Optics proves a tricky thing for FE theorists because it's so easy to just claim "distortion" or "perspective" or "fisheye lens" and dismiss the whole argument without budging from it. They'll claim that the atmosphere refracts the light upward not unlike how a mirage works. Of course, this is a load of garbage because mirages form under special conditions, none of which are present enough to cause the shadow effect.
There's a far easier debunk of the whole damn idea that the Sun is 32 miles in radius (if you're talking about diameter, it obviously gets worse). Doing a basic thermal energy calculation, one finds that the Sun at 32 miles in radius would run out of energy to give out in a cosmic heartbeat. The average kinetic energy of the gas particles in the Sun is capped by the highest temperature - 15 million K. This gives a value of about 3 x 10^-16 J per particle. Now one will quickly find that if gravity doesn't exist, how will the Sun hold itself together? Oh right, one of Tom Bishop's magical (and much weaker) "gravitation" forces. I'll be far more lenient and just assume that it holds itself together. We find that the proposed Sun has a volume of 5.58708453 × 10^14 liters. Now assuming that the proposed Sun has a density of 10 g / cm^3 (to give FE its best shot, we'll let the proposed Sun be denser than iron, although it can't reach this density). We find, then, that the proposed Sun has a mass of 5.58708453 × 10^15 kilograms. This yields 3.364621 × 10^42 hydrogen atoms floating about. So the proposed Sun has at most 1.0093863 x 10^27 J of thermal energy. Unfortunately, according to the Stefan-Boltzmann Law (where we assume that the surface temperature of the proposed Sun is 5000 K), this Sun has to radiate about 1.18 x 10^18 W of power. This means that the proposed Sun would only last at most 1 billion seconds, which a massive... 31 years. Your Sun would be dead in 31 years if it didn't have some way of replenishing its energy. This obviously contradicts the evidence that people have been alive for much longer than that and have seen the Sun (even if you don't buy the Earth is 4 billion years old).
Now that that long and arduous calculation is over, let's talk about what it means. FE theorists now have three choices:
Choice 1: Nuclear fusion powers the Sun so the calculation above is invalid. (This is true, and I'll address this below.)
Choice 2: Stefan-Boltzmann is bullshit (no it isn't, test it), your math is wrong (how?), or I don't understand it (well, I'll explain it to you, but that doesn't make this invalid), or some unquantified variant of "distortion"
Choice 3: Some other magical form of dark energy / quantum woo that I really don't even understand <insert Casimir> / relativity / wormholes / chemical reaction makes the energy inside the Sun. Remember Tom in the Occam's Razor thread, saying how FE theory was simpler than RE theory (hint: with all of the patches, it isn't! Of course if you don't understand basic physics and math and are inclined to believe conspiracies...)? So let me get this straight. You've already invented 3 forces (UA, gravitation #1, gravitation #2) to justify what can obviously be seen as an inability to comprehend scale; spheres locally look flat. You've already proposed physically impossible stuff, like things orbiting in circles above a disk (do you even understand how orbits work?). You've given a map whose distances do not line up with real world travel (direct flights from Sydney to Johannesburg). You've even asserted that the measured distances between cities are inaccurate! And now you're going to make up a new way of generating energy out of seemingly nothing?
Choice 4: Write it in. It probably rejects a ton of tested science.
So the only reasonable choice is #1 (or maybe I made a mistake, but 31 years is pretty hard to get to 4 billion years just by correcting mistakes). But this doesn't work. Nuclear fusion cannot occur with a star that is only 32 miles wide; it would have to be about twice the size of Jupiter to have a chance. The pressures and resulting temperatures just wouldn't be enough. We have tested and verified that the conditions for nuclear fusion are as high as we believe they are. These are the fundamental principles behind thermonuclear weapons, and also behind much of the fusion research (and hobbyism) today. People have built homemade nuclear fusion machines. These have demonstrated that nuclear fusion requires high temperatures. As I've said a thousand times before, if the pressure of the "gravitation" (and Tom Bishop implies this is far weaker than normal gravity) of the proposed Sun were enough to initiate thermonuclear fusion, I could build weapons of mass destruction in my backyard with some high explosive and tap water. Sorry, FE theorists, but asserting the Sun is 32 miles in radius is living in fantasy-land.