Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths modified by epicycles and at uniform speeds.
This is the heliocentrism that was condemned by the Church. Nobody believes this any more. Technically, this condemnation was never removed. When the Church allowed heliocentrism in the 1820s, the decree specified that it was for heliocentrism as it was understood at that time and there had already been changes to it by then. I don't believe in either of those. I am not ashamed or embarrassed to say that. There is no reason to be since they are considered obsolete.
From what I understand of modern science, the current model is not heliocentrism at all. It is
Cosmological Special Relativity (CSR). ...a theory on cosmology that was developed in the early 1990s by theoretical physicist Moshe Carmeli. It describes the large structure of space, time and velocity in the Universe. The CSR theory unites space and velocity analogically as Einstein's special relativity theory does with space and time,[1] however it is associated with cosmos or galaxies in the Universe, respectively, rather than with very fast moving particles. The substance of Carmeli's Universe is called spacevelocity instead of spacetime. Carmeli postulated that the Hubble Law that relates the velocity of the expansion of the universe to the distance of the source is fundamental to all observers in the universe although rewritten into the new form. He replaced the Hubble constant which value varies widely depending on the method used and on the distances to the sources that were used to determine its value with new truly universal constant which is the same for all observers regardless of epoch (i.e. regardless of when the measurement is made) and named it Carmeli-Hubble constant. The CSR theory predicts unusual effects in the cosmos, like length contraction and velocity dilation for large-scale structures in the Universe. By including matter into his theory, Carmeli developed also his theory on Cosmological General Relativity.[2][3]
I don't understand this. I can't say that I believe it or don't believe it. I don't have an opinion and don't expect that I ever will.
I am, however, prepared to say that spiritually, the earth, as the location of the Incarnation, is the center of the universe. I'm fine with calling that spiritual geocentrism. Or not.