How many different kinds of space stations are possible in t

[Battlehymn Republic]

These are the ones I can think of:

LaGrange systems around the Earth,
Surface and subterranean systems on the Moon, Mars, and maybe Mercury.
Asteroid bases

Now, this is the part I don’t understand- after I learned about LaGrange points, I’ve been expecting that there’s some sort of special gravitational quirk that causes those places to be better spots to build space colonies. However, hypothetically, can’t any orbital stations be built around the Earth as long the orbit is sound? What about around the Moon, Mars, Gas Giants, and any other planet?

(I’m guessing Luna is too small gravitationally speaking, but what about the Jovian planets’ larger satellites?)

[Guardsman Bass]

You could build an orbital station around just about any planetary body in the solar system, including the moon, as long as you had a stable orbit. Of course, you may have some difficulties if you want your station to orbit an asteroid, but even then, it would be possible.

[drachefly]

The only advantage of the lagrange points is that they get to share an orbit with another object. Like, you can't put an object into an orbit around earth that is NEAR 1 month, because the moon would knock it out quickly. But you can put it at EXACTLY 1 month, if you put it at one of the 5 lagrange points (especially one of the two stable ones).

That's all. Space stations can go almost anywhere else with little to no trouble beyond getting them there... of course, that's the hard part isn't it?

[Lord of the Abyss]

IIRC you could theoretically build a stable ring around a planet in geosynchronus orbit.

You can use Robert Forward's idea and build "statites" instead of satillites. A statite uses a solar sail ( or a superconductive/electrified cable that can "grab" the Earth's magnetic field ) to stabilize it's position. Since it uses a form of non-reactive thrust to maintain position, it can in theory be stuck almost anywhere, ignoring the normal laws of orbital mechanics.

[Admiral Valdemar]

Skyhook ideas would be possible too if you wanted something to help with LEO operations. Other than that, the O'Neill colonies at the various Lagrange points or in orbits around other stellar bodies are good enough.