the rescue. Ancient scientist have had constructed an instrument called gnomon. It is literally wooden stick, with circles around it. According to the shadow of the stick you could measure difference between zenith and current position of the Sun. It's really simple and it was of huge benefit for Eratosthenes. Gnomon is shown in the image below.

During the longest day of the year, Eratosthenes measured zenith difference in Alexandria, and he got the result of 7.1 degrees, and that is something around 50 times smaller than the full angle of 360 degrees. That means that Earth's circumference is 50 times bigger that the distance Alexandria-Aswan. Expressed in kilometers, Eratosthenes' result for Earths circumference was 39 000 km, and reality is only 1000 km bigger.

Eratosthenes had known value of number π and how to calculate radius from circumference. Now, Aristarchus' results could be expressed in proper units, and for the first time in the history of humanity we were aware of actual dimensions of the world and the Universe.  

What amazes people is simplicity of Eratosthenes' method. He had never seen that well in Aswan, he didn't measure the distance between Aswan and Alexandria personally, he didn't construct gnomon, he had just read the values from it, on the longest day of the year. His magnificent work didn't require any physical effort, but only  ingenuity.