The question "Why do the constellations change as we travel South?" may be answered as follows:
Firstly, we must understand that the stars in FE are small and a few thousand miles above the sea level of the earth. This change in distance compared to RE figures is due to an adjusted astronomical parallax on a Flat Earth. The angle of stellar parallax changes, as it does with the sun, when the earth is assumed to be a flat surface. By plane trigonometry, in special connection with carefully measured base lines, Dr. Samuel Birley Rowbotham has demonstrated and placed beyond all power of doubt that the sun, moon, stars are all within a distance of a few thousand miles from the surface of the earth. Therefore they are very small objects. Therefore not worlds. Therefore not light years across or from each other.
This considered, we go to Chapter 14, Section 6 of Earth Not a Globe where we read:
DECLINATION OF THE POLE STAR
Another phenomenon supposed to prove rotundity, is thought to be the fact that Polaris, or the north polar star sinks to the horizon as the traveler approaches the equator, on passing which it becomes invisible. This is a conclusion fully as premature and illogical as that involved in the several cases already alluded to. It is an ordinary effect of perspective for an object to appear lower and lower as the observer goes farther and farther away from it. Let any one try the experiment of looking at a light-house, church spire, monument, gas lamp, or other elevated object, from a distance of only a few yards, and notice the angle at which it is observed. On going farther away, the angle under which it is seen will diminish, and the object will appear lower and lower as the distance of the observer increases, until, at a certain point, the line of sight to the object, and the apparently uprising surface of the earth upon or over which it stands, will converge to the angle which constitutes the "vanishing point" or the horizon; beyond which it will be invisible.
What can be more common than the observation that, standing at one end of a long row of lamp-posts, those nearest to us seem to be the highest; and those farthest away the lowest; whilst, as we move along towards the opposite end of the series, those which we approach seem to get higher, and those we are leaving behind appear to gradually become lower.
This lowering of the pole star as we recede southwards; and the rising of the stars in the south as we approach them, is the necessary result of the everywhere visible law of perspective operating between the eye-line of the observer, the object observed, and the plane surface upon which he stands; and has no connection with or relation whatever to the supposed rotundity of the earth.
—"Earth Not a Globe", Samuel Birley Rowbotham
Ergo, when I stand outside and look into the skies, the star constellations I do not see are simply invisible past the vanishing point, beyond my perspective. When I travel south I am moving to a new location, changing my perspective, rising up a completely different set stars.