# Eratosthenes & Ptolemy

## Eratosthenes ≈ 200 BC, the size of the earth

Eratosthenes was librarian at the Royal Library of Alexandria. He read in a book that every summer solstice at noon, the water deep down in a well in Syene was all illuminated by the sun. He realized that at that moment the sun appeared at the zenith, directly above the well. At the same time in Alexandria the sun cast shadows. Alexandria and Syene are at about the same meridian, Alexandria is north of Syene. Eratosthenes estimated the distance between Syene and Alexandria. Then he measured the shadow of an obelisk of known height in Alexandria, on the summer solstice at noon, and calculated the circumference of the earth.

### Exercise

Find the radius of the circle above. The triangle representing the shadow is not a right-angled triangle but you may assume it is. If the picture was to scale, the error from such an approximation would be less than any other error in the measurements. What other approximation must you also do?

## Ptolemy ≈ 150 AD, the universe

Aristotle (≈350 BC) described the universe as spheres with the earth as the centre; all objects in the sky were attached to the spheres and moved in circles around the earth. Some observations of the sky were correctly explained by that model but not all.

Ptolemy came up with a different model were the distant objects were attached to, not the spheres themselves, but circles lying on the spheres, so called epicycles. This model could account for the motions observed at the earth.

By keep attaching epicycles on epicycles on epicycles...any planetary motion can be explained, in fact any orbit can be constructed.

# further info:

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License