4 ms·

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 stand

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.

jimmaswell 2y ago
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.
- t_mann 2y ago
  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.
  - benterris 2y ago
    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 ?
    - t_mann 2y ago
      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...
- somat 2y ago
  yes, we call it a sphere. I am just joking with you, I know what you mean, however the fruit was hanging too low not to pick.
  - t_mann 2y ago
    A sphere is only locally approximable by flat surfaces, but it's nowhere actually flat, which was a requirement in the previous post.
    - somat 2y ago
      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.
      - jimmaswell 2y ago
        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.jpg 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.
      - t_mann 2y ago
        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.
thombat 2y ago
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.
- mp05 2y ago
  Why do we still talk about these people? The more we stand in awe of their calculated ignorance, the more satisfied they are. I feel like there are better things to do with my time than be as fascinated by it as some people.
  - thombat 2y ago
    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.
tempestn 2y ago
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.
- munch117 2y ago
  If this mysterious disc-accelerating force also accelerated the people and things on the surface, we'd all be weightless. I guess it must be a pushing force from below. So, who's doing the pushing? I'm thinking a big turtle.
  - nkrisc 2y ago
    They mean it is actually accelerating constantly. 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.
    - jbeninger 2y ago
      Nah, when you move that fast, further acceleration stops increasing speed and starts squishing time instead, so you asymptotically approach C. So I guess what I'm saying is I see absolutely no problem with the flat earth arguments?
      - bryanrasmussen 2y ago
        wait, is the flat earth theory going to make me immortal?
        lukan 2y ago
        Only if you truly believe in it. Then you create a belive field, shaping your reality in any form you desire.
rendaw 2y ago
Doesn't the flat earth extend infinitely in all directions?
phkahler 2y ago
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 ;-)
Someone 2y ago
> 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.

jimmaswell 2y ago

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.

t_mann 2y ago
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.
- benterris 2y ago
  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 ?
  - t_mann 2y ago
    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...
somat 2y ago
yes, we call it a sphere. I am just joking with you, I know what you mean, however the fruit was hanging too low not to pick.
- t_mann 2y ago
  A sphere is only locally approximable by flat surfaces, but it's nowhere actually flat, which was a requirement in the previous post.
  - somat 2y ago
    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.
    - jimmaswell 2y ago
      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.jpg 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.
    - t_mann 2y ago
      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.

thombat 2y ago

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.

mp05 2y ago
Why do we still talk about these people? The more we stand in awe of their calculated ignorance, the more satisfied they are. I feel like there are better things to do with my time than be as fascinated by it as some people.
- thombat 2y ago
  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.

tempestn 2y ago

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.

munch117 2y ago
If this mysterious disc-accelerating force also accelerated the people and things on the surface, we'd all be weightless. I guess it must be a pushing force from below. So, who's doing the pushing? I'm thinking a big turtle.
- nkrisc 2y ago
  They mean it is actually accelerating constantly. 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.
  - jbeninger 2y ago
    Nah, when you move that fast, further acceleration stops increasing speed and starts squishing time instead, so you asymptotically approach C. So I guess what I'm saying is I see absolutely no problem with the flat earth arguments?
    - bryanrasmussen 2y ago
      wait, is the flat earth theory going to make me immortal?
      - lukan 2y ago
        Only if you truly believe in it. Then you create a belive field, shaping your reality in any form you desire.

rendaw 2y ago

Doesn't the flat earth extend infinitely in all directions?

phkahler 2y ago

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 ;-)

Someone 2y ago

> 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.