Ah, very good. So then, at distances of 173.5 AU and multiples thereof, an object's "apparent" diurnal position just so happens to coincide with an object's "actual" diurnal position. This number, 175.3 AU is then an important cosmological constant in LeGrandean physics. Take, for example, a galaxy in the northern hemisphere. Out of those millions of stars, a small fraction would happen to be nearly some multiple of 173.5 AU from the earth, and so these stars would, according to your theory, actually be in the galaxy that they appear to be in. The rest of the stars in this galaxy, although appearing to be in the same galaxy with the stars that are actually there, are actually strewn out along a circle around the Pole star.
I don't have a clue about what you are talking about. When you look into the night sky you are looking into the past, sometimes billions of years into the past. Nothing is actually where it appears to us now. Some of the stars that you see still shining brightly in the sky burned out ages ago and there are new stars whose light our ancestors won't see for a billion years, if they ever do.
This is a simple concept, why are you struggling so hard with it?