  We use analytic techniques to study the gravitational force that would be
produced by different Kuiper-Belt mass distributions. In particular, we study
the 3-dimensional rings (and wedge) whose densities vary as the inverse of the
distance, as a constant, as the inverse-squared of the distance, as well as
that which varies according to the Boss-Peale model. These analytic
calculations yield physical insight into the physics of the problem. They also
verify that physically viable models of this type can produce neither the
magnitude nor the constancy of the Pioneer anomaly.
