Well, if it wasn't a sphere, there would be no southern star to see the rest of the stars rotate around in the opposite direction, and you are looking in the opposite direction, down if south is down as opposed to up. if the north and north star are considered up. So yes, with the earth rotating, or even if it was true the stars are the ones moving and not the earth, the earth still has to be a globe for this to work as it does. Quite simply if the earth were a flat circle, there would be no way for a southern star to be seen or to see the opposite type rotation around it. The only way this would work the way it does, as I stated above in the longer above response, is if the earth were a sphere or maybe a cylinder, or some other sphere like, or cylinder similar type like shape.
And which constellations are visible does absolutely change with the seasons, and the relative position in the observable sky does change that are visible all year long. And as the earth is a sphere, when the earth rotates towards the direction of where the constellations that are still visible, why would they change?
As for the constellations themselves, again you are underestimating the scale. Actually the shape and distance between stars in the constellations has changed over the millennia, it is just the distances are so vast, no one will notice the change in ones lifetime, but there are star charts from many thousands of years ago that do record enough of a noticeable difference compared to today's star charts.
And now with our better telescopes and better measuring devices we can measure the much more subtle changes in distance in real time.
Even if the individual stars are rotating or moving around their individual own central point somewhere out there, again the distances are so vast that the size of their circular orbit would still be too small for us to see with the naked eye. And in general they are still staying relatively the same distance to one another as the distance between them is so vast.
And again, about the north star, if we are on a flat plain, you should absolutely still be able to see this central north star at the center top of this supposed dome, even if you are at the edge of this circle. And quite simply you can't.
As far as irrational numbers is concerned, the definition of irrational is not the same for normal use as to the definition in math. All it it means in math is the fact that when you divide the fraction that works, say to determine pi, the numbers don't seem to easily have a stopping place. If you leave the fraction alone, you don't need to worry about the never ending decimal places. And how can it be theoretical, if even when using the decimal, rounded to only a few decimal places, do we actually get real results, this is not irrational at all, it is real working results.
The experiment with the fruit and pi show that real rational results are achieved all the time. this is not theory.
Science isn't often wrong, actually it has changed very little from even the time of the ancients in most respects.
Sure, some things we get wrong, say for example, sweet n low, they used to believe that it caused bladder cancer. And now they don't. But that is only things more on the small individual scale, and because, yes, absolutely the individual scientists may be biased and trying to find the result they want or expect, i.e self serving. And in fact the problems with the original idea that sweet n low causes bladder cancer were found to be incorrect as the original testing conditions were flawed. Rats were used, and most lab rats get bladder cancer often, no matter what you feed them.
As it is often said or taught in science classes to warn about personal biases or expectations, if a scientist spends his entire career, say 40-60 years of his life, studying ravens, and finally after all that work and study, he determines that not including the rare albino, all raven are black. And on the day he is going to go public with his results, a yellow raven lands in front of him. What do you think most people would do? Yeah, he probably kills the thing and buries it before anyone could see it. This is certainly something all scientists are aware of and strive to avoid as not to be that guy.
And again, the Coriolis Force is observable by almost anyone with the above stated experiments in my first response above, with plain natural water.
These things aren't rocket science and anyone can observe them for themselves with little effort.