A man planted two sticks of length 1 meter at Place A and Place B which are 800 Km apart from each other. At 12:00 noon, at Place A, the length of shadow is 12.6 cm and at Place B, there is zero shadow. Find the circumference of the Earth.
Answers
Answer:
What is Earth’s circumference? In the age of modern technology this may seem like an easy question for scientists to answer with tools such as satellites and GPS—and it would be even easier for you to look up the answer online. It might seem like it would be impossible for you to measure the circumference of our planet using only a meterstick. The Greek mathematician Eratosthenes, however, was able to estimate Earth’s circumference more than 2,000 years ago, without the aid of any modern technology. How? He used a little knowledge about geometry!
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!
The resulting equation was:
Angle of shadow in Alexandria / 360 degrees = Distance between Alexandria and Syene / Circumference of Earth
In this project you will do this calculation yourself by measuring the angle formed by a meterstick’s shadow at your location. You will need to do the test near the fall or spring equinoxes, when the sun is directly overhead at Earth's equator. Then you can look up the distance between your city and the equator and use the same equation Eratosthenes used to calculate Earth’s circumference. How close do you think your result will be to the “real” value?