I know of a way to prove the shape of the earth.
You need 4 emitters and 2 sensors.
Place 4 emitters on the equator and the 2 sensors on the north pole, above eachother. Like this.

In which the red dots are obviously the emitters and the yellow dots the sensors.
Now. If you send out a strong signal (whatever the type of signal) out of the 4 emitters, you can recieve them with the sensors.
If the earth is flat, the sensors should pick up the signal at the same time, meaning that the emitters are positioned in the length of the right corner with the 2 sensors. Like this.

If the earth is round, the lower sensor should pick up the signal a little earlier than the higher sensor. Like this.

By measuring the difference in time and the distance between the sensors and emitters, you can calculate the angle that the signal comes from.
Only this would prove the shape of the earth. I think you will agree.
Has this been done? results?
PS: I'm trying to make perfect sense here. Please do that also.