Ah, but would they actually be parallel on a flat earth?
Say the earth is disc-shaped. Then the center of gravity is only directly beneath you if you're standing at the exact center. You get ever-so-slightly not parallel lines, just like on a round earth.
The fun part of a disc-shaped earth comes as you move towards the sides, and gravity, still pointing towards the center, makes you stand at an increasingly acute angle to the surface. The ground beneath you will then appear like one big endless mountainside, with an increasingly steep slope the further away from the center that you get.
Depends what causes things to stick to the flat Earth. IIRC flat earthers have various explanations for gravity, including the disc continuously accelerating upward; in that case you'd experience the same force everywhere on it.
My math might be wrong, but if we were accelerating at 9.8m/s/s for at least 4000 years (roughly as long as we have continuously recorded history and the minimum time “gravity” has been observed) then we ought to currently be traveling through space at over 1,000,000,000,000m/s.
Now I’m no physicist, but I reckon that might end up violating causality.
The problem with trying to "explain" this is that fundamentally, flat-earthers, to the extent that they could be said to have a coherent world view at all, are usually a kind of occasionalist[1]. They don't _believe_ in natural laws or cause and effect. For the most part, they believe that god is in complete control of all events, and things go down because god wants them to go down. There's no required explanation for _anything_. The sun moves across the sky because god wants it to, and he could stop it or make it go backwards if he wanted it to, etc.
Indeed, that a flat earth is incompatible with physics is part of the appeal of believing in it to begin with. They _want_ to overthrow Newton, because a clockwork universe is incompatible with their belief system.
It's also sort of immune to any kind of argumentation. The result of any experiment is simply that god wants it that way, that they're predictable and testable doesn't _prove_ anything, because you can do an experiment a million times, and god could still cause it to fail any time he wants to. God just doesn't want to argue with Netwon right now, for his own reasons, you see.
We should see this as all the celestial bodies traveling "down" at relativistic speeds by now. Unless maybe they are also experiencing 1 G in the same direction as us in addition to whatever other accelerations.
I imagine whatever magical force has been constantly accelerating the disc Earth for 4,000+ years also magically accelerates everything else uniformly in the exact same direction, at the exact same speed, and also magically solves every other hole in the theory.
It's not a bad way to look at it for a start. Things move down because it is their nature to move downwards. And this kind of empirical law is what we rely upon for most thought.
It takes a lot of work to get to a theory that makes more general predictions.
And even after having that, 98% of the time my thought is effectively just "things move down." Another 1.5% it's "things move down at 9.8 m/s/s". It's an extreme edge/special case when I'm thinking "massive things are attracted to each other, with a force proportional to their masses and inversely proportional to the square of their distances".
And even with "massive things are attracted to each other, with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?"
"with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?""
To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)
And in general, I was actually arguing with flat earthers recently a lot, I even met a flat earther in real life. It is an interesting intellectual challenge debating them. Basically rebasing all the physical theory I have. (Main summary is, they have a high ego, but lack understanding of everything and make up for it with make believe.)
If I found a school one day, one of the lessons will be the teacher telling the students: "The earth is flat! Proof me otherwise." Or more advanced, model a flat earth on a computer. Flat earthers try that for real - it gets weird very quickly, so much that I could not believe anyone taking it serious and it all is just satire. But they are for real (but with a very different concept of reality).
> To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)
Sure, and if we come up with some fancy unified theory, and ask "why" once more, the answer will still be "uh, because they do?."
> But they are for real (but with a very different concept of reality).
We think ourselves so advanced. I wonder what big counterfactual scientists believed in the 1900s and 2000s will be laughed at a few hundred years from now.
And, of course, some of that will be libel; e.g. that we thought the world was flat "just like Christopher Columbus's compatriots" [who didn't].
A huge thing about flat earthers is that they don't care if their explanations are self-consistent. They happily accept explanations for one thing that directly contradict their explanations for another thing.
Standard flat-earther response is to scornfully deny the existence of gravity. It's all density/buoyancy you see... Gravity is a hoax promulgated by the notorious cabalist Newton, in service to his Illuminati/Papal masters, etc, etc.
I periodically suffer the delusion that some of the nonsense-adjacent people may benefit from seeing that sensible answers can be found. Of course there's effectively no chance of reaching the proudly loudly ignorant, wearing their refusal of any good-faith discussion as a shibboleth, but perhaps their recruitment can be stayed.
> and gravity, still pointing towards the center, makes you stand at an increasingly acute angle to the surface. The ground beneath you will then appear like one big endless mountainside
That’s why you never hear of people who went to the edge of that dis: they slid down that mountainside, and dropped off :-)
Alternatively, you can postulate that disc to be arbitrarily thick.
That will decrease the deviations. If that’s not enough to make them immeasurable, postulate that the stuff “deeper down” has higher density.
In the limit, just postulate that there’s an enormous black hole millions of light years below the center of the earth.
Flat-earthers probably won’t accept Newton’s theory of gravity, however, so you can make up anything.
Even physicists have a hard time with disks and gravity. I can't tell you how many times I've seen them use the shell theorem on galaxies (does not apply). The only dark matter is in their head ;-)
I'm considering what flat-surfaced shape you could construct with equal gravitational pull at all points. Maybe something where the center is thin as a point, the edges have a lot of depth, and they curve towards the center either convex or concave. Might run some calculus to figure it out.
That way you should be able design a disc-shaped earth with constant strength of the gravitational force on the whole surface. But it would still have a center of mass (likely lying outside the shape you're describing, in the void beneath the center point), and the direction of the force should still be pointing towards that center, no? So the problem the GP has described, that you're starting to tilt as you move towards the edge, should remain in principle.
I believe the strength of gravitational force would not be constant either, as your center of mass would still have a fixed location, so every point on the disc have different distances to that center of mass (in addition to not being orthogonal to the surface). But maybe it might be approximated with an infinitely long cylinder, so the center of mass is infinitely far away below the surface ?
The thinking in the other post, that the mass increases as you move away from the center, in a manner that the two effects cancel out, intuitively seems like it should be feasible. Remember that the center of mass is just an abstraction, you need to take the full integral over all mass to get the force vector at each point. And if you're closer to more mass further away from the center, which a shape like the one described above should give you, it might work. But one would have to do the math to be sure.
Edit: come to think of it, maybe that effect would let you adjust the direction of the force, too. Thinking about center of mass can be treacherous with more complex shapes...
Eh, the original post wanted a convex disk that would have a uniform gravitational pull, flatness was already thrown out as a design requirement. Once convex disks are allowed, a specific category of convex disk that provides a uniform perpendicular gravitational field comes to mind. The sphere. The very object we were trying to avoid. It is one of those it's funny because of the irony things.
The post clearly described a non-convex shape, and "flat-surfaced shape" should be a pretty clear instruction as well. The shape described may be visualized as a cylinder with a cone cut out, where the base of the cone aligns with one of the bases of the cylinder, and its tip with the center point of the other cylinder base. Except that the cylinder may be modified so that, seen in a cross-section, the line going from the base to the tip on either side may be a (convex or concave) curve. It makes sense as a starting point in the search for a shape with the desired properties. And it can immediately be seen to be non-convex in both described configurations, given that there's a cavity cut out.
You misunderstood, I mean for the top to be flat but the "underground" to have some kind of shape to compensate for the gravitational pull at all points on the flat surface. For a 2Dish example in the ballpark, you could think of one of these wooden toy bridge blocks: https://thumbs.dreamstime.com/b/natural-wood-blocks-364582.j...
I think you could construct a curve such that the mass's gravitational pull on the right cancels out the pull on the left, for any point on the surface.
Say the earth is disc-shaped. Then the center of gravity is only directly beneath you if you're standing at the exact center. You get ever-so-slightly not parallel lines, just like on a round earth.
The fun part of a disc-shaped earth comes as you move towards the sides, and gravity, still pointing towards the center, makes you stand at an increasingly acute angle to the surface. The ground beneath you will then appear like one big endless mountainside, with an increasingly steep slope the further away from the center that you get.