What if the world was flat?

No, I'm quite aware the Earth is a sphere. You're just preaching to the choir trying to explain to me that its round. Nor am I trying to support the Flat Earth Society.

So...

• What would it take for the world to be flat?
• How would there be gravity?
• How would the atmosphere stay in?
• How could a day/night cycle be done?
• Are seasons possible? What season would it be?
and any other questions that may arise.

For the sake of argument, picture a large flat dish. To create gravity on the surface of this dish, you need something under it exerting a force down. The easiest way to do this is to put a large mass under the surface. This mass should be spread out so that all the dish gets a downward force. As an intresting note, you could also think of this as a sandwich because a force will also be pulling at the other side.

To have an atmosphere, you just need a wall around the edge of the dish (a la Ringworld). Gravity holds it nicely down and makes sure it dosn't escape.

A day/night cycle is more difficult. It involves either spinning the disk like a penny on a table (which will cause problems with the above atmosphere) or moving the sun either up and down or orbiting the dish. Neither are trivial.

I have no clue if seasons are possible.

If you want a flat world, there are two general categories into which it can fit:

1. Solar Annulus
2. 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
• Walls
• Inclination

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
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:

• 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.
• You get a spectacular view at the edge.
• You save construction material and maintenance costs.
• The outer portions of the disc recieve more sunlight.
• 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.