Analytic Gravitational-Force Calculations for Models of the Kuiper Belt

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 which varies with 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. April 5, 2008 PACS: 95.10.Eg, 96.50.Dj, 96.50.Jg