My reply from Mr Martin Selbrede: ( re 183, 184):
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There are two variations of the geocentric model that account for the phenomenon in question.
In the modified Tychonic model (the version of geocentricity that most geocentrists tend to adopt), the motion of the stars, etc., is tied to the Sun, so that the annual motion of the Sun is also geometrically shared by the stars. This gives a purely geometric explanation of the dynamics. This would be the form of geocentricity that secular scientists working within relativistic frameworks, for example, Einstein or Poincare or Hoyle would have adopted, as it is a simple coordinate transformation with all the relative velocities remaining constant. This, as has long been pointed out, is due to the general covariance of Einstein's field equations (which also has implications for forces present at the Earth's surface). This model also accounts for related phenomena alleged to "prove" heliocentricity (diurnal variation of meteoric influx presumed to be due to how the Earth scours out a path through interplanetary debris during its alleged journey around the Sun, etc.).
There is, however, a minority view among geocentrists, whom we shall call the purists, who don't think the modified Tychonic model is the right geocentric paradigm to promote. This smaller group is extremely well versed in high power mathematics, and were able to make some rather remarkable scientific concepts quite rigorous. In this variation of geocentricity, the stars do NOT partake of the annual motion of the Sun, but are rotating around a center that is still fixed on the Earth. The question them becomes, how then do these purists account for parallax and aberration? These two phenomena are distinct in the modified Tychonic (and conventional heliocentric) cosmologies, but not in the case of this "pure geocentric" model. What these men have discovered is that if you treat the Earth as the sink of a conformal mapping (an elaborate mathematical procedure that is tractable in two dimensions, but not yet in three dimensions), you discover that both parallax AND aberration are two orthogonal components of a single phenomenon tied to that mapping effect at the sink. Because this derivation was made rigorous in two dimensions, it has considerable scientific plausibility and provides a rather novel approach to the behavior of starlight that isn't anticipated in conventional heliocentric cosmology nor in the majority version of geocentricity, the modified Tychonic model (which leverages the same explanation as heliocentricity uses to explain these phenomena, namely, dynamic shifts in system geometry). The purists are interested instead on the behavior of the light and accounting for it directly as a property of the light and the position of the sink. The non-purists and detractors of geocentricity are interested in the geometry, assuming nothing unusual about the behavior of light in any way, shape, or form.
I hope this helps set forth the two options available under the geocentric paradigm to explain phenomena such as posed in the quote you affixed to your inquiry.
As to the interpretation of the Michelson-Morley experiment, the situation is rather simple: the heliocentrists assume the Earth to be in motion, and reject the zero-velocity reading of the interferometer as representing physical reality. In their view, nature conspires to hide the motion of the Earth. The geocentrists argue that the interferometer's readings should be taken at face value. Those physicists who hold to various ether theories have to also teach that the ether is "entrained" at the Earth's surface to create that null result, but that means that there is a gradient in the ether between the Earth's surface and outer space — and this gradient (required by this model) simply does not exist, and has never been found. There is also a massive disproportion in this effect between the daily and annual motion of the Earth, where the greater acceleration yields the smaller apparent effect — but such discrepancies are ignored. The geocentrists, to their credit, do not ignore this evidence, they make sure these serious problems with the modern cosmologies remain center stage wherever and whenever possible. Nobody should be given a free pass on a question of this nature, nor permitted to fudge the data.
Martin