  We give analytic expressions for the gravitational inner spherical multipole
moments, q_{lm} with l <= 5, for 11 elementary solid shapes. These moments, in
conjunction with their known rotational and translational properties, can be
used to calculate precisely the moments of complex objects that may be
assembled from the elementary shapes. We also give an analytic expression for
the gravitational force between two rectangular solids at arbitrary
separations. These expressions are useful for computing the gravitational
properties of complex instruments, such as those used in equivalence principle
tests, and in the gravitational balancing of drag-free spacecraft.
