Pioneer 10 looks like red shift, not blue

John,

I think the problem is merely one of unfortunate and misleading
notation rather than a genuine error:

if you look at footnote #38 in Anderson et al. 2002
(http://arxiv.org/abs/gr-qc/0104064 ) it is clear that
the basic frequency difference is actually defined as f0-f rather than
f-f0 (where f0 is the transmitted frequency and f the received
frequency). Note that this frequency difference is positive for a
redshift (ff0).
Now the (two-way) difference between the observed frequency difference
f0-f and the theoretical frequency difference f0-f' is then related to
the excess accelaration 'a' by

(1) (f0-f)-(f0-f') = -2*f0*t/c*a

or

(2) f'-f = -2*f0*t/c*a

The acceleration 'a' is defined such that it is positive if directed
towards the sun, so in this case the right hand side is negative and
hence it is required that ff' on the left hand side, which corresponds
to an excess blue-shift (which is consistent with the assumption that
the acceleration is towards the sun). In Eq.(15) in the above mentioned
paper they write f-f' rather than f'-f, so this may be a typo or
(probably more likely) just an unfortunate notation as they actually
were referring to (1) rather than (2) (i.e. to df-df' rather than
f'-f).

It is rather annoying that at this level they can't even manage to
produce a consistent notation throughout the paper, but I think the
problem here is just this and has nothing to do with a sign switch in
the data analyis itself.



There are in my opinion actually more important inconsistencies in
statements made in these papers, which suggest that the theoretical
modelling of the data is actually anything but clear-cut. At the
beginning of chapter 2.1 of the Turyshev paper
(http://xxx.sf.nchc.gov.tw/abs/gr-qc/9903024 ) they give the
acceleration due to radiation pressure at 20 AU as 5*10^-8 cm/sec^2 ( a
value which is also mentioned in the Anderson paper), but towards the
bottom of the same chapter it suddenly says that 'at distances 10-15
AU it (the radiation pressure) produces an acceleration that is much
less then 8*10^-8 cm/sec^2'. Now, 5 is certainly not much less then 8,
and taking also into account that the statistical error of the data is
about 2*10^-8 cm/sec^2 (as mentioned in the Anderson paper), this means
that errors in the modelling of the radiation pressure force could
completely alter the data. Additionally, as I have pointed out on my
webpage http://www.physicsmyths.org.uk/pioneer.htm , signal propagation
effects (due to an incorrect application of the principle of the
invariance of the speed of light) would also lead to a contribution of
the same order of magnitude. A combination of all these factors could
well explain the data.

Thomas