The Sun would switch it's apparent direction if the Earth turned upside down but kept orbiting in the same direction.
Earth has no reason to "flip", so it doesn't flip. No "on-point" change in the direction either.
The day would vary significantly if the orbit wasn't near perfect, but even if it was and you were using the Sun as a reference frame for each rotation and treat the stars as fixed true background then that means the stars are so far away that the earth's position around the sun would be near meaningless to our perspective of the stars.
And it
is nearly meaningless. There is something called stellar parallax, if I remember correctly, which is caused exactly by this slight change in where we look from at the stars from different points in orbit around the Sun. It is a known and measurable thing. It is kind of like looking at a crowd of people and moving your head to the side and seeing some of them who were previously hidden behind other people.
Because stars would be unaffected by movement side-real time would never change (well unless rotation speed changed).
And it doesn't, it is simply a different thing from the mean solar time we use in everyday life. Again, what is your point here?
So taking that into mind all that's left is apparent motion of the Sun. If Earth's traveling in a circular line or not it doesn't matter one bit in an orbit you have to completely change direction once per orbit, eccentricity doesn't change this fact one bit. Nor would it matter even if you were going in a square orbit or triangle orbit or anything completely bizarre.
True, but this change is not instantaneous. It is happening all the time slightly, and since the orbit is close to circular, the rate of change is also similar all the time. There is no "Hey, are we moving back now?" moment.
At one point in time you will be losing distance and at another point you will be gaining distance. Because side-real time would be real time it would always be an average of the two. You can swap the Earth for the Sun and the Sun for the Earth and it doesn't change this fact one bit on the 3 models I mentioned in the topic.
It isn't the same. Why would it be? We use mean solar time for clocks and timetables because it is more useful for everyday life - it stays tied to the day/night cycle by which we all operate. The noon is always around 12, midnight around 24 etc. And by the way, the mean solar time
does differ from the true solar time slightly, exactly due to the eccentricity of our orbit. It can be seen with a solar clock(?) large enough - like using a shadow from a tv tower or a tall building, and a good watch which doesn't need to be adjusted for a year - if you have the patience to do it. At different points through the year, the shadow's exact direction will not be exactly the same when viewed like once every week at
exactly 12:00. The shadow will probably blur a lot on such a large scale, so perhaps looking along a loooong wall at the Sun and noting down at what
exact time it shows up/hides is a better idea instead.
But anyways the main point I was getting at if side-real time is a true measure of Earth as a planetary body rotating then by all physical laws that would be the mean average of the solar day
No, god dammit. No. In all cases like this you should check the extremes, as long as doing so doesn't break the laws of physics. If a theory/hypothesis/idea doesn't work then, it doesn't work at all like stated.
Think of an Earth which does exactly
one rotation a year, in the direction that the Sun is always in the same position in the sky. Like it always is directly above the 0N 0E point on the map. At some place on the globe it is always noon, at some other it is always 11am, and it doesn't ever change. It is possible. In fact, this seems to happen over time to all the bodies in the solar system(most of the moons are always facing their planets with the same side, like our Moon). Now, is the sidereal time locked in place the same way? No! Through the course of the year, the shadow, night part, faces different stars as we circle around the Sun. This would give exactly zero rotation relative to the Sun, and exactly one rotation relative to the stars, each year. So, no, the sidereal time and mean solar time do not really have to be some "reflection" of each other. They exist as two different beings, both useful in different cases.
and if the Solar day was 24 hours part of the year it would also be forced to be 23 hours 52 minutes the other opposite part of the year and to top this off when the direction changed you would have a quick snap from 23 hours 52 minutes to 24 hours and vice versa this is reality of what a rotating object will do when rotated in one complete rotation you will always have the mean average average out to equal the amount of rotations. So the simple fact that we have one less star day per year then solar day means this is only possible if we have TWO bodies of motion counteracting each other. This is simply impossible if you have a single body rotating around another object with TWO fixed objects. If your frame of reference was solar you would simply gain +2 minutes average per day for half the year and -2 minutes average per half the other year. This simply cannot be changed. With flat Earth theory and geocentrism you actually still have the problem present because you would see the stars go faster and slower throughout the year if they were rotating around the Earth with the Sun as well. The only reason concave Earth theory doesn't suffer from this problem is concave earth is "Counter-Space" balanced.
Have a look at all the things earlier. I really hope one day you get how it works. Not even to change your mind about this whole RE/FE/CE stuff, but really to help you understand how it is all supposed to work. Right now your idea of it right now is seriously flawed.