[LeGrande]

Suppose the sun was 173.5 AU from the earth. At this distance, it would take 24 hours for light to travel from the sun to the earth. According to LeGrande's theory of diurnal lag, this would cause the sun's "actual" position to lead its apparent position by 24 hours. So, the "actual" position would be the same as the apparent position. The sun would actually be where it apparently is. Furthermore this would be the case if the sun's distance were any multiple of 173.5 AU.

Only if you consider a stopped clock to be right twice a day : )

[Ethan Clive Osgoode]

Only if you consider a stopped clock to be right twice a day

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.