Well, to make a somewhat reasonably plausible what-if, lets just pick a radius of the earth that is much (say 10 to 100 times) the actual one. 10X = Saturn. 100X might make the sun wobble quite a bit, but I guess we’d still have similar “rising” and “setting” of the sun in re the earth. That might change people quite a bit, but at least they wouldn’t turn out with flat heads or something.
Anyhow, we’re told hereabouts in CA-US that we’re supposed to be able to see the top of Mt. Shasta from the top of the Mt. Diablo, 32.5 km east of Berkeley and almost 390 km due south of Shasta, and with nothing but the Sacramento Valley, and low hills at the far end, in between. I don’t think I ever made this observation, given the past and present problems here with air quality. Right now, you’re lucky if you can see Carquinez Straits from Diablo, about 18.5 km north of there. There are still fires raging in Yolo County, 129 km to the north. The sun has been very orange for over 1/2 a week in Berkeley, and there was only a half-light Sunday when I hiked in eastern Napa County.
However, let’s check out this claimed view, in theoretically transparent air:
Height of Mt. Diablo: 1.173 km
Latitude of same: 37.8 deg
Height of Mt. Shasta: 4.316 km
Latitude of same: 41.4
Difference in latitude (theta) then = 3.6 deg
The longitudes of the two differ only by a negligible 0.2 deg
Surface distance between the two: 390 km
Earth’s radius ®: 6717.2 km
The rise (roundness) of a segment of a circle or sphere, in this case, that between the two mountains, = R(1 - cos theta/2). This calculates to 3.3 km. If you figure the rise would cut off the view from one mountain to the other at a point halfway between, you then conclude that a line of view from Diablo, starting 3.3 - 1.2 = 1.1 km below this midpoint hump, would shoot a tangent of this hump that could see a mountain as low as 3.3 + 1.1 km above the midpoint impediment, or 4.4 km,. . .but Shasta is only 4.3 km high. OK, so the atmosphere would pro bably usually bend the image of the top of Shasta, by that much, into view. . .on the rare days, these days, that it is clear enough. Maybe, if the earth had a 10X diameter, and no cars or industry, we could see that poster up in Alberta from Mt. Diablo, but not exactly the whites of his eyes. . .but I think the Rockies would get in the way.
A post mentioned defocusing at larger distances. Of course, eyes that will focus 20 ft away will focus at infinity, but thermal air currents and inversions will distort distant images and raise them above the horizon (mirages), and and particulate matter in the air will disperse light to distort their color (purple hills).
Ray (Haven’t checked on this out with the Flat Earth Society.)