An explanation of the Pioneer anomaly involving accelerated atomic clocks

The Pioneer anomaly stands for unexplained frequency shifts of the Doppler radio-tracking signals received at the ground stations from the Pioneer 10 and 11 spacecraft in disagreement with expectations based on model calculations. We consider here observations of Pioneer 10 at heliocentric distances between 40 ua and 70.5 ua over a time interval of 11.55 years from 1987 to 1998. The anomaly has been interpreted in the literature either as a Doppler shift caused by an apparent spacecraft deceleration not accounted for by known effects, or as an unexpected clock acceleration of the frequency standards at the ground stations. The reasons for the anomalous behaviour are not understood in both cases. Based on a gravitational impact model – requiring a secular mass increase of all massive bodies – a solution is proposed that implies a clock acceleration with a value close to that of the Hubble constant.