If the earth was flat and you were in the middle of the Pacific Ocean on a clear and sunny day would you see a cirlular horizon all around you ?
If not, what would you see when your visual focus transits from the sky to the earth?
You might note that you can’t see a circular horizon now. The field of your acute vision isn’t wide enough to do that. Looking out toward the horizon on a flat earth wouldn’t look a whole lot different than it does now. Yes, the horizon would be far more distant but your visual acuity wouldn’t be enough to tell the difference.
The Master answers a related question. And, in the interest of balance, the honorable opposition.
I don’t think there would be any clues visible to our unaided vision that would tell us a difference between a flat earth and a spherical one.
Prior to space flight the best evidence of the spherical nature of the earth that I know of was in surveying. Plane geometry doesn’t fit the surface of the earth over long distances nearly as well as does spherical geometry.
Of course there would be:
[ul]
[li]The shadow of the Earth on the Moon during lunar eclipses always has the same curvature.[/li][li]When travelling, you see the tops of distant tall objects first, then gradually, you can see more and more of them.[/li][li]No matter where you go on the planet, the horizon always appears roughly the same distance away.[/li][/ul]
All of these things were noticed long before space travel.
If the Earth were completely flat, the horizon might appear to be slightly higher than it does at present. Part of the reason the Earth appears flat has to do with how totally insignificant we are in comparison to it. You’ve got to get quite aways up before the Earth’s curvature is noticeable. The other part of it is due to refraction of light as it oasses through the air. This refraction makes the horizon seem slightly higher than it really is. If our atmosphere was sufficiently dense, the refraction would make it seem as if the observer was in a large bowl. So if the Earth were flat, the true horizon would be (slightly) higher and the apparent horizon higher as well. At least if you were in a flat area like the Pacific Ocean or West Texas.
Would the view change as you walked toward the edge?
Just like a cliff, if you go too far, sure!
But it wouldn’t be like a cliff. No one has said anything about changing gravity. If you stepped off the edge of a flat earth you would simply fall back onto it. Actually, it would be more of a stumble than a fall.
Course, you may end up on the edge of the flat earth, or even on the underside. Both would radically change your horizons.
If we’re not changing gravity, would getting to the ‘edge’ of flatworld be like climbing up a cliff? 
The pull of gravity would not be straight “down” out near the rim, (ie not perpendicular to the flat surface,) but would be over, towards the center of mass of the disc. Unless we have different theoretical models of how our flat world is shaped. 
Hijack: On a flat earth/Dyson sphere/ringworld, how thick would the sheet/sphere/ring have to be to exert the same gravitational pull on its inhabitants?
I don’t think this is true – the errors don’t show up until you’ve taken accurate measurements over long distances. Long before that happened, you’d be aware of the sphericity of the earth through two different clues:
1.) the shadow of the earth on the moon during lunar eclipses.
2.) The way that distant ships first become visible from the top down. Masts appear before the hulls. On a flat earth the hull and masts would vecome visible at the same time.
By the way, the geometrical argument would prove that the earth was spherical, but not whether it was convex or concave. I’m sure the Cyrus Teed “Koreshan” cult made a big deal over this. It also showed up in Hal Clement’s classic SF novel “Mission of Gravity”, where the Mesklinites (inhabitants of a high gravity planet) knew their world Mesklin was spherical because of the geometrical reason you cite, but thought it concave because gravity affected the atmosphere which affected the optics, giving a visual image via gradient index optics of them being in a concavity.
What do you mean, IF?
** Join The Flat Earth Society! **
A horizontal line of demarcation?
I knew that. :smack:
Well obviously it’d have to be thick enough so that the overall mass was the same as the earth. The big difference would be that the gravitational pull would be unbalanced, unless you were standing in the very middle of the flat earth. So if you jumped straight up at the edge, you’d come down at an angle further in from where you started.
The flat earth itself would have the same problems. It would have a distinct tendancy to start folding in on itself, and eventually end up a sphere.
You’d also find the further away from the central point you were, the weaker the gravity. Unless you made the earth thicker on the outside edge, and paper thin in the middle. Or something…
If the Earth were flat and of uniform thickness and density, the gravitational field would be mostly uniform everywhere not too close to the edge. The thickness required would be independant of the radius of the disk, so one can’t say the Earth would have to have the same mass. Specifically, the surface gravity would be g = 2piG*sigma, where G is Newton’s constant and sigma is the area mass density. Using g = 9.8 meters/second[sup]2[/sup], we find sigma = 2.33735717 × 10[sup]10[/sup] kg / m[sup]2[/sup]. Assuming a density of 6000 kg/m[sup]3[/sup] (about that of the Earth), this would mean a thickness of about 3900 kilometers.
Please note that this does not work on a Dyson sphere (at least not on the inside) since the gravitational field anywhere on the inside of a uniform spherical shell is zero (the opposite side of the shell is pulling you up as much as the near side is pulling you down). And on a ringworld, it’d be irrelevant, since one would spin a ringworld to generate whatever gravity is desired, independant of the mass of the ring. This information will, however, doubtless be of interest to the inhabitants of Ankh-Morpork and surrounding regions.
What if the earth was shaped more like a huge Shakespearean collar, but with a kind of lumpy pentagram dangling from where Argentina should be?
“Men of science believe that in millions of years the earth will lose the shape of a globe and become a sort of pyramid or tetrahedron.” Or at least they did in 1918.
Of course the world is round! Yes, of course!
Pssst. The turtle moves.
I also suspect the horizon would be difficult, if not impossible, to distinguish. Consider a flat Earth with the same diameter as we now know the Earth to have. As a flat disk, it would have a radius of about 3,900 miles, which is how far away the flat-Earth horizon would appear. Viewing the horizon through that much atmosphere would blur the image via atmospheric scattering, which would also make it appear nearly the same color blue as the sky–note how the tops of distant tall mountains appear very blue and indistinct, and this is the result of viewing through only a hundred miles or so of atmosphere. Imagine how it would appear through several thousand miles of air.