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Well, I do not believe that Earth is flat, but I met some conspirationistas believing that all physics we learn in school is twisted, all the Earth's pictures from space are photoshopped by NASA, etc, etc.
So those guys wanted to put a satellite into orbit, take some pics, and see for themselves.
Of course, a satellite won't stay above a flat Earth, but what other very simple means to prove/check that earth is round (well, geoid) do we have?
I am looking for simple means, available to anyone, that do not need any external tool or knowledge that a naysayer would reject.
Some things I've considered:
Meteorological balloon with camera and a phone with GPS, with a parachute to recover it. It has been done by amateurs, and in good conditions, you can see the Earth's curvature.
Measure the Sun's height above horizon at noon at two different latitudes. The difference, along with some simple geometry would give you Earth's diameter.