Wednesday, September 21, 2016

Three Tests, Part Three: Extending Eratosthenes

Since the last experiment involved either getting wet or waiting for lakes to freeze. there is a way to show whether or not the Earth is curved quite easily with the same equipment we used in the sunset experiment (those of us who actually bothered to do it), and some international cooperation.

Around 240 BCE, the librarian at the Library of Alexandria, Eratosthenes, devised a clever way to measure the circumference of the Earth. The method is described here for those who would like to repeat the experiment.

Flat-Earthers have pointed out that this experiment does not prove that the Earth is a sphere, because the same results could have been obtained from a close sun and a flat plane. And they are right about that; the experiment assumed a spherical Earth and a distant sun, because others before Eratosthenes had made compelling arguments to establish those facts, and Eratosthenes was only trying to figure out how big the Earth was.

But one little addition to the experiment would prove the sphericity of the Earth. And it is as simple as adding a third data point. Because the geometry of a curved surface does not match the geometry of a flat surface (see, for example this blog post of mine).

So, through the power of connecting over the Internet, all you need to do is find two people who live a latitudes quite a bit different from your own. More than two is even better. Each of you will need a yardstick, a level, and a measuring tape, and access to Time and Date and Google Maps.

I won't complicate this too much, because the details aren't nearly as important as the basic idea. You and your teammates choose a day, bury the yardsticks to the same depth, and measure the length of the sticks' shadows at solar noon (that's where Time and Date comes in). 

Google Maps will help determine the distances between the parallels from each location. Now, you can map out the triangulations on a flat plane, and then on a sphere and compare, but you can simplify it. Just assume a flat plane and try to use the triangulations to determine the distance to the sun. If the Earth is flat, and the sun is close, then the distances to the sun should be consistent. If they are not, then the assumptions of a flat plane and a close sun are incorrect.

Having determined that, you can then extend the math to conclude that the Earth is, indeed, a sphere, and that it was pretty close to the size that Eratosthenes worked out over 2200 years ago.

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