Yup, a thousand and a half characters again proving you don't get it.

n order for a geocentric observer to conclude that the sun orbits the earth, they would have to disagree with the inverse square law of gravitational attraction.

Uh, no. Look at the animation, look where the sun is when the other planets move, look how they're being 'tugged' by the sun. There is no deficiency in geocentric math regarding gravity or the inverse square law.

You only think there is because these drawings are an ultra-simplifaction, the orbits are not perfect circles, and the scale is nowhere near accurate. I promise you, the gravity calculations are the same as Newton's.

They are identical, gravity works the same in both of them, relativistic effects work the same in both of them because they are functionally the same, mathematically the same, and physically the same.

The only 'difference' is 'where you focus the camera'.

If your calculations significantly include other planetary bodies, like on a gravity-assist mission to Mercury, then it is easier to do the math through the heliocentric model because your motions will be perturbed enough by the other planets that you will need to do the math to get to Mercury accurately.

If you were just returning to Earth from the ISS, the Sun, Venus, and Pluto have almost no impact so you can just use the geocentric model and you're fine and saved a lot of time.

Neither one is 'right' or 'correct' outside of the context 'more useful in this case'.

There is no 'middle of the universe', or all places are the 'middle of the universe' (Doppler shift in stars seems to indicate that everything is moving away from us in all directions, making us appear as the center of the universe, but this is actually an artifact of space expanding uniformly).

There is no 'stationary point' at the center of everything that everything is measured against, there is no center.

One can argue that the barycenter for the solar system is a point that usually exists within the physical volume of the sun, but that isn't exactly right either because the lopsided mass of the solar system keeps tugging the barycenter around, and sometimes its actually pretty high up in the corona.

Not to mention, since gravity is subject to time, Earth isn't even orbiting the barycenter, it's actually orbiting where the barycenter was 8 minutes ago, which may not even be within the Sun's physical presence, depending on what your relational speed to the Sun is as an observer.