How far is the horizon

Math What is the maximum distance from the horizon?

There is no real upper limit. The higher the viewer's point of view, the further away the horizon is. The surface of the earth is curved, and if we imagine that a viewer climbs a tower or a large ladder, then he can look a little further with every step. One can also make this clear to oneself if one draws a large circular arc on a piece of paper and imagines that this circular arc represents the surface of the earth. Then you draw a short line perpendicular to the arc - that's the viewer. From the top of the line - draw a line that just touches the arc. The point of contact would then be the horizon. And then it is clear that the longer the line, the longer this connecting line becomes an arc.

Of course, the proportions are not realistic on paper. But if you paint that on, it becomes clear: If you know the eye level of the beholder - and of course the radius of the earth at around 6000 km - then the distance to the horizon can ultimately be calculated using Pytagoras' theorem. And just to give you an idea:

For a person right on the beach at eye level 1.80, the horizon is just under 5 kilometers away. If this person stands on a 20 meter high cliff, he can see 17 kilometers far. On a hundred-meter-high tower, the horizon would be 36 kilometers away. The horizon is 360 kilometers away from an airplane flying at an altitude of 10 kilometers in a cloudless sky. And there are basically no upper limits.

But the earth is not infinitely large?

No, but a viewer can of course be any distance from the earth and the horizon would then be correspondingly far away. Therefore, this calculation becomes pointless at some point. For example, one could now calculate how far the horizon is from the moon for an observer, the moon is just under kilometers away. He also sees a horizon - that is then the edge of the visible earth. And then, of course, this horizon is about as far away as the moon - that is, almost 400,000 kilometers. But this distance is mainly determined by the distance between the observer and the surface of the earth. But the calculation is basically the same.

But if you formulate the question something, namely not: How far is the horizon from the viewer? But: What is the maximum distance on the earth's surface that you can see? Then it is clear: even from the moon, you can only see half of the earth. And if you know that the circumference of the earth is around 40,000 kilometers, then half of it is 20,000 kilometers. This is the distance from one end of the earth to the other, so to speak.