The Pioneer anomaly as acceleration of the clocks

Details The Pioneer anomaly as acceleration of the clocks The Pioneer anomaly as acceleration of the clocks

2004-10-18

arxiv.org/abs/gr-qc/0410084v2

Found.Phys. 34 (2005) 1955-1971

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, no figures. The notation for $a_{\tm t}$ has been changed in order to use the same as Anderson et al. This amounts t

Scientific paper

10.1007/s10701-004-1629-y

This work proposes an explanation of the Pioneer anomaly, the unmodelled and as yet unexplained blueshift detected in the microwave signal of the Pioneer 10 and other spaceships by Anderson {\it et al} in 1998. What they observed is similar to the effect that would have either (i) an anomalous acceleration $a_{\rm P}$ of the ship towards the Sun or (ii) an acceleration of the clocks $a_{\rm t}=a_{\rm P}/c$. The second alternative is investigated here, with a phenomenological model in which the anomaly is an effect of the background gravitational potential $\Psi (t)$ that pervades all the universe and is increasing because of the expansion. It is shown that $2a_{\rm t}={\rm d}\Psi /{\rm d}t ={\rm d}^2\tau_{\rm clocks} /{\rm d}t^2$, evaluated at present time $t_0$, where $t$ and $\tau_{\rm clocks}$ are the coordinate time and the time measured by the clocks, respectively. The result of a simple estimate gives the value $a_{\rm t}\simeq 1.8\times 10^{-18}{s}^{-1}$, while Anderson {\it et al} suggested $a_{\rm t}= (2.9\pm 0.4)\times 10^{-18}{s}^{-1}$ on the basis of their observations. The calculation are performed near the Newtonian limit but in the frame of general relativity.

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