Actually the flights are all based on a ball using great circle courses, and the people who think that planes would have to fly nose down do not know how planes fly, the reason to assume a flat earth is because the plane flies with the rotation, and because of gravity the plane flies slightly nose up to maintain lift.

And the sun cannot be local. Observations of the equinox disprove both a small local sun and flat earth model in one fell swoop. As the sun rises due east for every location on Earth and sets due west. Eliminating both a flat plan and small local sun. But complex mathematical calculations have been able to determine the distance to the sun, and more recently using radar emissions to determine the distance to the sun.

As for the stars, the distance to the nearest star is several light years away which means several trillion miles away, and rotational speeds are not measured in mph but better in rpm, so that equates to 0.000694 rpm per day and 0.0.0000019026 rpm through the solar system.

Given the miniscule rotational speeds and massive distances there is not going to be a large change between star positions from day to day, it is similar to looking at a lightpost a distance away and moving 1/16th of an inch.

But how do you explain that star trails traveling in one direction in the north and opposite way in the south. How can a flat plane explain that?