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TMM;DR (Too Much Math, Didn't Read): For anyone who doesn't want to go through the derivations and calculations below, here are the important points from my answer: We're not working with the same space as normal, friendly, Euclidean space. This means that while we can still integrate and differentiate scalar functions defined on this space, we need to ...


61

I know you are expecting a distance answer but I'll give a time answer. A good rule of thumb is a maximum of one to three months of travel. There are exceptions, but most civilizations that have direct contact are no more than one to three months away from each other. The distance varies with the terrain and type of travel. Most of the time when ...


51

The world would become progressively more alien as you moved across it. Unlike on Earth, where animals and humans can move across the entirety of the world given a few thousand/million/tens of millions of years, an infinite flat earth would always have somewhere that's far enough away that nothing from where you are has ever been there. This would probably ...


37

If you are okay with breaking every laws of physics, simply get rid of euclidean geometry and get "overlapping" space. Your world can be the size and shape of Earth. You start on point 0, walk to East, at some point if you trust stars and such you are back at your starting point, but in fact you got to a second point, overlapping with point 0. You can make ...


35

Assuming the cube world is the same as from your previous question things would be very different. The edges of the cube are mountains so high that they are literally impossible without the magic you added to keep them there. This would create six realms that are, essentially, totally isolated from one another. Six worlds, one planet. A sentient race ...


29

It'd be possible for one to exist for a time, but a naturally occurring, non-spheroid planet would be incredibly unlikely. More on that at the end. It's an easy thing to imagine of course, but that's because we think of things like cube shaped rocks that occur naturally and think 'why not?'. The problem is that objects on a planetary scale don't behave the ...


28

"Infinite" is really a big, big word. If you want to keep any semblance of physics, consider a world that is finite, just really big. Even a mundane Niven ring is big enough for all practical purposes - at 1AU radius, to walk around it would take about 20 thousand years of nonstop walking (and that still leaves several Earth worth of width unexplored). And ...


27

Donut-shaped planets are indeed possible! The article cites a paper which concludes that certain kinds of toroidal planets are at least internally stable, although not likely and possibly would get ruined by any external interference. It's true that gravity will make a randomly-shaped blob of matter coalesce into a sphere over time, but there's no reason ...


27

No The necessary condition for a liquid body to be in a gravitational equilibrium is that gravitational potential should be constant over its surface. For the cube with density $\rho$, by integrating $$ V(\mathbf r) = \int_{cube} \frac{G \rho}{\lVert \mathbf r - \mathbf r' \rVert_\lambda} d^3 \mathbf r' $$ for various locations $\mathbf r$ on its surface, ...


26

This would actually be really awesome. It wouldn't really be a planet anymore, but it could conveniently be called a plane or plane-et. We could find the epicenter of life. Presumably, abiogenesis is quite rare. On an infinite flat Earth it will certainly have occurred elsewhere, but not likely very near to us. Theoretically, we would eventually be able to ...


22

With this sort of cosmology, you can't get orbits. Plus the gravitational attraction between objects on a human scale is too small to notice. With that in mind I'd just get rid of the notion that gravity is attraction between mass. Instead, just define a uniform gravitational field across all of space, pointing perpendicular to the infinite plane of the ...


19

There are a lot of cool effects - and some problems. Formation Planets form after a long, drawn-out process that starts with grains of dust colliding and forming planetesimals. These then become protoplanets, which can be kilometers across. More collisions result in small, rocky planets, some of which become terrestrial planets; others form the cores of ...


19

As Danijel has pointed out, the question can be reframed as "what is the shape of the equipotential surface under this force law?" There are further two different ways to view the results: the external perspective, where we see what shapes these "planets" map onto if we overlay them on our normal Euclidean space, and the internal perspective--what would ...


17

Well, if you're already accepting that there is some magic, you could try an infinitely long cylinder, orbiting a cylindrical sun. Obviously in our universe, these would collapse in on themselves lengthwise, but with magic anything is possible. Another possibility - the world is an infinite sheet, with a hole in it through which the sun passes back and ...


16

It sounds like what you want / need is astonishingly (but not precisely) like that of the Unicorn Jelly web comic. A Khex class cosmos is defined as being those that contain infinite planes of matter in some fashion. The cosmos of Widlan, here, is a prime example of one kind of khex class cosmos. Description of Widlan and Khex class Cosmos ...


15

My answer isn't going to be anywhere near as in-depth as your question but I'm happy to supply a few inputs. First, I'm going to take a look at your particles: 1. Particles can only move at one constant speed. 2. Particles can only move in six directions. (Or four in my 2D model.) 3. Particles have "gravity". I'm going to imagine two particles in a two-...


15

Nightsky cooling will be important. The sky is cold. Even with a full atmosphere in the way, it can act as though it is -50F. With no atmosphere, it can get down to almost 0K. That lets you radiate a lot of heat! Clearly the only source of heat or UV radiation or whatnot is the sun, which we know orbits closer to the center of the flat earth, so there ...


14

Yes, we live on one :-) Strictly speaking, the Earth is not a sphere, it's an oblate spheroid. Its rotation makes it bulge somewhat, so the equatorial radius is ~30 km greater than the polar. A faster rotation would make a planet even more oblate: Saturn's polar & equatorial radii differ by almost 10%: https://en.wikipedia.org/wiki/Saturn#...


14

You ask at what point would communication be impossible? Technically speaking I don't think it would ever become impossible. Though it would probably become too delayed to be of any real utility. For example the Pony Express (USA circa 1860) was able to get a letter from the Atlantic to the Pacific in just 10 days. If we estimate that distance at ...


13

Some time ago, I calculated a toroidal planet numerically. In this answer, I give the parameters I obtained for reference to anybody who would be interested in this question. Method Rock and metals may seem solid, but on the scale of planets and in the pressures in their interiors, they are in a very good approximation liquid. To have a stable toroidal ...


13

This gives a good treatment of the subject at hand, with a surface gravity map provided as well. Regarding the magnetic fields, if the (presumably metallic/liquid) core was in motion or somehow had a ring current induced within, it would produce a magnetic field which will direct particles to pass through the center of the torus. The image shows the ring ...


13

The world can be made up of an infinite 2-dimensional plane of arbitrary thickness. In this plane, there exists an array of holes which pass through the plane. For ease of visualisation, the infinite plane would be similar to this picture, but with smaller holes relative to the normal land area than pictured. Around this plane, there exists an infinite ...


13

It depends on the size of the planet. A key concern is whether the body is in hydrostatic equilibrium. An object in hydrostatic equilibrium is approximately spherical, although it may become oblate due to rapid rotation. The question, then, is whether the division of the planet places it below the critical size required for hydrostatic equilibrium. It turns ...


12

A lot of people ignored the question and delved into the rabbit hole of physical impossibilities given the physics of our known universe that were ruled out in the question. Given an infinite, planar type world with similar characteristics and physics to earth (though I am not sure how different temperate zones would come about) I agree that with others that ...


12

The first thing to remember is how gravity would work. It wouldn't be perpendicular to the cube faces; rather, it would pull toward the center of the planet. (Diagram taken from Gizmodo.) This is close enough to gravity on a spherical planet that our intuition for Earth can help. Let's imagine that your planet started as a sphere, with radius 3500km. This ...


12

The Spherical World Society and Evil Twins There is a model of the projective plane known as the projective sphere. It has the following properties: Since it is based on a sphere, which is orientable, you can consistently assign objects orientations which do not change as you move along it. Unlike the hemisphere model, the sphere model is basically unique. ...


10

The sphere shape is entirely based on gravity. That is actually one of the parts of the definition of a planet. That is is large enough that it's gravity will make it a sphere. The objects that are not spheres are much smaller or they would have to be artificially created and maintained. (unless shortly after a large event that distorted the planet, like ...


10

Life starting from a single point will create a so called Fairy Ring. Life will move outwards, expanding the ring seeking for a new resources. Many concentric ever expanding rings may be created as a new life evolves, that is able to use resources that the life in the previous ring was not able to use.


10

A small cube can have magnetic poles. A planet-sized cube cannot. A cube shape neodymium magnet, its top painted by a black marker. I approach it with some other magnets and — click — they snap together, with the lone magnet having flipped around to align its poles with the others'. But no, you cannot have a cube shaped world with a magnetic field since a ...


10

This will change both the continent and the sea in unusual ways. 1) The ocean floor will create itself anyways. Bear with me on this one. If your world has light (solar radiation), it will have a water cycle, because water molecules will be warmed to the point of vaporization. The water cycle drives weathering and erosion, which wears down the land over ...


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