No David, it doesn't. It's close but not quite.
In fact, it is very close. Close in the same sense the surface of water is level. It's actually very slightly curved but so slightly that for practical purposes, it's fine to discuss it in terms of being flat and level.
But close isn't exact. In actual fact, the theoretical horizon (i.e. the horizon line assuming no hills or other obstructions) is .043° below "the middle of our eyes", as you put it. A long way below the resolution of our vision.
The horizon line drop is much slower as you ascend than it is as you move along the surface. This is because you can see more and more of the surface as you ascend. But you can actually see the drop, if you go high enough and are paying close enough attention. At 40,000 ft, where large commercial aircraft cruse, the drop is about 2.5° which is the equivalent of about 5 widths of the full Moon. That not so much that you'd likely notice it from a plane for two reasons. First because it's not a huge difference and second because from that altitude, you lose easily recognizable reference points. But, as I said, if you're paying close attention, it would be detectable with the naked eye.
It would be all but physically impossible to "set the camera at the horizon" in a weather balloon, which is anything but a stable platform.
Further, something pretty close to 100% of cameras sent up on high altitude air craft (including balloon) are equipped with extremely wide angle, if not actual 'fish-eye' lenses, which give nice wide field of view images in exchange for distortions.
Interestingly, the distortions could actually be used to do the measurement. The horizon would only look flat in such a camera when the horizon line was passing directly through the center of the image (i.e. when the camera was pointed directly at the horizon). Any deviation above or below the horizon line would "bend" the horizon in the image. You could conceivable set up a computer to make constant adjustments to the camera angle to maintain a flat horizon line, which would force it to look further and further down as the altitude increased. This wouldn't give a perfect reading of the down angle because, while adjusting for the horizon line drop, it would also adjust for the actual curvature of the Earth itself which becomes more and more pronounced with altitude. As a result, any such experiment would give a larger down angle than is actually caused by the horizon line drop itself.
The Pythagorean Theorem has nothing to do with assuming anything at all. It has to do with the nature of right triangles - period. But no one suggested that the calculations themselves prove anything anyway, David.
If this were a new idea and this were still in the hypothesis stage of scientific inquiry, then the calculations would be considered a prediction of the globe Earth hypothesis.
The FET says the horizon line doesn't drop but the reality is that it does. Not only does it drop but it drops exactly in accordance with the math that you've been shown.
Yes, people have actually measured it...
Measuring Horizon Drop And Earth's Equatorial Bulge From Rocket Launches
Once again, the FET is flatly falsified by empirical data and the Pythagorean Theorem.
Once again, you will not be convinced.
Clete
