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Illustration: Rhett Allain
You can see that we have a right triangle with the hypotenuse equal to the distance from the observer’s eyes to the center of the Earth (R + h), with the other two sides being just R and the distance to the horizon (s). Using the Pythagorean theorem, we can solve for s:
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Illustration: Rhett Allain
Now we just need to plug in our values for R and h to get a distance of 4,657 meters, or about 2.89 miles. Of course, if you increase your distance from the surface (h), then you can also see farther. But standing on the shore of a lake, it only needs to be 3 miles wide and you won’t be able to see the other shore. Yes, it’s because the Earth is spherical.
Swinging a Pendulum
This second experiment is a little tricky to set up, but you don’t need a giant lake. You need to get a mass hanging on the end of a string and let that mass swing back and forth—yes, that would be a simple pendulum. However, if you were to carefully let it go (without giving it any circular motion), the pendulum wouldn’t just swing back and forth. Instead, it would slowly change the direction that it swings. This is often called a Foucault pendulum (named after Leo Foucault).
Why does this happen? Let’s take this to the extreme case so that it will make more sense. Imagine you have a mass hanging from a point exactly at the North Pole (assuming there is still some ice there for you to stand on). As the pendulum swings back and forth, the Earth below it will rotate (because the rotation of the Earth is what causes night and day). Here’s an animation of what that would sort of look like (not in real time).
Video: Rhett Allain
The pendulum just swings back and forth, but it’s the Earth that rotates underneath it. This makes the pendulum appear to change directions as it rotates, and it would take half a day for the pendulum to again swing in its original direction (as seen from the North Pole). A full cycle would take one day.
But wait! This doesn’t prove the Earth is spherical. Maybe it just shows that the flat Earth rotates like a record on a record player. OK, fair, but how about this? If you take that same pendulum to the South Pole it will also rotate—but in the opposite direction, since you would be standing in Antarctica, completely upside down with respect to the North Pole pendulum.
But you don’t have to go to the North or South Pole to do this experiment. You can do it at home. The pendulum will again swing in different directions as the Earth rotates, but it will take longer than half a day to return to its original direction, and the time will depend on your latitude.