Eratosthenes and the Circumference of the Earth

Portrait of Eratosthenes

Eratosthenes was an astronomer, historian, geographer, philosopher, poet, theatre critic and mathematician, who lived in the 3^rd century BC in the greatest metropolis of the age, the Egyptian city of Alexandria. His envious contemporaries called him ‘Beta’, the second letter of the Greek alphabet, because they said, Eratosthenes was second best in the world in everything.

However, it was quite an underevaluation of the greatness of the man.

He was the first person to use the word “geography” and invented the discipline of geography as we understand it. He also invented a system of latitude and longitude.

He was the first person to calculate the circumference of the earth with remarkable accuracy. He was also the first to calculate the tilt of the Earth’s axis (also with remarkable accuracy).

The story of the calculation of Earth’s circumference is very interesting. Eratosthenes was also the director of the great library of Alexandria. There, one day he read in a book that in the southern frontier outpost of the ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on June 21 at noon, the Sun would appear at the zeith, which means directly overhead. Thus on this day at this time at this location, a vertical stick would cast no shadow. On the summer solstice, June 21 (the longest day of the year), as the hours crept towards noon, the shadows of the temple columns drew shorter and shorter. At noon precisely, the reflection of the Sun could be seen in the water at the bottom of a deep well.

This was a fairly simply observation that someone else might easily have ignored. What significance could sticks, shadows, reflections and wells  have on the simple everyday matters? But Eratosthenes was a scientist and his musings on these commonplaces changed the world; in a way they made the world.

Eratosthenes had the presence of mind to do an experiment, actually to observe whether vertical sticks cast any shadows at noon on June 21 in Alexandria as well. And his discovery was that they do.

Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow while a stick in Alexandria, could cast a pronounced shadow.  In case, at both places had there been no shadows, or had the shadows been of equal lengths, it would have been easy to explain considering the earth to be a flat surface and the Sun’s rays to be inclined in both cases at equal angles. This would have been easily explainable. But this was clearly not the right explanation under the present observation.

Hence, the only possible answer that he saw was that the surface of the Earth was curved. Not only that, the greater the curvature, the greater would be the difference in the shadow lengths.  Since the Sun was so far away, its rays falling on any two locations on the Earth can be considered parallel for all practical purposes. Thence, according to the difference in shadow lengths between the two observations, Eratosthenes was able to calculate that the angular separation of Alexandria and Syene to be of 7 degrees along the surface of the Earth and this 7 degrees was approximately 1/50th of 360 degrees, which was the total angular circumference of the Earth. Knowing the distance between the two cities was approximately 800 Kms, because he hired a man to pace it out, Eratosthenes was able to calculate that 800 Kms times 50 is 40,000 Kms and so that must be the circumference of the Earth.

It was a brilliant deduction, especially in an age where the only tools he had available for this scientific experiment were a few sticks, eyes, feet and brains. Most importantly, he had a taste for experimentation, a thirst for knowledge and a curiosity to understand the basic tenets of nature, which were all ahead of his own age.

The story of Eratosthenes and how one man changed our understanding of our world is an awe inspiring example of the power of scientific inquiry and inquisitiveness. He drew his conclusions objectively from the observed facts of the world and not according from his personal wishes and preferences.

Further Reading:

“Cosmos” by Carl Sagan (book)

http://www.pbs.org/wnet/hawking/cosmostar/html/cstars_eratho.html (online reading)