The angle sum of a triangle on a sphere is dependent upon the area covered. It ranges from 180 degrees when it covers no area, up to 540 when half the area is covered, and 900 when the entire surface is covered. i.e. if you take whatever fraction is covered and multiply it by 720 degrees, then add 180 degrees, that will give you the angle sum.
You suggest covering a distance of 0.8 km. Approximating this as a square that gives 0.64 km
2, compared to Earth's surface of ~510072000 km
2. That means your suggestion covers less than 1.25 billionths. This gives an additional angle of less than 900 billionths of a degree or 0.003 arc seconds.
That will require extremely accurate measuring. (to change it back to a triangle, you have roughly have half the value due to how small this is)
Lets say we want an angle difference of 1 degree (still quite small and other errors could cause issues). That is 1 720th of the maximum angular excess for a sphere, and thus needs 1 720th of the area of Earth. That means we need a triangle with an area of roughly 700 000 km
2. Again approximating it as a square, that means you need a length of roughly 850 km. (Again, as it is over such a small area, you can probably just double the required area to go from square->triangle, giving a required length of over 1000 km).
This can be done a lot easier with the help of the stars, at least on a qualitative level. At the equator we can observe 2 celestial poles. We start at one point and notice the poles are 180 degrees apart. This forms one line of our triangle. We now move along the equator for a decent distance (or have someone already there). The exact direction and distance isn't important (but it should be a significant distance, preferably thousands of km). We now observe the stars again, and measure the angle between the poles.
If Earth is flat, this angle needs to be less than 180 degrees, with the poles now appearing back towards where we came from. i.e. if we went east, the celestial poles should appear slightly to the west.
Instead we find them 180 degrees apart, always, clearly showing Earth is round.
You´re right in my opinion I can´t explain any other reason for day and night than a round earth orbitting a star.
All you need is a round Earth, a distant light, and some relative motion.
The main cause of day and night is Earth rotating. But the light orbiting us has the potential to explain it. But it then runs into issues with variations around the year which shows it isn't orbitting and instead circling in a complex pattern, meaning Earth would be rotating and either orbiting the light or having the light orbit us.
my biggest question to the FE really is why would al this be a conspiracy.
The only explanation that has any semblance of sense is Satan leading people away from God.