For reasons not currently relevant, I've done a good deal of thinking about this.
If you want a flat world, there are two general categories into which it can fit:
- Solar Annulus
- Planet-like Disk
While vastly different in scale, both kinds of structures remain stable in the same manner: While a large mass generally tends to pull itself into a sphere, a rotating mass also has centripetal acceleration cancelling a portion of the force of gravity at its equator. If the mass rotates fast enough for the centripetal acceleration to equal the gravitational acceleration, the particles of the body will experience zero net force in all but one axis (the axis of rotation), essentially remaining in freefall around that axis (not quite sure if it would count as orbiting, as it's all one huge solid mass), and will collapse into a disc rather than a sphere. Proof of this can be seen in every major theory on The Formation of the Solar System
Another, possibly counter-intuitive, property of any discworld large enough to generate 1g of surface gravity: Just as with a round planet, there would be volcanism, and possibly continental drift, as the 'core layer' of the disc can be made just as hot as the round core of ordinary ball-shaped planets.
A Solar Annulus, while incredibly cool, is probably not feasible without the resources of several Type II or a Type III civilization. In this incarnation, the world would consist of a solid disc the thickness of a planet 2 AUs or more in diameter with a hole cut out of the middle for the sun to rest in. As the annulus would require several thousand solar masses, it would not so much be positioned around a star so much as the star is positioned in the middle of it. Some approximation of day and night can be acheived by having the sun bob up and down through the hole, alternately lighting opposite sides of the annulus. If this motion could be made slow enough, it might pass off for seasons. As the sun would always be on the horizon, there would be perpetual twilight on the entire world. A thousand-klik high wall would be required along the inner edge to prevent atmosphere from draining into the sun, but the outer edge could be left open.
A Planet-like Disc can take multiple incarnations, each a combination of the following properties:
- Relative Mass
Relative to the star, that is. If the disc is massive enough to cause the sun to orbit around it, one could end up with a very large Greek World. The Earth would be flat, the sun would orbit the Earth, and at the end of every day it would descend below the edge of the Earth to light the Underworld. Unfortunately (for earthlings, at least), the sun would likely be red, as a yellow dwarf in an orbit close enough to provide useful days rather than extreme seasons would fry the surface. Also unfortunately, while not requiring nearly as much mass as a Solar Annulus, this sort of construction is still mind-boggling huge, and probably infeasible without the resources of several Type II civilizations. Of course, if your population is large enough to require the amount of area this would provide, you probably have those resources, so by the time we need one we'll know how to build it..
More practical constructions, requiring perhaps ten Earth masses, would be doomed to go without Earthly days and nights. Spinning the disc in order to simulate motion of the sun around it is impossible, due to gyroscopic precession, and putting the disc into a small enough orbit for seasons to be reduced to the scale of a few days would require a red dwarf sun, the same problem encountered by the supermassive disc.
Walls are not entirely necessary. Some may prefer them, some may not. To decide whether or not to put walls around the outer edge of your flat world, consult the following list of advantages and disadvantages:
Advantages of Walls
Advantages of Foregoing Walls
- You can be extra secure in your knowledge that the atmosphere will never leak away.
- You can maintain constant pressure across the entire surface.
- No one will ever mistakenly fall off of the edge of the world.
Disadvantages of Walls
- You get a spectacular view at the edge.
- You save construction material and maintenance costs.
- The outer portions of the disc recieve more sunlight.
Disadvantages of Foregoing Walls
- Useful walls must be several hundred kilometers high at least. This is likely to be far above the Geostatic Limit, the point at which the crust of the planet can no longer support the weight of the structure. Additionally, you will be hard-pressed to find a material that can support that much of its own weight. You will either require magic construction materials, or a low-gravity world.
- The outer portions of the disc will be in shadow.
- You may require a bit of replacement atmosphere every few million years.*
- Atmospheric pressure will decrease from the center to the edge, likely leaving the outermost portions uninhabitable.
If the disk rotates in exactly the same plane as it orbits its sun, there will be perpetual twilight over both sides of the disc. There will be some variation in intensity between the edges closest to and farthest from the sun, but like the The Smoke Ring there will never be total darkness, unless you happen to be in the shadow of a mountain. Seasons might be simulated with the aid of gigantic mirror satelites or statites, but would not be inherent to the structure.
If one were to tilt the disc in an attempt to gain seasons, even a very slight tilt will result in extreme variation. For approximately half the year, both sides of the disc will be in twilight, as with an uninclined disc. For the other half of the year, one side will be in total cold darkness, while the other side will recieve more direct sunlight, the amount depending on exactly how much the disc is tilted. Were I to design an inclined disc, I'd put as close to perpendicular to the orbital plane as possible- that way, you would have a very warm 3-month summer to make up for the frigid winter.
Expert, but I beleive that can be solved rather simply- spin the disc just slightly slower than required to completely balance the inward gravitational force, and slope the ground from the center such that it remains perpendicular to the direction of the net gravitational/centripetal force. Thus, no particles of air at the edge will be moving fast enough to escape in the plane of the disc. The shadow of the central bulge might even be used to provide a more Earth-like
approximation of a day/night cycle, but it still wouldn't be perfect.
I've been playing around with numbers for a while attempting to come up with a disc suitable for human habitation, and have discovered that while my equations seem to work on the large scale, I'm getting numers far too large on the small scale. Ergo, I'm probably using the wrong formulas, or plugging in numbers wrong. Hopefully, someone else knows what the correct formulas are and can help clear this up.