How can one prove that the earth is a sphere (or close to it)?

Which would be a great line of discussion with them because they’d then have to explain how gravity and light works in their model because it surely doesn’t fit with any other empirical evidence out there.
There is also the minor problem a sun at an orbit of 5000 miles must be tiny, certainly not massive enough to sustain nuclear fusion of the observed levels.

But those are all rational questions to ask and seeing as we aren’t dealing with rational people such lines of inquiry are doomed to fall on deaf ears.

If we can’t prove definitively that the world isn’t flat, well then, maybe it is?

How about a gyroscope?

Start at any point on the earth with a powered gyroscope mounted on a 3-axis gimbal. Orient it so that it aligns with the local gravity vector, and then wait. If the flat-earth model is correct - regardless of whether it’s mounded, or truly flat as a pancake - then the gyroscope will forever remain in this orientation. If the spherical-earth model is correct - specifically, the part of the spherical-earth model that says the spherical earth spins on its axis - then the gyroscope will deviate from its original orientation, with its own axis tracing out a cone over the course of any given 24-hour period. The half-angle of that cone will vary from zero (if the gyro is at the earth’s north or south pole) to 90 degrees (if the gyro is at the earth’s equator).

After 24 hours, the gyro will return almost to its original orientation with respect to the local gravity vector. It will be off by a bit, because the earth will have moved about 1/365 of the way along its orbit around the sun; 24 hours brings you back to facing the sun again, which is not the same as completing one full spin in an absolute sense. If you wait 365 days, then the gyroscope will finish tracing out another cone, returning to align almost perfectly with the local gravity vector, just like it did when you started this whole test. The flat-earth model won’t have a good explanation for this.

I’m probably not accounting for all of the various celestial movements - a real astrophysicist can probably nail down exactly what to expect - but you can see the general idea, i.e. a gimbaled gyroscope provides an unbiased reference vector that always points in the same direction and can provide objective proof that the earth itself is in motion, contrary to the flat-earth model.

I retract this after reading subsequent posts and links describing how flat-earthers think that the sun revolves above the Earth disk like a flashlight throwing a narrow beam on the parts where it’s day.

Plus he sucks on Match Game!

Turns. It’s easy enough to say you ended up back where you started because you made a circular trip around a flat world as it is to say it was a straight trip around a sphere. Since facts and logic don’t matter to them, “easy to say” is all it takes.

This model of the sun is rather problematic, though, given their geographic model. The shape of the illuminated portion of the world at any given time is like a big slice of pie. At equinox, for example, the sun is directly over the equator, and it somehow casts a pointy lobe of light up towards the North Pole that gets ever narrower, and at the same time a giant fan of light towards the Great Ice Wall that gets ever wider.

One thing I’ve wondered is how flat earthers think satellite TV works. I mean, anyone who’s ever put up a satellite dish can tell you that aiming them is finicky as hell. And basic geometric principles tell you that they really are pointed at a fixed spot far above the surface of the earth. Something in that direction is sending a signal. If it’s not a geostationary satellite in orbit over a globular earth, how does it stay in that fixed position?

Actually, the apparent direction of all objects in space is a real problem for the flat earth model. For example, if you take the angular distance of the sun above the horizon at noon at two different locations, the difference in that angle is compatible with the sun being far away and the earth being a globe, or the sun being near and the earth being flat. But as soon as you add a third point the flat earth model falls apart because the geometry doesn’t work. And this is especially the case if you start looking at east-west variations - if you calculate the apparent difference in direction of the sun between Cape Horn and Lima, you’ll get a very different height of the sun over the pancake earth than you will if you calculate based on the difference between Cape Horn and Auckland. This is complicated geometry and requires precise timed observations, however, so I expect it wouldn’t make a dent in a flat earther’s beliefs.

If flat-Earthers won’t be persuaded by a simple photo showing them that the Earth is round, then all of these other complex mathematical proofs are rather unnecessary.

It’s like trying to prove that a giraffe has four legs. If showing the skeptic a photo of a 4-legged giraffe won’t persuade him, then what else is needed?

It works by pushing the buttons on the remote, and the show comes up on the TV. And you can’t explain that if the Earth is a sphere. Therefore, the Earth must be flat!

Don’t bother trying to explain it as if the Earth is a sphere. I just said you can’t do that, so you’re wasting your time.

They don’t even believe in satellites.

The problem will soon go away as all Flat Earthers, not using GPS since it can’t work without satellites, get lost forever.

If I believed in the flat earth, I would probably say the sky (which is a solid dome) reflects the radio signal from a ground-based transmitter.

We can prove that the earth is round, not flat (and have done so, abundantly). The problem is not a lack of proof, it is a reflexive dismissal of any proof, either by claiming it to be measurement error, or by showing that the flat-earth model can also account for those observations (without going into the details of the exact values/calculations, which would unequivocally show the flat-earth model to be incorrect), or by claiming fraud/conspiracy.

It’s a bit like the speed of light being constant no matter what, with all else bending to conform to that constant: flat-earthers hold that the earth is flat, and that this is an incontrovertible truth, and all else must be made to somehow conform to that constant. The existence of satellites, the Apollo missions (and any “photographs” that come from it), the durations of long-haul international flights (which fit a sphere but not a flat earth), the measured details of the apparent motion of the sun and moon as seen from multiple locations on the earth’s surface (which can’t be duplicated by solar/lunar discs circulating above a flat earth), transantarctic flights - all can be dismissed as fraud/conspiracy, error, or unverified by someone who hasn’t personally experienced/measured them and never will.

This doesn’t prove anything if you believe that the people who operate the GPS network are part of the conspiracy. There were ground-based navigation systems before GPS, like Loran-C. They weren’t as accurate as GPS, but it’s not easy to explain or demonstrate why GPS is inherently more accurate.

For those with an idle curiosity of the flat earthers, I’d recommend just click on the comments button on any NASA Facebook post. They are legion. You’ll get a good idea of their main talking points (“The horizon is always eye level!”, “Water always finds a level”, “Where are all the satellites?!”, and “water doesn’t stick to a spinning ball!”), as well as see several truly committed people who dedicate far too much time trying to engage them with actual facts.

They have been struggling with this. How can you get on an airplane and fly in a straight line from Santiago Chile to Sydney Australia without passing over California, as the FECT map would suggest? In order to deal with this, they have been investigating some sort of discontinuity theory, akin to the Earth itself being populated with wormhole-like distortions that make curved lines seem straight. I am at a loss to find a link for this, though.

A map of Magellan’s 1521 route on a flat Earth.

Hmm, how about compasses? There is a magnetic north, and all compasses point to that, but how does magnetic south work?

The magnetic field from a simple dipole magnet looks like this. If a vertical magnet was deep under the center (north pole) of a flat earth, all compasses on earth would point to it.

Imagine an array of bar magnets arranged in a circle under the flat earth: the magnetic-north of each bar magnet points toward the north pole, and the magnetic-south of each bar magnet points toward the antarctic ice-wall (maybe I’ve got that backwards?). Consistent with our observations of compass behavior, the magnetic field lines would be parallel to the surface of the flat-earth, and would form radials from the north pole (at the center of the flat-earth) to the antarctic ice wall.

This would not explain magnetic dip, particularly the fact that dip reaches 90 at the magnetic south pole (see map at link). But the common flat-earther won’t accept any measurements of this that he does not make for himself.