On the possible onset of the Pioneer anomaly

Abstract: We explore the possibility that the observed onset of the Pioneer anomaly after Saturn encounter by Pioneer 11 is not necessarily due to mismodeling of solar radiation pressure but instead reflects a physically relevant characteristic of the anomaly itself. We employ the principles of a recently proposed cosmological model termed "the theory of inertial centers" along with an understanding of the fundamental assumptions taken by the Deep Space Network (DSN) to attempt to model this sudden onset. Due to an ambiguity that arises from the difference in the DSN definition of expected light-time with light-time according to the theory of inertial centers, we are forced to adopt a seemingly arbitrary convention to relate DSN-assumed clock-rates to physical clock-rates for this model. We offer a possible reason for adopting the convention employed in our analysis; however, we remain skeptical. Nevertheless, with this convention, one finds that this theory is able to replicate the previously reported Hubble-like behavior of the "clock acceleration" for the Pioneer anomaly as well as the sudden onset of the anomalous acceleration after Pioneer 11 Saturn encounter. While oscillatory behavior with a yearly period is also predicted for the anomalous clock accelerations of both Pioneer 10 and Pioneer 11, the predicted amplitude is an order of magnitude too small when compared with that reported for Pioneer 10.