One small problem in your conjecture:
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An obvious if unlikely candidate the Pioneer 10 and 11 acceleration anomaly is a second order derivative of the ‘G constant’. ...
...Then I fit a log/log curve to this equation, and calculated what the density of each system would be if they were in the Earth's orbit. This is assuming “G” is indeed variable, diminishing with increasing distance from the Sun.
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(my empahsis)
The anomaly is opposite what you presume. If Gee was decreasing with distance the spacecraft would be further than expected. They aren't. The anomaly places the spacecraft closer than expected.
Quote:
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Indeed, the spacecraft move as if they were subject to a new, unknown force pointing towards the Sun.
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From
here.