The Blue Marble, taken by the Apollo 17 crew in 1972

The Blue Marble, taken by the Apollo 17 crew in 1972

By Scott Hamilton

I was reading an article this week on a site that was trying to prove the earth is round to the flat earth society. I found the math involved to be way simpler than expected and thought it would make an interesting topic. That led me down the path to find the first person to not only prove the earth was round, but to make the first calculation of its size. As it turns out, the earth was first measured somewhere around 250 B.C. by Eratosthenes of Cyrene.

Erastosthenes used knowledge from prior mathematicians and some simple trigonometry to calculate the size of the earth based on the angle of shadows cast in two different cities at the same time of day. To make his calculations, he used information that was gathered at the Library of Alexandria, where he was the chief librarian. A much simplified version of his calculation can be done by any high school student without too much trouble. He first measured the distance between two cities on the same meridian; he then measured the angles of shadows cast by the sun at noon on the summer solstice. His calculation showed that the circumference of the Earth was the distance between the two cities divided by the difference in the shadow angles. The numbers he used resulted in the earth having a circumference of 40,000 kilometers, which is extremely close to the accepted circumference of 40,070 kilometers used by scientists today.

There is a simpler way we can calculate the circumference of the earth today using information easily available on the internet. It requires two simple numbers that tell us how fast the earth is moving, and we can use those numbers to calculate the circumference of the Earth. Let’s take an example using two United States cities on the same latitude – Elkins, W.Va., and Colorado Springs, Colo.

We need to know three numbers, the exact time of the sunset in each city and the linear distance between the two cities. On November 12, 2023, the sunset in Elkins, W.Va., was at 5:02 p.m. (EST) and 4:42 p.m. (MST) in Colorado Springs. First we have to pretend they are in the same time zone, so let’s bring them to CST, which will make them match Licking, Mo. This makes them 4:02 p.m. and 5:42 p.m., respectively. So now we can calculate the time difference between sunset in each city, which is exactly 100 minutes. The rough distance between the two cities is 1477.5 miles, which means that the sun traveled 14.775 miles per minute. We know that the sun travels at a constant speed, or rather the earth spins at a constant rate, so we don’t expect the sun to speed up or slow down. We know it takes 24 hours, or 1,440 minutes for the earth to make one revolution. Using the simple formula of the speed multiplied by the time, we can get the circumference of the earth: 14.775 times 1,440, which gets a circumference of 21,276 miles, and if we convert that to kilometers we get 34,240 kilometers, which in the grand scheme of things is fairly close to the real circumference of the earth. In fact, the accepted circumference of the Earth at the 40th parallel, which is the closest I can find in a chart, is 34,735 kilometers.

If you want to make a fun exercise of this, you can try to find this information for different cities and do the same simple calculation. What you will find is that as you pick cities further north, your calculation will get smaller, and further south it will get larger, until you reach the equator, and then it will start to get smaller again. This is because the Earth is a sphere, and what we actually measured was the circumference at the 39th latitude, which will be shorter than the circumference at the equator. This method of calculation not only shows that the Earth is round, but that it is a sphere and not a cylinder spinning in space. Until next week, stay safe and learn something new.

Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to shamilton@techshepherd.org or through his website at https://www.techshepherd.org.

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