In my previous question I asked about evaluating the following integral over the surface of a sphere in 3D: $$ \int_{\partial D} \int_{\partial D} \frac{1}{|x-y|}dxdy, $$ and it turned out that the answer is $(4\pi)^2$ for a unit sphere.
Now what about the case where $x$ and $y$ are not on the surface of the same sphere, but are actually on the surfaces of different spheres (both of the same radius)? That is, the integral $$ \int_{\partial D_2} \int_{\partial D_1} \frac{1}{|x-y|}dxdy, $$ where $x$ is on the surface of $D_1$ and $y$ is on the surface of $D_2$. Unfortunately we don't have the same level of symmetry in this situation so I am uncertain if an analytic solution is possible? Can this be solved explicitly or will numerical integration be required?