# Math Help - Eratosthenes: size of the Earth

1. ## Eratosthenes: size of the Earth

Eratosthenes made a remarkably precise measurement of the size of the earth. He knew that at the summer solstice the sun shone directly into a well at Syene at noon. He found that at the same time, in Alexandria, Egypt, approximately 787 km due north of Syene (now Aswan), the angle of inclination of the sun's rays was about 7.2 degrees. With these measurement, how did he compute the diameter and circumference of the earth?

2. Taking the view that the sun's rays when meeting the earth are parallel, the angle subtended at the centre of the earth by radii from the two locations will be 7.2 degrees.
So, if $r$ is the 'radius' of the earth,
$r\theta=787$ where $\theta=7.2\frac{\pi}{180}$ radians.
Solving for $r$ leads to a value of approximately 6263km.

3. Originally Posted by matgrl
Eratosthenes made a remarkably precise measurement of the size of the earth. He knew that at the summer solstice the sun shone directly into a well at Syene at noon. He found that at the same time, in Alexandria, Egypt, approximately 787 km due north of Syene (now Aswan), the angle of inclination of the sun's rays was about 7.2 degrees. With these measurement, how did he compute the diameter and circumference of the earth?