> Given: Alderson Disk system, disk inner radius R1, outer radius R2, thickness T, density Rho,
> star mass M (irrelevant due to superposition?).
> How to find amount and direction of gravity force at some point in the system, including
> points in-disk, in the solar gap and out in space (preferably in a real-time calculable way)?
g exerted by an alderson disk can be approximated by that of an infinite plane, which is 2*pi*G*T*Rho (using your variables). This is uniform near the disk itself, away from the edges. At a density 1/2 that of steel (assuming you have internal, pressurized structures within the disk) or 6 g/m3, you'd need a disk 4,000 km thick to approximate 1 Earth gravity. The theoreticial habitible zone around most main-sequence stars is considerably larger than the diamater of the earth, so I assume one extends the disk the diamater of the Earth inside and outside of the hab zone in order to avoid edge effects (not detailed here... complex math required, and not usually relevent).
the influence of the star is calculated normally, G*M/r^2. I assumed a 4x sol brightness star, which would put r1 at about 1 AU and r2 at about 3 AU (minus and plus diamiter earth, as explained above). since a 4x sol star is only marginally more massive than sol (about 2x), the direct effects of it's gravity would be minor, and could be compensated by having the disk rotate (perhaps in separate sections... haven't worked this all out yet). This would also aid the material strength issues encountered in construction (which could be further relieved by masses in evacuated tubes traveling at superorbital velocities applying supportive force to the structure and accelerated via a Dyson "bubble" of solar sails exterior to the radius of the disk itself, similar to the "space fountain" idea... but that's another story.)
within the disk, since infinite parallel planes of equal density have NO gravitational influence on objects within, the math is easy. double the fraction of the depth of the object and multiply that by the surface gravity to find the gravity at that point. ex: an object 1/8th of the way through the disk (in the above example, 500 km "down") would experience 1/4 Earth G.
within the solar gap, and sufficently distant from the edge, I'm guessing gravitational effects from the disk itself would be neglagible within the thickness of the disk itself (see the Shell Theorm), and a slight attraction towards the plane of the disk otherwise (again, steller attraction is calculated normally). I have not done a rigerous proof of this.
"Above" the disk, gravity would remain constant and only diminish once the distance from the surface became a significant percentage of the distance to the edge. At a sufficent distance, of course, the mass of the disk could just be treated as part of the system itself.
I realize this is not all of what you requested, but I hope it helps. Also, I hope that you're still working on it... just started looking into this recently.
