You know how science is based around making predictions? Well even as I was writing my post I was thinking 'I bet Tom replies to this and mentions something along the lines of negative parallax'. The three stars I mentioned are quite near by, near enough at any rate for the parallax angles to be measured accurately with the equipment available at the time.
I can tell from reading through the FE Wiki that it is not unusual for FE believers to dismiss this sort of evidence as 'illusion' or 'errors' or whatever and I would expect that. You would naturally try to find alterative explanations for scientific experiments or observations which seemed to place any element of doubt on their accuracy. FE theorists say the Earth is stationary (and central) in the Universe and of course they would wouldn't they. They also say the stars are fixed in some heavenly dome above that flat Earth. So how would you account for a tiny but measurable, repeating change in the position of some stars which coincides with the length of the year without resorting to the older and long since discarded idea of epicycles and such like? I know you will find one, of course you will but that has got to be backed up with directly observed evidence.
So the parallaxes of Alpha Centauri and 61 Cygni are large enough to be measured accurately and have always been positive since they were first measured in the 1830s. Alpha Centurus is only 4.3 lightyears away, hence its parallax is a tad over 1 arc second and 61 Cyg is 11.4 lightyears away so its parallax is a little under 0.3 arc seconds.
As for the Sagnac and Wang experiments, perhaps you would like to compare the description given in your FE Wiki page with that given in the mainstream wiki page
https://en.wikipedia.org/wiki/Sagnac_effectWhile Laue's explanation is based on inertial frames, Paul Langevin (1921, 1937) and others described the same effect when viewed from rotating reference frames (in both special and general relativity, see Born coordinates). So when the Sagnac effect should be described from the viewpoint of a corotating frame, one can use ordinary rotating cylindrical coordinates and apply them to the Minkowski metric, which results into the so-called Born metric or Langevin metric.[12][13][14] From these coordinates, one can derive the different arrival times of counter-propagating rays, an effect which was shown by Paul Langevin (1921).[15] Or when these coordinates are used to compute the global speed of light in rotating frames, different apparent light speeds are derived depending on the orientation, an effect which was shown by Langevin in another paper (1937).[16]
This does not contradict special relativity and the above explanation by von Laue that the speed of light is not affected by accelerations. Because this apparent variable light speed in rotating frames only arises if rotating coordinates are used, whereas if the Sagnac effect is described from the viewpoint of an external inertial coordinate frame the speed of light of course remains constant – so the Sagnac effect arises no matter whether one uses inertial coordinates (see the formulas in section § Theories below) or rotating coordinates (see the formulas in section § Reference frames below).
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