How far could you see the Andes from the Pacific on a flat Earth?

Question

Several questions on related subtopics of vision distance on a flat world have been asked before, but this one remains unaddressed. Specifically:

• The answer from Euclidean geometry would be infinite (no horizon). That's not what I'm looking at here.

• The answer from general relativity would be on the order of a light year (assuming constant 1g, bending light rays down). That's not what I'm looking at here.

• The answer assuming diffraction-limited seeing would depend on the angular size of the object you are looking at. But in practice the limit would be set by the atmosphere, not diffraction, so take a mountain range as the object to eliminate angular size as a consideration.

• Many locations on land have line of sight obstructed by nearby trees, buildings etc. So I'm taking the ocean as a starting point, to eliminate that limit.

• Smoggy city air would be unusually limiting. The Pacific Ocean is a good baseline; the air there isn't perfectly clear, but it's about as clear as air tends to get.

So: on a flat Earth, from a boat out in the Pacific, how far could you see the Andes? That nails down the limiting factor as absorption and scattering by air. (And someone asked how high above the water. Okay let's say ten meters above the water, high enough the waves won't obscure your vision, low enough to be effectively zero compared to the scale height of the atmosphere.)

Apparently there are known equations from which this can be calculated, but they are not particularly accessible to a nonspecialist. I'll start by throwing in some data points.

https://www.flickr.com/photos/lattaj/6896706847 'Atlanta Skyline From Brasstown Bald'. That's apparently 90 miles (145 km), and the Atlanta buildings are somewhat faded, contrast-reduced, but still clearly visible. The height of Brasstown Bald is 1458 m, not that high as mountains go. In particular, a horizon calculator says Atlanta is somewhat below the horizon from that height and distance, which explains why we only see the tall buildings. It's worth noting that the curvature of the Earth impairs visibility of even the tall buildings, by bringing the middle part of the line of sight to lower altitude, therefore denser air, which will absorb and scatter light more strongly than would be the case on a flat world.

https://www.reddit.com/r/MapPorn/comments/5i333o/the_longest_ground_to_ground_line_of_sight_ever/ 'The longest ground to ground line of sight ever photographed is 381 km (237 miles), from Mont Canigou in the French Pyrenees to the French Alps, against the background of the rising sun'. Canigou is 2785 m. Horizon distance for that height is 188.5 km. Of course in this case the other end is at significant elevation also, but still the line of sight distance is not small compared to the horizon distance, so the curvature of the Earth is significantly impairing visibility by bringing the line of sight down into denser air. On the other hand, that same curvature aids visibility by silhouetting the target mountains against the rising sun, which massively boosts contrast.

From the discussion linked above, 'Actually, this record was beaten by the same person who did this sighting, and now stands at 443 km between the Pic de Finestrelles (In the Spanish-French border in the Pyrenees, near Mont Canigou) and the Pic Gaspard (Massif des Écrynes, French Alps).' Pic de Finestrelles 2826 m, Pic Gaspard 3880 m. Horizon distance from the latter altitude is 222.5 km. Again, there is elevation at both ends, but still, the horizon distance is not large compared to the line of sight distance.

For reference, the highest peak in the Andes is Aconcagua, 6962 m, somewhat less than twice the height of Pic Gaspard. It's clear that higher altitude aids visibility. Even on a flat world, with no horizon to worry about, raising the altitude of either end, aids visibility by moving the line of sight into less dense air.

Based on the above data, I would tentatively conclude that on a flat world, objects near sea level would vanish into haze at a few tens of km, but high mountains could be visible on the order of several hundred km away, with the caveat that this would be true only on a clear day, and you might have to wait many days for such excellent seeing conditions. If both ends were high mountains, it's conceivable that visibility might go into thousands of km, though at that sort of distance, the probability of no clouds anywhere in the line of sight becomes small, as does the angular size of even a large object, so that distance might not be practical.

Is there a way to nail this down more precisely? Are there any factors I'm not taking into account?

Answer 1

You can go by your answer that estimates 100-120 kilometers because of air diffraction.

I was living in south france, Toulouse, for a long time, near the pyrenees. They were about 100 kilometers away; and they were about one and a half thumb above the horizon. But you could nearly never see them because of dust in the air and diffraction.

On a day when the pyrenees themselves were in the sun, and there were clouds on the way so no diffraction would hinder your sight, early in the year so they were still snow covered, they looked as if they were next to me. That happened about ten times per year maybe.

On a day when it didn't rain for weeks, I've seen just blue or even yellow sky. As if they were not there.

In northern germany there is the tower of Laboe. Northern germany is perfectly flat. The tower has 70 meters height. Theoretically you have the perfect unobstructed view from there. If you want to see something, you have to be early in the day or on a cloudy day. As soon as the sun shines and gets some time to do it's work, the baltic and northern seas fill the air with a haze that just doesn't let you see very far.