FET has not come to a conclusion on the subject but basically, whatever you want. Some kind of unknown force moves the stars around and since stars aren't giant balls of gas burning billions of miles away, it's easy.
Two popular ideas are the sky mirror and celestial gears. In both cases the sky of each hemisphere is only visible when you're in that hemisphere and they both rotate around separate points.
Nothing can or ever will be proven mind you but that's why it's a popular theory for FEers: You can't disprove it without resorting to using NASA and that's not acceptable to Flat Earthers.