Partially because of @Niala joining this conversation and not immediately being able to present the counter arguments, I finally feel I'll have to give a try at teaching you cool cats, some calculus, and maybe explain some of the finer points of vector calculus, or at least some trigonometry, lol.
Maybe I am part grey I do have a huge forehead, lol. Just call me Bob MacG, ha ha ha.
Umm, sorry nope. These do not hold up at all to closer scrutiny -- by anyone that has even some of the basic understanding of physics, geometry and calculus.
Sigh... this might take quite a bit of writing...
I'll try and keep it simple and not actually use too high a level of physics nor calculus actually, if I can, lol. As, in fact, that would likely actually take months -- like a real high-school or college course on the subjects.
First, let's try and get some perspective, as far as actually being able to see curvature, shall we?
You can't even normally start seeing the curvature of the earth until above 50,000 ft, and maybe not significantly noticeable until above 60,000 ft. The very minimum altitude at which the curvature of the horizon can be detected is at or slightly below 35,000 ft. as long as you have a field of view wide enough (60°) and nearly cloud free.
The minimum of 35,000 feet is a realistic cruise altitude of a commercial airliner, but a passenger window probably won't give you the necessary 60° field of view to be able to notice the curve.
And if there is any cloud cover, you can forget it -- because those clouds are at about your level and will then look un-curved, just as if you were on the ground trying to see the curvature of the ground.
To try and help everyone understand the magnitude of scale we are talking about, think about this -- if the earth was shrunk down to the size of a billiard ball it would be SMOOTHER than the billiard ball! Although, ever so slightly egg shaped.
Before I even get into the calculus and trigonometry, there are some very basic problems with the video descriptions of a flat earth.
For one, the flat earth theories above neglect to address the fact that in the southern hemisphere, "the north star", Polaris -- is not visible, and many, many stars and constellations that we take for granted in the northern hemisphere are not visible from the southern hemisphere.
And the southern hemisphere has many stars and constellations that can't be seen from the northern hemisphere.
If these constellations were on a "dome", "the north star", Polaris, would have to be at the center apex of this dome, and therefore it would certainly be visible from any part of the Antarctic "ice wall".
Also, in the northern hemisphere the stars appear to rotate anticlockwise around the northern celestial pole and "the north star" -- Polaris. In the southern hemisphere there is a star that comes close to being a "southern Polaris". It is Sigma Octans, which is 1 degree away from the "south celestial pole". This star, along with the rest of the stars, appears to rotate clockwise around the "south celestial pole", as you would expect on a rotating sphere or cylinder.
And another thing, in the southern hemisphere we see a much different view of the moon compared to the view from the northern hemisphere.
And in the southern hemisphere the phases of the moon work differently.
And although it isn't entirely true that water goes down all drains counterclockwise in the northern hemisphere and clockwise in the southern hemisphere, if you do place water in a drain-able container, say in a large cone funnel, or drum, that doesn't have any geometric structure that would influence rotation, plug the bottom, fill with water and let completely settle so it is stable and not moving, as you don't want any energy from the way the water was introduced into the container to influence rotation, and then carefully unplug the to bottom of the container -- then, more often than not, you will get the proper rotation for your hemisphere.
-- In 1908, the Austrian physicist Ottokar Tumlirz described careful and effective experiments that demonstrated the effect of the rotation of the Earth on the outflow of water through a central aperture. The subject was later popularized in a famous 1962 article in the journal Nature, which described an experiment in which all other forces to the system were removed by filling a 6 ft (1.8 m) tank with 300 U.S. gal (1,100 L) of water and allowing it to settle for 24 hours (to allow any movement due to filling the tank to die away), in a room where the temperature had stabilized. The drain plug was then very slowly removed, and tiny pieces of floating wood were used to observe rotation. During the first 12 to 15 minutes, no rotation was observed. Then, a vortex appeared and consistently began to rotate in an anticlockwise direction (the experiment was performed in Boston, Massachusetts, in the Northern Hemisphere). This was repeated and the results averaged to make sure the effect was real. The report noted that the vortex rotated, "about 30,000 times faster than the effective rotation of the Earth in 42° North (the experiment's location)". This shows that the small initial rotation due to the Earth is amplified by gravitational draining and conservation of angular momentum to become a rapid vortex and may be observed under carefully controlled laboratory conditions.https://en.wikipedia.org/wiki/Coriolis_force#cite_note-47
Also, I do competition target shooting, as well as my favorite paintball, and for super long distance shooting, not unlike in marine sniper school ( on an aside, my dad was with a platoon of marines in Vietnam, and in marine boot camp -- he tested expert marksman), you do actually have to take the spin of the earth into account in your windage calculations.
According to the Greek biographer Diogenes Laertius, he wrote that the Greek scholar, polymath, and scientist -- Pythagoras, gets the credit for the first ancient that said he believes the Earth is a sphere, and generally the credit goes to Aristotle for proving that the surface is indeed curved.
However, it is very likely that many cultures knew, even before Pythagoras, that certain things observed in the measurements of the Earth itself, and the way constellations appear in the sky -- alluded to a spherical earth.
Easily, by the birth of Christ, much of the educated world understood the world was spherical.
And contrary to popular legend, Christopher Columbus did not discover that the Earth was round. There was no debate over the Earth's shape before his voyage. Only, the circumference of the Earth was what was was not exactly known or understood, they had a very hard time believing it is as big as it is.
An interesting thing is, that many of the ancients had already calculated how big it was using trigonometry, and were only off by a very slight margin, and come very close to our more accurate measurements with more advanced measurement tools -- as well as measurements from orbit.
One well known example is from about 200 years before Christ, Eratosthenes (275-194 B.C. in Alexandria, Egypt) was an accomplished Greek scholar and polymath. He respectfully earned the nickname "Beta" because being so good at mathematics, geography, philosophy, and astronomy, that at worst, he was only the '2nd best' in each field, lol (he prepared a star map containing 675 stars, suggested that a leap day be added every fourth year, tried to construct an accurately-dated history, determined the obliquity of the ecliptic, and developed the "sieve of Eratosthenes" method of finding prime numbers).
Here are some links with some exercises you can do to help understand it better. They also go into more detail about exactly how Eratosthenes calculated how big it was using trigonometry:
Eratosthenes Measures Earth's Circumference
The Earth's Curvature is Tasty
And then if you understand vector calculus and can understand how Newton modified Kepler's third law to explain gravity, you clearly see why it completely proves our accepted heliocentric model, thus determining the flat earth model false as it relies on a geocentric model.
And not only that, let's discuss this idea of buoyancy. There is a way a regular person can test gravity and it is not just buoyancy, lol. And this is very simple to demonstrate.
Actually, a common scale in your bathroom works with spring tension, if it was because of being buoyant, you'd weigh more in a vacuum, which isn't the case. And so, you can measure gravity, as a measurable force, very different than buoyancy.
If you put a weight on a spring in a vacuum container, you can go to different parts of the earth and it will stretch more or less depending on how strong the gravity is in those specific areas.
Gravity is more intense where the earth is made of things with more mass, for example, like lead as opposed to just sand.
And so, as a matter of fact, as proof the earth is indeed a spinning sphere, you could take the same device to the equator, and although the centrifugal force is not enough to counter gravity and throw the water off the surface of the earth as some of the above videos like to try and make it seem, the centrifugal force will make things weigh a little less at the equator, than at, or nearer, the poles, and the weight will stretch the spring less than it would at the poles.
Happy Physics learning,