Backyard experiments to falsify the Flat Earth theory I recently became aware that the flat Earth theory still exists in the 21st century, and has colored the views of a friend of mine. Roughly speaking, the tenets are:


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*The Earth is a flat disk, with the south pole blown up into a circular "ice wall" where one would expect Antarctica to be.


                                        


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*The sun and moon are either spheres or disks floating above the earth and moving in a spiral pattern with the seasons.

*NASA is part of a conspiracy to conceal the truth, and sends us animations and faked photo shoots.
The Flat Earth Theory is a scientific theory, in the sense that it makes falsifiable predictions about the universe that can be seen to match observation (or not). What are some good arguments or backyard experiments that could convince a layman that in fact the Flat Earth Theory is false?
A similar question and useful related reading is What is the simplest way to prove the Earth is round?, but it focuses more on the theoretical and conceptually simple side, applicable to the proverbial "numskull cousin". This question is more focused towards convincing a doubtful scientific person using (preferably low-tech) experiments and observations.
 A: If the sun is a disk (or sphere) that is a certain distance above the earth, close enough that you get it at different angles above the horizon depending on where you stand, then it has to look like a different size to different people. If it looks the same size, then you cannot explain that it's at a different height above the horizon. See this diagram:

If they can explain at what height $h$ the sun is "affixed to the sky above" to give rise to the observation that the angle of the sun changes as you move in the North-South direction, then it immediately follows that the sun must appear to have a different size in the sky. Which a simple sextant measurement will tell you is not true.
A: Can you convince your friend that time zones are for real?  If he will believe that it is nighttime in China when it is daytime in the US, then his disk theory can't be correct.
A: Airplanes. Note that dozens of flights cross every ocean and the equator in all directions every day. If the Earth were a disk, it would actually be impossible to do that.
For example, if the border of the disk were more or less where the borders of a planisphere are, it would be impossible to cross the Pacific. How would your friend explain how flights from LA to Tokyo only take 11h if it had to cross the whole of the US, the atlantic, and the whole of Eurasia?
A: Take an arrow which you put tangent to the earth (assume it to be a perfect sphere). Now, travel around in such a way that

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*you enclose some finite area,


*do not rotate the arrow locally.
Coming back to your starting point you will notice the following: Although you did not rotate your arrow locally, you will end up with an arrow which is rotated compared to the one you started with. The reason is: Due to the finite curvature of the sphere, you will gain a geometrical phase. The latter is the angle about which the arrow was rotated.
For more information read about: Parallel Transport
A: If you believe that anyone lives on antarctica at all, or really anywhere south of the antarctic circle, then you can use the "midnight sun" effect, which should not happen in the flat earth theory (because the sun moves around the "antarctica ring" during northern winter). Surveillance cameras will also work for this, if eyewitness accounts are not believable.
A: Try https://www.insecam.org/ .Take a flat map of earth and make them go to the cities and watch the light and the online clocks. Nothing but a sphere fits the data.
If the sun is going around a disk there would be night almost simultaneously over the flat disk, whereas the cameras will show progressive changes and night for half of their flat earth.
A: I live close to Lake Erie and often see scenes like in this picture.  Note that the bottom of the cargo ship cannot be seen due to the curvature of the Earth.

A: Related to the Andrea di Biagio answer. Here is a typical flight path for the Beunos Aires-Auckland route. The distance is approximately 10,300 km by the shortest route along a sphere. Direct flights are offered by Air New Zealand and take 11h40m - an average speed of 882 km/h.
Looking at the map you present, the distance from Auckland to Buenos Aires looks to be about twice this by the most direct route. Therefore the plane would have to fly supersonically. But Jumbo jets and the like, cannot and do not fly supersonically.

A: Have them pull out their smart phone and open up Google maps and touch the icon to zoom to their current location. Remind them that what they just did is only made possible by satellites in orbit using clocks specially tuned according to general relativity to maintain accurate synchronization with clocks on the surface (i.e., in the smart phone). Welcome them to believe in a flat Earth as long as they remember they are lucky that everyone involved in making GPS work believes it's an oblate spheroid.
Have them travel to a dark spot in the northern hemisphere and observe and partially catalog the night sky. They should make notes on the big and little dipper, Orion, Cassiopea, and other major constellations. Have them travel to a dark spot in the southern hemisphere and repeat the process, noting that none of the familar constellations are visible but all new ones like the Southern Cross are visible. Have them return to the north one more time to verify that it is their travel that made the sky look different. Have them attempt to explain this with a flat Earth.
Many refutations on the Flat Earth Wiki rely on the "vanishing point" of perspective. The assertion is that things don't disappear from sight because of a curved Earth, but because of them "sinking to the vanishing point". Commision a helicopter ride on a calm day. As the helicopter rises, point out that while perspective makes the helipad seem smaller with distance, it doesn't move laterally through the field of view.
Do they really think that a secret known to more than 500 people can be kept for more than 50 years? https://en.wikipedia.org/wiki/List_of_space_travelers_by_name
If the Earth is flat, the entire American space program was/is fake. If that's the case, why would the Russians, Chinese, Iranians, North Koreans, etc, continue to say nothing about the American space program being fake? Why would they all strive to create their own space programs and ballistic missile systems? Perhaps some nations, like Russia, might also have a vested interest in the conspiracy, but not Iran. Not North Korea. Not Venezuela.
In history, people who have made demonstrably true realizations and discoveries that are inconvenient or contrary to those in power have been persecuted. Why are no flat Earthers persecuted? Why does the Catholic Church not support flat Earthers? Why does everyone pretty much ignore them?
I think a flat Earther might have said it best:

...even cults seem to all be ball earth.

Source
Go with your friend and re-create all of the experiments from the seminal flat Earth book, starting here: http://www.sacred-texts.com/earth/za/za06.htm and using this math for calculating what should be visible: https://en.wikipedia.org/wiki/Horizon
I'm pretty sure your friend will prove to themselves that the alleged results of these experiments from Earth Not a Globe are actually falsely reported.
Alternatively (as in experiment 7) the alleged expected result for a round Earth from the experiment is falsely reported. For example, the author wrote that if the Earth were round, the horizon should seem to curve downwards left-to-right. Anyone considering a globe for only a few minutes could see that makes no sense. Suppose the round Earth expectation were true. Would not the necessarily fake Moon landing footage have showed such a curvature? Especially since the wrong-headed thinking that creates the expectation of curvature would further suggest the curvature expected would be greater for a smaller round body like the Moon. Yet the curvature was not faked in moon photos for the simple reason that we should not see curvature of the horizon on a round body as suggested by experiment 7. See: http://science.nationalgeographic.com/science/photos/moon-exploration-gallery/#/tranquility-base_1255_600x450.jpg
Really, just reading this book should be enough to do it. Chapter III begins in especially hilarious fashion by supposedly using science to prove the Earth does not rotate while instead actually showing the author knows nothing of science: http://www.sacred-texts.com/earth/za/za21.htm
A: Foucault Pendulum is a great example.
The original purpose of this experiment was to prove that earth rotates relative to the stars and not the other way around, yet nevertheless it proves that the earth rotates in a way which contradicts the "flat earth" theorem.
This experiment can be easily recreated at home, if you don't live close enough to equator.
A: You need three flat Earth theorists on different continents (or otherwise well separated) all in on a (video) conference call, and have them measure the azimuth and elevation angles of the sun at the same time.  The set of angles that they report will be inconsistent with their locations being on a flat disk laid out as in the map in the question.
This is a more modern way of doing Eratosthenes's experiment.  Here we need three observation points to eliminate a possible objection of the conspiracy theorists: the sun actually isn't all that far away. (Eratosthenes used the fact that the rays from the sun are all parallel -- I'm not giving the flat Earthers that much credit).
This is easy to spell out if you pick the times/places such that
1) For one person the sun is directly overhead,
2) Another person is due north of person 1,
3) Another person is due east (on the same line of latitiude) as person 1.
If you assume that the sun is at  the location consistent with observations (1) and (2), person (3) cannot see the sun just being to his/her west given the
geographic layout in the original question.
