# This is how far the horizon would (ideally) be at different altitudes

Long story short, this is my first post into a new and marvelous idea.

(drumroll)

Here it is: I’m going to also start posting things that can be summed up easily in a picture/graph – and as such don’t require a story behind them to make sense.

I plotted the below by using the formula Hd = 3.57√Ee (Hd = horizon distance; Ee = eye elevation), and made the horizontal axis logarithmic for two reasons:

1. it reads better
2. it looks cool

In real life, we should compensate for errors brought upon by atmospheric refraction, and we should also consider that past a certain point the concept of horizon serves no purpose.

But in ideal terms, if you were at an altitude of 1000 kilometers, your horizon would be 3570 kilometers away.

Later edit: as luck would have it, someone did the math on this after looking it over. Since my thing is nowhere near an educated approach, I asked if I could copy the input as an addendum.

Here it is:

The concept of a horizon is always valid, it just approaches 1/4 of the circumference of Earth. Atmospheric refraction: Yes, let’s ignore that.

For a spherical Earth, the exact formula is range = R arccos(R/(h+R)) where R is the radius of Earth and h is the height. Plugging in h=1000km, we get a range of 3357 km, while your approximation suggests 3570 km. An error of 6%, I guess that is still acceptable.