HOW TO MEASURE THE EARTH WITH A STICK
Have you ever heard of the Greek mathematician and astronomer Eratosthenes? His name is probably best known among astronomers. Why do they think so highly of him?
Eratosthenes was born about 276 B.C.E. and received some of his education in Athens, Greece. He spent a good part of his life, however, in Alexandria, Egypt, which at that time was under Greek rule. In about 200 B.C.E., Eratosthenes set out to determine the dimensions of the earth by using a simple stick. ‘Impossible!’ you may say. How did he do it?
In the city of Syene [now called Aswan], Eratosthenes observed that at noon on the first day of summer, the sun was directly overhead. He knew this because there was no shadow cast when the sunlight reached the bottom of deep wells. However, at noon on the same day in the city of Alexandria, which was located 5,000 stadia to the north of Syene, a shadow could be observed. That gave Eratosthenes an idea.
Eratosthenes set up a gnomon, a simple upright stick. When the sun was overhead at noon, he measured the angle of the shadow that the stick cast in Alexandria. HE determined the angle to be 7.2 degrees from vertical.
Now, Eratosthenes believed the earth to be spherical, and he knew that there are 360 degrees in a circle. So he divided 360 by the angle he had measured, 7.2. The result? His angle was one fiftieth of a circle. He then deduced that the distance from Syene to Alexandra, or 5,000 stadia, must be equal to one fiftieth of the circumference of the earth. By multiplying 50 by 5,000. Eratosthenes came up with the figure of 250,000 stadia as the circumference of the earth.
How close did this figure come to present-day calculations? The figure of 250,000 stadia is equal to between 40,000 and 46,000 kilometers in current measurements. Using orbiting spacecraft, astronomers measured the earth’s polar circumference and submitted the figure of 40,008 kilometers. Thus, over 2,000 years ago, Eratosthenes came astoundingly close to the modern-day figure. His accuracy is all the more remarkable when you consider that the man used only a stick and geometric reasoning! Astronomers today use this geometric method as a basis for measuring distances outside our solar system.