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We use analytic techniques to study the gravitational force that would beproduced by different Kuiper-Belt mass distributions. In particular, we studythe 3-dimensional rings (and wedge) whose densities vary as the inverse of thedistance, as a constant, as the inverse-squared of the distance, as well asthat which varies according to the Boss-Peale model. These analyticcalculations yield physical insight into the physics of the problem. They alsoverify that physically viable models of this type can produce neither themagnitude nor the constancy of the Pioneer anomaly.Comment: 11 pages, 8 figures, final corrections for publicatio

Analytic gravitational-force calculations for models of the Kuiper Belt, with application to the Pioneer anomaly