Over 2,000 years ago a Greek scientist, Eratosthenes measured the circumference of the earth. His method involved: 1) measuring the angle between the Sun’s rays and the zenith and 2) using parallel lines to find the circumference of a circle.
In the city of Aswan, Egypt, Eratostheses observed that at noon on the longest day the Sun was directly overhead. It reflected off the bottom of a deep well. At exactly the same time in Alexandria, the Sun was not directly overhead and caused a tall pillar to cast a shadow. By measuring the pillar and shadow, Eratosthenes found the angle between the Sun and the zenith to be 7.2 degrees. Pacers had found the distance from Alexandria to Aswan to be 474 miles. Knowing that light rays from the Sun striking the Earth seem to be parallel, Eratosthenes was able to calculate the size of the Earth.
Examine the diagram below. Using Eratosthenes method, the circumference of the Earth is calculated using a proportion.
360 degrees X 474 miles = 23,700 miles
1 7.2 degrees (circumference of the Earth)
Figure available in printed form
If the earth circumference is 23,700 miles, what is the diameter? (Hint: Circumference equal 3.14 X Diameter); Answer is 7,569 miles. Eratosthenes’ method is still used today by surveyors who measure the Earth. They have discovered that you must travel about 66 miles on the earth to make an angle of one degree at the center of Earth. To find the diameter of the Earth from these measurements, first the circumference must be calculated.
360 degrees X 66 miles = 23,760 miles
1 1 degree (circumference of the Earth)
23,760 / 3.14 = 7,569 miles (diameter of the earth)