Size of the Earth
The first step toward determining the size of the cosmos is to find the diameter of the Earth. This crucial step was taken by an ancient Greek astronomer named Eratosthenes in approximately 330 BCE.* Eratosthenes was the chief librarian of the great library at Alexandria and had access to approximately half a million scrolls. In one of these scrolls, Eratosthenes learned that 500 miles** to the south in the city of Syene, currently Aswan, at noon on June 22, sunlight would penetrate to the bottom of a deep well and reflect back upward; so the Sun must be directly overhead. At the great city of Alexandria, Eratosthenes measured the shadow angle of a tall obelisk on June 22 at noon to be 7.5o from the vertical (see fig). Using only this information and the distance to Syene he was able to calculate the circumference of the Earth. He started by reasoning that the Sun is so far away that rays striking the Earth are essentially parallel.
Now set up a ratio of θ to the number of degrees in a complete circle to a ratio of distances.
So what must the circumference of the Earth be?
Circumference of Earth = ______
Find the Earth’s diameter too. (Circumference = πD)
Diameter of Earth = ______
Pretty neat, don’t you think?
______
* Rogers, Eric M. Physics for the Inquiring Mind
Princeton University Press, 1960. pp 233-234.
** Of course Eratosthenes didn’t use a distance unit of miles: he used the unit of stadia. He said the distance between Alexandria and Syene was 5,000 stadia. Unfortunately, we don’t know today exactly how long a stadium was in ancient times. If Eratosthenes used an Olympic stadium as his standard, then he would have got the circumference of the Earth to within 20% of its modern value. If he used 1 stadium = 1/10 mile then he would have gotten the circumference within 1%!