Ranging and Pioneer

Thus spake "
Of critical importance is the timescale between initial state and final
state when modelling the motion. This timescale is determined by the
accuracy with which we can measure. Local distances can be measured with
great accuracy, equivalent to a short timescale. Remote distances are
intrinsically less accurate (e.g. radar distance measurements to mars
are accurate to about 12m).

I'm not familiar with the details of Mars
ranging but I have looked at Pioneer in
some detail. I will comment on that as it
may be of interest to you but it doesn't
seem to answer my original question.

The signal from Pioneer uses an effective Doppler frequency of 1MHz,
equivalent to a distance scale of 300m.

Although the final digital analysis is done
around 1MHz, the RF is heterodyned down
to that against the reference. It means that
the measurement resolution is still that of
the 2.291GHz carrier. Further the MDA is
capable of measuring phase to 1/256 of a
cycle or about 0.5mm in range. While the
ranging system itself wasn't available, the
frequency measurements are still taken
from that same hardware and have that
resolution.

This might be true if everything were perfect, but it is not. To
interpolate higher frequencies than the 1MHz effective Doppler frequency
one has to assume no such thing as cycle slip, for example. In fact even
GPS systems are plagued with cycle slip.

Note the residuals from Galileo
in Figure 10 of gr-qc/0104064 and the
discussion to the left that indicates
consistency to about 4m over a day.

The discussion seems to indicate that they cannot tell whether the
acceleration was present. If they are suggesting that radar was accurate
to 4m, then I would expect it not to be present. I am not sure that that
is what they are saying because I had been given to believe that the
measurements of Mars are the most accurate within the Solar system.

The actual measurements are limited to a
few metres accuracy mainly due to the
group delay in the somewhat unpredictable
solar plasma and the unknown angle of
refraction through the atmosphere and at
the boundary of the ionosphere, but the
resolution of the instrument which I think
is the determining aspect from the QM
point of view is better than 1mm.

All these things have an effect, but the reason given by Anderson on p7

"Currently, two types of Galileo navigation data are
available, namely Doppler and range measurements. As
mentioned before, an instantaneous comparison between
the ranging signal that goes up with the ranging signal
that comes down would yield an â~@~\instantaneousâ~@~] twoway
range delay. Unfortunately, an instantaneous comparison
was not possible in this case. The reason is that
the signal-to-noise ratio on the incoming ranging signal
is small and a long integration time (typically minutes)
must be used (for correlation purposes). During such
long integration times, the range to the spacecraft is constantly
changing".

The long integration times appear to me to introduce uncertainties much
greater than 1mm. Certainly the uncertainties can be reduced in
principle by using a stronger signal, and more accurate measurement may
be possible, but if this idea is right that will merely extend the
distance to a space craft at which ranging becomes impracticable and the
Pioneer acceleration becomes observable.



This was the gist of my original question and
where I am still puzzled. The conventional
linear Hubble law if applied to Pioneer 10
predicts an apparent acceleration some
15000 times smaller than the anomaly given
by the equation a_H = 2 H v. I don't understand
why you think your analysis produces a result
four orders of magnitude larger than the normal
Hubble Law under either of the regimes you
explain above.

Sorry if I'm being a bit slow but it is this factor
of 15000 increase that I cannot fathom.

I am not quite sure where the 15000 increase is, or what the equation
a_H = 2 Hv refers to. I have it that quantum coordinates introduce an
acceleration in time which can be shown by a coordinate transformation
equivalent to an acceleration Hc.


Regards

--
Charles Francis
substitute charles for NotI to email