Friday, August 5, 2011

Top 10 Greatest Physics Experiments: 8. Measurement of the Earth's Circumference by Eratosthenes

Here we have another experiment, which enhanced our knowledge about Earth. However, this experiment is very unique, as it was carried out more than 2000 years ago. 

As the title says it, this experiment was set up to measure the circumference of Earth. Eratosthenes, a Greek mathematician and the librarian of the great library at Alexandria, in Egypt came up with a brilliant idea how to geometrically calculate the circumference of Earth using shadows in two different cities.

Eratosthenes knew that in Syene (a city almost due south of Alexandria) the sun was directly overhead at noon on a particular day of the year. This meant that at noon a yardstick wouldn’t cast a shadow. Also he knew that Sun is so far away that light rays coming from it would basically be parallel. Thus light rays at the same time in Alexandria should cast a shadow (see the diagram)

Now since Eratosthenes knew that the angle between the vertical and the shadow is equal to the central angle inside the circle (diagram). He also knew that there is 360 degrees in a circle. Thus all he needed to calculate Earth’s circumference was the distance between Alexandria and Syene.

To understand this more clearly let’s look at an example. Let us say the central angle is 7.2 degrees. This is an angle between Alexandria and Syene. Thus if we divide 360 by 7.2 we get 50. This means that Earth’s circumference is 50 longer than the distance between the two cities.

So all that Eratosthenes needed to do is pay for someone to measure the distance between the two cities. In case you’re wondering how correct was Eratosthenes, depending on the units that he used, he was somewhere between 1% and 16% off, which is amazing having in mind that the experience took place 2000 years ago. 

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sheena said...

Interesting info, I am waiting for the next info
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abdul wahab said...

nice Physics Experiments

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