What this mean is, if an observer is looking straight out and level (that is, at a 90 degree angle to a line from his feet to the center of the Earth, the visible horizon will always appear to be at his own eye level. You can check this easily by standing on the beach and looking out level, then going to the top of a tall building and looking out level, and then go up in a jet liner and looking out. Sure enough, the horizon line will seem to rise up with you, at least up to jetliner height – 30,000 feet.

Now here’s my question. If you were to go high enough, up to the level of the space station, say, it seems like the horizon would eventually have to drop below your eye line – I mean, the Earth’s only so big.

Has anyone out there (an astronaut or a U2 pilot?) seen if this happens? And if it does, how high do you have to go before it kicks in?

This has been bothering me for years, which will give you an idea of what a quiet life I lead…. answers would be appreciated.

It is a very accurate and quite simple formula when compared to those shown above. It doesn’t get any simpler than this.

It reads: distance to the horizon equals the square root of altitude (a) times (diameter of the sphere (s) plus altitude (a)):

d=sqrt|(a(s+a)|

a= altitude above sphere
s= diameter of sphere
d= distance to horizon

For example:

At an altitude(a)of 1 mile above Earth(s),7910 miles in diameter,the distance(d)to the horizon would be 88.9438 miles.
or
At an altitude(a)of 1 mile above the Moon(s),2160 miles in diameter, the distance(d)to the horizon would be 46.4865 miles.
or
At an altitude(a) of 1 mile above the Sun(s),864,000 miles in diameter, the distance(d)to the horizon would be 929.5165 miles.

This formula, in its simplicity, can be used with any unit of measurement, size of sphere or altitude, however small or large.

In the present case, A = you, Γ = Earth, and you can compute the power by using two different lines Δ, namely the tangent line and the vertical line; this directly yields

(distance to horizon)² = (altitude).(diameter of Earth + altitude)

or, if you are in a plane or lower (and thus altitude is negligible compared to the diameter of the Earth),

(distance to horizon) = √(altitude.diameter of Earth)

Thus, at low altitudes, when going four times higher, you see twice further.

Of course, this is assuming that the Earth is a perfect sphere. When you are on the beach, you are probably actually a bit above sea level (on a jetty) and looking at an object that itself is above sea level (island, ship mast). To see that object, there must be some horizon that both you and the target are able to see, and thus you need to add the horizon distances for you and the target. For example, one pirate ship could see (from the crow’s nest, 30m above sea level) up to 20 km away, thus two such ships would see each other from 40 km apart.

And as far as window seats go, my favourite one was flying over (and actually, around) the western Himalaya range, including the conflictual zones of Pakistan and Afghanistan. Man, those mountains in the background are *high*.

Isn’t perspective causing things to shrink the further they are away. Imagine a long straight lane with lamp posts next to it, each of the same height. You will see that each lamp posts gets smaller than the one in front of it. This causes our feeling of perspective. Now, could the horizon simply be the location where these lampposts become so small, we can’t see them anymore?

Just a question!

Alright everyone – Flame on!

I was above the haze, clouds, and light pollution — and I had nothing better to do. I pulled the navy Delta Airlines blanket over my head and peered out the window. There was a ‘boy scout’ looking little boy in the row in front of me who asked what I was doing. He also got a blanket and we “ooh”-ed and “ahh”-ed the whole way.

Best meteor shower, ever!