Lesson 2.19 - Eratosthenes and the Circumference of the Earth
Watch the video below to learn about Eratosthenes and the circumference of the earth.
Eratosthenes wanted to estimate the circumference of the earth. At the time Eratosthenes was in the city of Alexandria in Egypt. He read that in a city named Syene south of Alexandria, on a particular day of the year at noon, the sun’s reflection was visible at the bottom of a deep well. This meant the sun had to be directly overhead. (Another way to think about this is that perfectly vertical objects would cast no shadow.) On that same day in Alexandria a vertical object did cast a shadow. Using geometry, he calculated the circumference of Earth based on a few things that he knew (and one he didn’t):
- He knew there are 360 degrees in a circle.
- He could measure the angle of the shadow cast by a tall object in Alexandria.
- He knew the overland distance between Alexandria and Syene. (The two cities were close enough that the distance could be measured on foot.)
- The only unknown in the equation is the circumference of Earth!
To solve we cross multiply and solve for x. 7.2x = 360(800) 7.2x = 288000 x = 40000 This estimate of 40,000 km is close to the actual circumference of 40,075km!
You Try!
Martin the Martian lives on Planet Mart. Martin wants to know the circumference of Planet Mart, but it is too large to measure directly. He uses the same method as Eratosthenes by measuring the angle of the sun’s rays in two locations. The sun shines on a flagpole in Martinsburg, but there is no shadow. At the same time, the sun shines on a flagpole in Martville, and a shadow forms a 10° angle with the pole. The distance from Martville to Martinsburg is 294 miles. What is the circumference of Planet Mart?
Use Erastosthenes' formula to solve for the circumference.