If we look south in any location in the southern hemisphere, we are going to see the same set of stars. The stars are seen rotating around the south celestial pole, in the Octans constellation, nearby the star Sigma Octantis.
This phenomenon is unexplainable in the flat-Earth model. Looking at the so-called ‘flat-Earth map’, we should see the different set of stars on the different location in the southern hemisphere. The reason is that the so-called ‘flat-Earth map’ does not represent the real Earth.
For example, let’s take three locations in the southern hemisphere: Perth (Australia), Papeete (Tahiti, French Polynesia), and Buenos Aires (Argentina) during the peak of southern winter, on June 21. During this time, the south part of the Earth is having longer nights than daytime, and a pair of opposing cities —like Perth and Buenos Aires— is possible to have night time at the same time.
Looking at the so-called ‘flat-Earth map’, Perth and Buenos Aires are opposite of each other and thus, two persons looking south from each of the cities should be looking opposite of each other and should be looking the different set of stars. But in reality, both can observe the same set of stars; only their orientations are different.
The flat-Earth map fails to explain this phenomenon. The reason is that the real figure of the Earth is a sphere, not flat.