My apologies if this has been brought up before, but I couldn't find anything that was directly on point. Some of these topics have definitely been covered tangentially, but I'm curious about how they interact. I'm adding numbers only to make it clear what stuff belongs to what arguments.
1. The wiki says that FEers can calculate the distance to the Sun to be 3,000 miles, triangulating its position from the equator and from 45 deg of latitude. It quotes an article
on this experiment to measure the circumference of the Earth that says,
http://theflatearthsociety.org/wiki/index.php?title=Distance_to_the_SunThat is, as we move from Florida to Pennsylvania, our distance from the sun increases by about 30%. As a consequence the apparant size of the sun should decrease by 30%. We see no noticeable change in the apparent size of the sun as we make the trip. We conclude that the flat earth/near sun model does not work.
That is to say, if the Earth were flat and the Sun near the surface, its angular size would regularly change. The angular size of the Sun never changes, therefore the premise cannot be true.
2. FEers counter this by arguing that the atmosphere magnifies the angular size of the Sun as it recedes from us.
http://theflatearthsociety.org/wiki/index.php?title=Magnification_of_the_Sun_at_SunsetQ. If the sun is disappearing to perspective, shouldn't it get smaller as it recedes?
A. The sun remains the same size as it recedes into the distance due to a known magnification effect caused by the intense rays of light passing through the strata of the atmosphere.
3. In order to explain nighttime in an FE model, something
must block the Sun's rays from being visible to half of the Earth at any given time. The wiki argues that it is blocked by the atmosphere:
http://theflatearthsociety.org/wiki/index.php?title=The_Setting_of_the_SunThe cause of night is simply due to a non-transparent atmosphere. As the sun recedes its light is dimmed and lost to the increasing number of atoms and molecules which intersect the light rays.
4. The contradiction should be obvious. Numbers 2 and 3 cannot both be true. If the atmosphere magnifies the angular size of the Sun as the Sun recedes from us on a flat Earth, then we would live in permanent daylight, especially if its angular size is magnified exactly proportionally to its distance from any observer (required for FET).
If the atmosphere blocks light from the Sun to create nighttime, then the angular size of the Sun would change as it recedes from us.
I don't see how this can be resolved. Clearly, FET directly conflicts with our most basic daily experiences.