Foundations of Physics

, Volume 34, Issue 12, pp 1955–1971 | Cite as

The Pioneer Anomaly as Acceleration of the Clocks

  • Antonio F. RañadaEmail author


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 et al. in 1998. What they observed is similar to the effect that would have either (i) an anomalous acceleration a P the ship towards the Sun, or (ii) an acceleration of the clocks a t =a P /c. The second alternative is investigated here, with a phenomenological model in which the anomaly is an effect of the background gravitational potential Ψ (t) that pervades all the universe and is increasing because of the expansion. It is shown that 2a t =dΨ /dt=d2τ clocks /dt2, evaluated at present time t0, where t and τ clocks are the coordinate time and the time measured by the atomic clocks, respectively. The result of a simple estimate gives the value a t ⋍ 1.8× 10−18 s−1, while Anderson et al. suggested a t =(2.9±0.4) × 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.


Pioneer anomaly Pioneer acceleration acceleration of the clocks background gravitational potential 


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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  1. 1.Facultad de FísicaUniversidad ComplutenseMadridSpain

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