SIMBAD references

The one-dimensional, ordinary differential equation (ODE) that satisfies the midplane gravitational potential of truncated, flat power-law disks is extended to the whole physical space. It is shown that thickness effects (i.e. non-flatness) can be easily accounted for by implementing an appropriate ``softening length'' λ. The solution of this ``softened ODE'' has the following properties: i) it is regular at the edges (finite radial accelerations); ii) it possesses the correct long-range properties; iii) it matches the Newtonian potential of a geometrically thin disk very well; and iv) it tends continuously to the flat disk solution in the limit λ->0. As illustrated by many examples, the ODE, subject to exact Dirichlet conditions, can be solved numerically with efficiency for any given colatitude at second-order from center to infinity using radial mapping. This approach is therefore particularly well-suited to generating grids of gravitational forces in order to study particles moving under the field of a gravitating disk as found in various contexts (active nuclei, stellar systems, young stellar objects). Extension to non-power-law surface density profiles is straightforward through superposition. Grids can be produced upon request.