So let me get this straight - the sun circles the northern like for one half of the year, describing circles in the sky over a localised point away from the southern countries.
It then, like clockwork, shifts to a similar track around the southern pole, describing the same circles in the opposite direction, going west to east in the sky.
It's not rotating over a localized point for half the year. Remember, the sun is constantly traveling North-South between the Tropic of Cancer and the Tropic of Capricorn. When the sun gets to the equator it switches gears into the opposite system.
The "switching gears" is a problem - what determines the switch? Is it on a timer, or does it just happen? And you'll have to clarify what you mean by "traveling North-South" too - what is its periodicity? What makes it stop and turn back? Is it on a track?
Of course, it could keep going in the same direction, but that would mean that half way through the day, it would stop in the sky and go retrograde at the equinox, signalling the shift from summer to winter in the north and vice versa in the south.
Why would it stop? Does a point following the path of a figure 8 stop?
Read it again - in a figure 8, an object makes one circle around a point clockwise, then chicanes and circles the other point anti-clockwise. This comment here was an alternative to that: if we want to maintain the direction of the sun around each point (i.e. if it circles each point in the same direction), it has to stop at the point where one circle meets the other and reverse apparent direction.
Look at it this way - put two clocks side by side: the hands when pointing at the 3 go "down" towards the 6 and "up" towards the 12. They are rotating in the same direction but to jump from the 3 on one clock to the 9 on the other, you have to change apparent direction at that point.
Unless the sun circles each point int he same direction, it would go east to west in the north and west to east in the south. This is not the case.
It would also mean that the sun would never be overhead in the northern latitudes in southern summer - and this would happen abruptly one day when the sun just "changed gears"
The sun isn't overhead when it is winter in northern latitudes. The idea that the sun goes overhead every day is fiction, and every middle school student should know this.
The subsequent ellipses drawn in the southern sky would make it draw little, flat rings, never reaching the eastern or western points at higher latitudes or, in the northwestern or northeastern latitudes, these circles would be in the eastern or western sky respectively
I don't know what you are trying to say here.
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Obviously.
From an observer on the ground witnessing the Flat Earth sun making these circles around one point and then the other, it would describe flat ellipses centered over said point over the horizon. Any observer not on the line directly between the poles would see these ellipses traced in corners of the sky, as opposed to the circular arcs we actually observe.
What's more, when the sun "changes gears", they would start going around in the opposite direction.
I don't know about you, but I have never seen the sun go backwards in the sky.
None of your cited sources explain this - none of your sacred texts account for this - none of your own theories do anything but propose more models that don't match what is actually seen.
The sun goes from east to west at all latitudes, tracing arcs of a circle - the
same circle - varying only in its relative angle to the horizon.
No gear changing, no reversals.
This model does not work.