I'm not sure it proves that.
Your argument relies upon the sun being so far away that moving around Earth will have no significant change in the distance.
All it proves is that the sun is not something you can spatially move towards. This doesn't mean it's distant though.
Unless you want to try claiming you are magically fixed in place and unable to move, or that the sun is magically tied to you so as you move around the sun has to move with you, then it does.
Morever, I have been as far east as China and as far south as South Africa. And you know what? No matter where I was, the sun was the same size. Oh yeah, it's easy to say you are just too far away from the sun.
Again, all you are doing is showing that the sun is really far away, with the distance to the sun being much larger than the size of Earth.
The thing is, can we really even see objects that far away? No, it apoears we cannot.
Do you mean objects on Earth? If so, no, as Earth blocks the view.
But objects in the sky can be seen from that far away if they are large enough or bright enough.
If you wish to assert we magically can't see after some distance, please explain what happens to the light form the object or what other magic stops us from seeing it.
When the sun is up, you know how far we can see? I do because I've looked it up.
Yet you can provide no reference nor justification. Instead all you can do is pull a number from no where.
And are you really trying to claim that the sun and moon are within 11 miles, yet their distances doesn't appear to change?
No matter how big the sun supposedly is, this view is more consistent with an object being projected.
And that view is entirely inconsistent with reality.
Why do I say that? Because the sun actually being "up" massively distorts vision. That can't happen from a distant object. Remember the two-way mirror example? This only works if light is cast from within a mirrored surface. If light is on the other side, you can see the two-way mirror for what it is.
And we can add analogies to the growing list of things you either fail to understand or intentionally lie about.
That only needs a mirror to get a mirror effect.
But the light doesn't need to be cast from within that.
You could even theoretically have a very bright spotlight inside the dark room pointing directly into the bright room, as the only light source for that bright room.
You would then be able to see that light source, but nothing else from the dark room.
This effect is quite simple to understand, you are in a bright environment so your eyes adjust to that level of brightness so dark things can't be seen.
If something is bright enough, you will see it, if it is too dark, you wont.
You can even get the same effect at night by having someone in a dark area shine a flashlight in your face.
All you will see is the flashlight and a few things illuminated by it.
No need for any mirror.
A similar perspective problem happens here, stars only show up when the sun is gone, and while it's near, distance is very distorted.
Again, pure nonsense.
Distance is not magically distorted by the sun.
Instead it is bright (and light scattering from the atmosphere is also fairly bright), making it much harder to see darker objects.
What we observe is just what you would expect with the RE model of a very distant and large sun.
It is nothing like what you would expect for a FE with a close sun.
Either we have basically a column of light effect (what you'd really see if a massive distant object cast light, not a tiny version of it)
In order to have a column of light effect you need a thin column of light surrounded by regions which aren't as well illuminated.
Just what makes you think the sun should produce a column of light all on its own?
it is a normal sized cat that nonetheless trolls you by always keeping pace whether you are running or walking and even if you are moving away.
So what you are saying is that the sun magically follows you? Maintaining your distance?
The one time I got the sun's position to change, we were moving around a curved road that had hairpin turns, and somehow my parents, while driving got the sun to set twice.
And you have had that addressed.
It in no way helps support a FE.
So what are we talking about here? We are talking about Occam's Razor in this case favoring the weird. The simplest explanation is usually the right one.
And the simplest explanation is that the sun doesn't appear to change size because of how far away it is. That the distance you move is tiny compared to the distance to the sun.
That it appears to set because Earth blocks the view.
No need for any FE magic.