Pioneer anomaly not gravitational

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Zman
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The Pioneer anomaly
I read that the Pioneer anomaly is a sunward acceleration that is larger than Newtonian gravity predicts.
This extra acceleration has been measured at;
(8.74 ± 1.33) × 10−10 m/s2 between 10AU and 90AU from the Sun.

But because the ‘extra acceleration’ is constant across about 80 AU of space, how can it be gravitational in nature?
If it was gravitational surely the value of the ‘extra acceleration’ would fall, the further away the Pioneer was.

At some point this ‘extra acceleration’ would swamp the Newtonian component.
 
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The Pioneer anomaly is essentially solved (IMHO). See this paper:

http://arxiv.org/abs/1103.5222v1

The spacecraft contains an onboard radioistope energy source, so it is radiating energy to the environment. Because it is not a symmetrical object, it does not radiate uniformly in all directions. Since EM radiation carries momentum, the non-uniform radiation results in a force on the spacecraft . This force has been calculated quantitatively in the attached paper, and explains the observed acceleration of the spacecraft rather well.
 
Thanks phyzguy

That has put that question to rest for me.

The constant value of the anomaly across vast distances was more likely going to be due to an onboard source than gravity.

Although I think the paper still leaves a very small opening for alternative interpretations as they still undershot the value slightly.