A submission for aisantaros's challenge.
Download the code from GitHub.
* Please feel free to ask for clarification if something isn't clear *
Overview
This model demonstrates the possibility of accurately predicting the location of any star from any location on a flat earth, specifically, the Octans Constellation.
The earth is surrounded by a large "celestial shell", which is normally opaque to visible light. There are numerous holes in the celestial shell, which allows directional light to penetrate the shell and reach the earth. Each hole corresponds to a specific star seen at a specific spot on earth. For each star, there is exactly one hole in the celestial shell that allows a ray of light to hit a specific spot on earth. Given a high enough resolution of the shell (which can be arbitrarily increased by increasing its radius and thickness), the non-continuous nature of the stars would go unnoticed. While this specific arrangement of directional holes seems improbable in the extreme, there is a plausible natural explanation for it, which will be explained in the next section. This plausible natural explanation can be demonstrated to result in the exact same arrangement of stars as what we would expect to see on a globe shaped earth.
Origin of Directional Holes in Celestial Sphere
Imagine a small sphere sitting at the North Pole of the earth. The sphere explodes. Particles are shot outwards in all directions. Once these "guide particles" hit the celestial shell, they drill holes in the shell. These holes allow light from outside the shell to shine back on the earth. Due to the thickness of the celestial shell, the light that penetrates the holes will be highly directional. In fact, the light will only hit the exact spot where the original small sphere exploded. If a person stands in the exact spot where the sphere exploded, he will be able to see light leaking through the numerous holes in the celestial shell. However, if he moves slightly to the side, those holes will disappear, and the sky will again be black.
Now imagine billions (or more) identical small spheres covering the surface of the earth in a single layer. Each sphere is completely identical in every way. When each sphere explodes, it will emit the exact same arrangement of guide particles as every other sphere.
However, each sphere is facing a slightly different direction. Each sphere is rotated towards the North Pole by an amount corresponding to its latitude. Whereas when a sphere at the North Pole explodes, it will shoot a "Polaris particle" straight up, a sphere at 45° north latitude will shoot its "Polaris particle" at an angle of 45°, resulting in a hole that can be seen at an altitude of 45°. The exact same altitude that Polaris would be expected to be seen at from a globe earth.
Likewise, each exploding sphere has its own "Sirius particle", "Betelgeuse particle", "Rigel particle", etc, which allows those stars to be seen from anywhere on earth.
This is roughly illustrated in figure A. This is a side view of the earth. I know it looks like a confetti bomb, but bear with me. Each sphere has exactly 5 rays coming from it, corresponding to 5 major stars. The colored rays are emitted by each sphere at the exact same angle relative to the north (red) side of the sphere. The spheres and rays are each rotated to match the latitude that they are located at.
Figure A: Side view of exploding spheres and guide particles rotated according to latitude
[continued]
So you have the entire volume of the dome (or at least everywhere man has been to) covered in spheres which all explode at the same time and are oriented just right.
That makes no sense at all, especially as the particles would be colliding with one another, and they would fall due to whatever equivalent they have for gravity, and you are missing all the holes below us.
Besides, you would have different constellations for every location on earth...for example, in Europe you can see the big dipper and orion, but in Japan you shouldn't be able to see these with this theory, but instead you should see different constellations at those exact spots,which is not true.
most constellations or other sets of stars like Orion, the big dipper, pegasus, Leo, etc. can be seen from at least half the globe, depending on where in the sky it is located.