What is your view of the Tychos model and its rotating, Mars-centered universe?

It is wrong, first, because it has the earth rotating on its axis. If we go by the Church's statement that a non-rotating, non-revolving earth is a matter of faith, because that is what Scripture says, then any model with a rotating earth is wrong, ipso facto. The other problem is that the Tychos model centers the whole system on Mars, as if the universe moves in conjunction with Mars, and that is simply not true. In the geocentric model the earth, not Mars, is the pivot point, because the earth is the center of mass of the universe. The Tychos model is just another geometric analysis of planetary motion, like those of Ptolemy, Copernicus, Kepler, and Tycho, all of which put the planets at the same distances and motions relative to the sun and differ only in how they shift the rings. And like them, it is missing the crucial thing: what forces make the bodies move that way. Newton was the first to give a cause, F equals ma. The Tychos model has no forces behind its motions, so it cannot be the model we use; it does not get us anywhere.