Vector potentials for the gravitational interaction of extended bodies and laminas with analytical solutions for two disks

The mutual gravitational potential and the force and torque components between two solid bodies are formulated in terms of vector potentials. If one of the bodies is a flat lamina of arbitrary shape and uniform surface density, then the potential and the force and torque components in Cartesian coordinates are expressed in terms of line integrals. For a uniform circular disk, the various potentials are given explicitly in terms of elliptic integrals, and these are applied to a second homogeneous disk of arbitrary orientation and position relative to the first. Simplified formulas are given for disks with parallel axes. Analytical solutions in terms of elliptic integrals are given for the mutual force and potential for coaxial disks and coplanar disks. Numerical results are given for two disks for a selection of relative orientations and positions.