Scalar potential model of the Pioneer Anomaly

Abstract

The unexplained sunward acceleration $a_\mathrm{P}$ of the Pioneer 10 (P10) and the Pioneer 11 (P11) spacecraft remains a mystery. A scalar potential model (SPM) that derived from considerations of galaxy clusters, of redshift, and of H{\scriptsize{I}} rotation curves of spiral galaxies is applied to the Pioneer Anomaly. Matter is posited to warp the scalar potential $\rho$ field. The changing $\rho$ field along the light path causes the Pioneer Anomaly. The SPM is consistent with the general value of $a_\mathrm{P}$; with the annual periodicity; with the differing $a_\mathrm{P}$ between the spacecraft; with the discrepancy between {\textit{Sigma}} and CHASMP programs at P10 (I) and their closer agreement at P10 (III); with the slowly declining $a_\mathrm{P}$; with the low value of $a_\mathrm{P}$ immediately before the P11's Saturn encounter; with the high uncertainty in the value of $a_\mathrm{P}$ obtained during and after the P11's Saturn encounter; and with the cosmological connection suggested by $a_\mathrm{P} \approx cH_\mathrm{o}$. The effect of the $\rho$ field warp appears as the curvature of space proposed by general relativity (GR). The Hubble Law and $a_\mathrm{P} \approx cH_\mathrm{o}$ are manifestations of the Newtonian spherical property. Therefore, gravitational attraction, the equivalence principle, and the planet ephemeris remain as described by GR. GR corresponds to the SPM in the limit in which the Sources and Sinks may be replaced by a flat and static $\rho$ field such as between cluster cells and on the Solar System scale at a relatively large distance from a Source or Sink.