So Andy... I have a large Newtonian Reflector telescope capable of extremely high resolution and magnification. I frequently use it to observe planets and their moons, and our moon, and I've gotten some pretty awesome views of the ISS, so I know for a fact that they're all up there. NASA is not lying about the ISS being in orbit. I know where to look because I get regular emails about when it will be overhead.
And, using my own eyes, I have seen that our moon is spherical, Jupiter is Spherical, Mars is Spherical, Venus is Spherical, Saturn is Spherical with rings, etc.. All those spherical planets (and moon), and you're trying to tell me that our planet is conveniently FLAT?
Second, that photo you conveniently posted about being able to see Chicago from 52 miles away.. You do realize that what you're seeing is slightly truncated, right? We're not seeing the very bottom of these buildings, because they're being 'cut off' by the horizon. Second, have you never heard of refraction?? Our atmosphere causes refraction - very slight curving of light - enough refraction, in fact, that objects that we would not normally be able to see from great distances, will still APPEAR to be in our direct line of sight (above the horizon) even after they have gone below the horizon.
A perfect example of the above is the sunset. When we see the sun go down, it's actually lower than what we're seeing. Typically, when the sun first 'touches the horizon' from our perspective, it's actually already set, but the atmosphere is curving its light so much that to us,
it will still appear to be above the horizon.