I am a RE'er who believes perspective cannot describe the setting of the sun. I am not here to convert you. I would like a FE'er to explain if my calculations or assumptions are in error. I'll start off with a "worst case" scenario.
On this page:
https://wiki.tfes.org/Erathostenes_on_Diameter, the diameter of the Earth is claimed to be 25,000 miles. So if the sun orbited over the Antarctic "ice wall", it's path would have a diameter of 25,000 miles. That means, the farthest a person on Earth could possibly be from the sun is 25,000 miles. This is the adjacent side of our triangle.
According to:
https://wiki.tfes.org/Sun, the sun is 3,000 miles above the surface of the Earth. That is our opposite side.
The angle we are using is 90°. We solve the triangle using a Side-Angle-Side formula, and get 6.843°. If I understand the geometry correctly, that should mean the sun could never be visibly lower than 6.8°. Since the sun at its southernmost point orbits the Tropic of Capricorn, the actual angle would be larger. My calculations yield about 8.5° as the minimum for that distance.
Now I'll use a scenario that I have personally observed. I vacationed in Hawaii a few years ago and watched the sun set on the ocean. The sunset time there was about 18:45. That is when we saw the sun disappears at the horizon. At that same time, is is approximately noon (11:45 AM) in Bangkok. The distance between these two locations is about 6,596 miles (using globe Earth measurements, it may be less on the flat Earth). If we create a right triangle with an adjacent side of 6,596 and an opposite side of 3,000, we get an angle of 24.457°. If the Earth was flat, that would mean that someone watching the sun set at 18:45 in Honolulu would see it at more than 24° above the horizon. However, I have personally seen the sun set on the ocean from Honolulu. I know that it was lower than 24°. I did the math, and for the sun to be 1° above the horizon, Bangkok would have to be 171,869 miles from Honolulu.
But 1° is still 60 times greater than the angle Samuel Rowbotham (
http://www.sacred-texts.com/earth/za/za32.htm) claims that objects disappear due to perspective. According to my calculations, for the distance between the sun and the horizon to be imperceptible (1/60°) at a 3,000 mile altitude, the sun would need to be a little over 1 billion miles away from the observer. This, obviously, creates other problems.
I could possibly be talked into perspective making up 6.8°, but not 24°. Are there any errors in my calculations? Have I made any incorrect presumptions?
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