How to convince your flat-Earth friends that the Earth is round

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That part of the circle on which the stick figure is moving.  A triangle is formed from the central point of the circle to a point...

Illustration: Rat Allen

You can see that we have a right triangle whose hypotenuse is equal to the distance from the observer's eyes to the center of the Earth (R+H), while the other two sides are equitable R and the distance to the horizon (S, Using the Pythagorean theorem, we can solve S,

s is equal to the square root of R plus h squared minus r squared

Illustration: Rat Allen

Now we just need to add our values 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), so you can see far away. But standing at the edge of the lake, it's only about 3 miles wide and you won't be able to see the other shore. Yes, that's because the Earth is spherical.

swinging a pendulum

This second experiment is a little more difficult to set up, but you don't need a huge lake. You would hang a mass on the end of a string and let that mass swing back and forth – yes, that would be a simple pendulum. However, if you let it go carefully (without giving it any circular motion), the pendulum will not just swing back and forth. Instead, it will gradually change the direction in which it rotates. It is often called the Foucault pendulum (named after Leo Foucault).

Why does this happen? Let's take this to the extreme case so it makes more sense. Imagine you have a body 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 beneath it will rotate (since the Earth's rotation causes night and day). Here's an animation of what it would look like (not in real time).

Video: Rat Allen

The pendulum simply swings back and forth, but the Earth rotates beneath it. This makes it appear that the pendulum changes direction as it rotates, and it will take half a day for the pendulum to rotate again in its original direction (as viewed from the North Pole). A complete cycle will take one day.

But wait! This does not prove that the Earth is spherical. Maybe it just shows that the flat Earth spins like a record on a record player. OK, fair, but what about this? If you take the same pendulum to the South Pole it will also rotate – but in the opposite direction, because you will be standing in Antarctica, completely upside down with respect to the North Pole pendulum.

But to do this experiment you do not need to go to the North or South Pole. You can do this at home. The pendulum will swing in different directions again as the Earth rotates, but it will take more than half a day to return to its original direction, and the time will depend on your latitude.