For zones, I7d suggest dividing them up like the face of a clock with 12 or 24 zones. Once you work out the size and rate of rotation, you could size up the zones based upon how long it takes for the ring to revolve around the star. Perhaps each zone is the amount of territory that would move in one "month", so in 12 months the zone would be in the same location.
BTW, There is a bunch of hard math stuff from other Sci Fi games that I could hunt down for you, depending on just how detailed you want to get with this. THings like the amount of light recieved, density, etc. can be worked out to more detail than you would probably ever need.
Oh, one way to handle the large open spaces would be to have the orignal builders install some sort of teleoprtation devices along the ring. Think Star Treks transporter, or the stargates from SG-1. This could make travel from telepter to teleporter easier than other travel. If only some of the teleporters still work, and the humans haven't discovered all of the telporters yet, you could encourage the players to adventure in certain areas.
Set the teleporters up so they only worth from one to the other, and the coordinates for the desitnation need to be entered in (any one the humans find should have the lcoodinates for the last setting used still programmed in, so each should be good to go somewhere.)
You could even have advnetures where people go off to try and find other teleporters, or have some cultures that know of some teleporters that other do not. Perhaps even a trade of information ("We'll trade you the coodinates for New London for the coodinates for Roma Nova.")
BTW, There is a bunch of hard math stuff from other Sci Fi games that I could hunt down for you, depending on just how detailed you want to get with this. THings like the amount of light recieved, density, etc. can be worked out to more detail than you would probably ever need.
Oh, one way to handle the large open spaces would be to have the orignal builders install some sort of teleoprtation devices along the ring. Think Star Treks transporter, or the stargates from SG-1. This could make travel from telepter to teleporter easier than other travel. If only some of the teleporters still work, and the humans haven't discovered all of the telporters yet, you could encourage the players to adventure in certain areas.
Set the teleporters up so they only worth from one to the other, and the coordinates for the desitnation need to be entered in (any one the humans find should have the lcoodinates for the last setting used still programmed in, so each should be good to go somewhere.)
You could even have advnetures where people go off to try and find other teleporters, or have some cultures that know of some teleporters that other do not. Perhaps even a trade of information ("We'll trade you the coodinates for New London for the coodinates for Roma Nova.")