Maybe I don't remember the argument very clearly ...

So what is the geocentrist explanation for stellar parallax, then?

However, just as the geocentric system could answer stellar parallax by means of a reciprocal geometry, so was the case for stellar aberration. In fact, the alignment of the stars with the sun that provided the geocentric answer to stellar parallax also provides the geocentric answer to stellar aberration. Since the geocentric star field is offset from the Earth by 1 astronomical unit, then, as the star field rotates around the Earth on a 93 million mile radius, it will produce the same circular and elliptical formations of Gamma Draconis as that which is claimed for the heliocentric system.
[...] stellar aberration not only produces a circular star trail for stars near the north celestial pole, but it also produces elliptical trails for stars at a lower declination. For example, for a star situated at a 45 degree declination with respect to the Earth, its star trail over the course of a year would resemble the typical ellipse. But for a star situated at the equatorial celestial plane, its star trail would look like a hyperbola or straight line. These various formations will be exactly the same in both the heliocentric and geocentric systems for the same star.
Thus, neither stellar parallax nor stellar aberration could prove the heliocentric system. This fact was recognized in 1901 by the famous physicist Henri Poincare:

Quote

The observation of the aberration show us, therefore, not the movement of the earth, but the variation of this movement; they cannot, therefore, give us information about the absolute motion of the earth.

Here's what Dr. Sugenis has to say about it in Geocentrism 101, p. 64-65:

Since the geocentric star field is offset from the Earth by 1 astronomical unit, then, as the star field rotates around the Earth on a 93 million mile radius, it will produce the same circular and elliptical formations of Gamma Draconis as that which is claimed for the heliocentric system.

That proposition was condemned as heretical by the Holy Office.

That proposition was condemned as heretical by the Holy Office.

Leaving aside the geostatic model, would it be sufficient to still call modern science's model of the universe geocentric considering the scale of the universe? Of course by that logic the sun could be said to be just as much the center as the earth, but considering the size of the universe that would be an insignificant distinction.

A flaw with this line of thinking may be that modern science only knows about the visible universe, and therefore can't know for sure where we are located within its distribution of space and matter since we see equally far in all directions.

You might want to look at the link below by MHFM on the matter of Geocentrism and the Holy Office.

You might want to look at the link below by MHFM on the matter of Geocentrism and the Holy Office. It's a good proof that the Holy Office itself is not protected in its decrees as would a teaching by the Pope on Faith or Morals or those teachings which are part of the authentic Magisterium of the Church.

Further, unrelated specifically to Geocentrism, they get into this because of the condemnation the Holy Office raised against Fr. Feeney with Card. Cushing's heretical letter Suprema haec sacra. Which, if the Holy Office is infallible, then the condemnation of Fr. Feeney would in fact be true and we are heretics for not believing that non-Catholics can be saved outside of the Church without baptism.

https://schismatic-home-aloner.com/the-holy-office-geocentrism-fr-feeney/

I still believe that Geocentrism is the Catholic position, as, again, the Church Fathers are unanimous about it, as proved by Dr. Sugenis.