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The Pioneer anomaly as an effect of the dynamics of time

Antonio F. Ranada
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Abstract

A model is presented in which the Pioneer anomaly is not related to the motion of the spaceship, but is a consequence of the acceleration of the cosmological proper time $τ$ with respect to the coordinate parametric time $t$, what is an effect of the background gravitational potential of the entire universe. The light speed, while being constant if defined with respect to $τ$ ({\it i. e.} as ${\rm d}\ell /{\rm d} τ$), would suffer an adiabatic secular acceleration, $a_\ell={\rm d}c/{\rm d}t >0$, if defined in terms of $t$ ({\it i. e.} as ${\rm d}\ell /{\rm d} t$). Such an adiabatic acceleration of light, and a small acceleration of the Pioneer towards the Sun $a_{\rm P}$ could be mistaken the one for the other, because they do have the same fingerprint: a blue shift. However, this shift would be quite unrelated to any anomalous motion of the Pioneer, being just an observational effect of the acceleration of light with respect to time $t$. The Pioneer anomaly turns out then to be an interesting case of the dynamics of time, its explanation involving the interplay between the two times $τ$ and $t$.

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Antonio F. Ranada. 2004-11-25. The Pioneer anomaly as an effect of the dynamics of time. https://arxiv.org/abs/gr-qc/0403013

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