The distance from pole to pole is approximately 20,000 miles; the diameter of FE, then, is about 40,000 miles.
If the sun is only 7000 miles up, you can make a right angle triangle from where you are standing, to directly below the sun, up to the sun.
For a right angle triangle:
tantheta = (the height of the sun) ÷ (the distance to the point directly below the sun)
Where theta is the angle of the height of the sun versus the ground from where you're standing.
If you're at the outer circumference of the FE, and the sun is over the opposite side of the circumference, theta is 10°. Which is to say, the sun never goes beneath 10°.
But wait, the sun orbits above the equator, so the max distance is 30k (pole to pole, plus half again to the far equator).
So the lowest the sun can go, according to this model, is 15°.
Of course, by this point the sun should have faded due to distance, so the actual minimum angle is necessarily higher.
Therefore, if I observe the sun below 15°, at any time, this FE model is false.
If I'm at the north pole, and the sun orbits the equator, then the distance is fixed. Either I would always see it, spining in complete circles around the sky at the same angle, or I would never see it because it's too far away.
Here's some napkin math to try on for size.
The distance from pole to pole is approximately 20,000 miles; the diameter of FE, then, is about 40,000 miles.
If the sun is only 7000 miles up, you can make a right angle triangle from where you are standing, to directly below the sun, up to the sun.
For a right angle triangle:
tantheta = (the height of the sun) ÷ (the distance to the point directly below the sun)
Where theta is the angle of the height of the sun versus the ground from where you're standing.
If you're at the outer circumference of the FE, and the sun is over the opposite side of the circumference, theta is 10°. Which is to say, the sun never goes beneath 10°.
But wait, the sun orbits above the equator, so the max distance is 30k (pole to pole, plus half again to the far equator).
So the lowest the sun can go, according to this model, is 15°.
Of course, by this point the sun should have faded due to distance, so the actual minimum angle is necessarily higher.
Therefore, if I observe the sun below 15°, at any time, this FE model is false.
Oh wait, how about this?
If I'm at the north pole, and the sun orbits the equator, then the distance is fixed. Either I would always see it, spining in complete circles around the sky at the same angle, or I would never see it because it's too far away.