Scope for a small circumsolar annular gravitational contribution to the Pioneer anomaly without affecting planetary orbits

All proposed gravitational explanations of the Pioneer anomaly must crucially face the Equivalence Principle. Thus, if Pioneers 10 and 11 were influenced by anomalous gravitational effects in regions containing other Solar System bodies, then those bodies should likewise be influenced, irrespective of their shape, composition or mass. Although the lack of any observed influence upon planetary orbits severely constrains such explanations, here we aim to construct by computer modeling, hypothetical gravitating annuli having no gravitational impact on planetary orbits from Mercury to Neptune. One model has a central zone, free of radial gravitation in the annular plane, and an 'onset' beyond Saturn's orbit, where sunward annular gravitation increases to match the Pioneer anomaly data. Sharp nulls are included so that Uranus and Neptune escape this influence. Such models can be proportionately reduced in mass: a 1 % contribution to the anomaly requires an annulus of approximately 1 Earth mass. It is thus possible to comply with the JPL assessment of newly recovered data attributing 80 %, or more, of the anomaly to spacecraft heat, which appears to allow small contributions from other causes. Following the possibility of an increasing Kuiper belt density at great ranges, another model makes an outward small anomalous gravitation in the TNO region, tallying with an observed slight indication of such an effect, suggesting that New Horizons may slightly accelerate in this region.