Massive Photon as Solution to Anomalous Acceleration of Deep-Space Probes and Some Other Cosmological Anomalies

All deep-space probes seem to experience small anomalous acceleration. Although original thermal modelling of Pioneer spacecraft effectively ruled it out, newer modelling suggests that the anomalies do arise from the anisotropic thermal radiation, mainly associated with radioisotope thermoelectric generators. However, although the results are convincing, alternative solutions are not ruled out. Here, it is proposed that the thermal anisotropy is generally only a part of the solution and may not be a dominating part in all cases. The other contribution is hypothesized to come from a non-zero photon mass and its gravitational coupling. The exact solution for the Pioneer anomalies is presented, in remarkable agreement with measurements, and with the original thermal modelling. In addition, the solution provides an alternative explanation for the Schwarzschild radius of the observable universe and could potentially explain different cosmological anomalies, not limited to the anomalous acceleration of deep-space probes.