  New exact solutions are derived for the gravitational potential inside and
outside a homogeneous torus as rapidly converging series of toroidal harmonics.
The approach consists of splitting the inter- nal potential into a known
solution to Poisson's equation plus some solution to Laplace's equation. The
full solutions are then obtained using two equivalent methods, applying
differential boundary conditions at the surface, or evaluating a surface
integral derived from Green's third identity. This surface integral may not
have been published before and is general to all geometries and volume density
distributions, reducing the problem for the gravitational potential of any
object from a volume to a surface integral.
