If the earth was flat, then why is it that when you travel long enough in one direction you see different stars?
I would think that on a flat earth the same stars would be visible the world over.
Rowbothman's book Earth: Not a Globe explains this as a result of perspective. Though I do not think that adequately explains what we observe. For example:
Let's assume we are standing on a flat Earth. Three people stand at the same North latitude equidistant from each other (say one person in the US, on in Europe, and one in Asia, for example). Each person sees the celestial north pole (the point in the sky about which the stars rotate) at equal degrees of inclination. Now, because the Earth is flat, the lines of sight from each observer intersects at a point some distance above the North Pole of the Earth.
In the South, stars rotate about a celestial point commonly called "the south celestial pole." Three people stand equidistant from each other at the same South latitude and notice a specific inclination of the south celestial pole. On the Flat Earth these lines point away from each other above the surface of the Earth, but they intersect at a point some distance below the surface. This point of intersection is exactly below the geographical north pole, and is co-linear with the north pole and the "northern" point of intersection (examined above).
This means that in the FE model, using empirically observable evidence, the axis around which the celestial south pole rotates is the same as the axis around which the celestial north pole rotates. That's funny, isn't it?
Now to make the evidence sufficiently redundant:
Anyone that has experience as an amateur astronomer is familiar with equatorial mount telescopes (this author being one). They are set up to track the motion of the stars through the night sky by tilting the telescopes' azimuthal axis in line with a celestial pole. That is a very empirical and mechanical process; there is no reliance on any established theories or facts.
Now it just so happens that the angle at which ones telescope is tilted is equal to ones current latitude. As an example, when I use my telescope I incline the azimuth 39 degrees from the horizontal, and I live in Denver, CO. Thus, from each latitude -- North or South -- there is an angle equal to each latitude pointing to its respective celestial pole.
While perspective can account for some change in inclination angle based on latitude, it cannot account for the equality of latitude with said angle.