Ranging and Pioneer

Oh No wrote:
Thus spake "
Oh No wrote:
The signal from Pioneer uses an effective Doppler frequency of 1MHz,
equivalent to a distance scale of 300m.

... the MDA is
capable of measuring phase to 1/256 of a
cycle or about 0.5mm in range. ...

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.

Surely the quantum effects are only
affected by the equipment, not assumptions,
but no matter, this was just FYI. Cycle slips
were sufficiently infrequent that many were
corrected by hand by the analysts going
over the data. I believe Anderson et al may
have excluded any measurement with a cycle
slip from subsequent processing but I'm not
sure on that without rechecking the paper.

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.

They are saying their checks showed the
integrated Doppler velocity was consitent
with the ranging result to within 4m over
one day. The anomaly is comparable or
smaller so needs longer timescales to
show up.

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.

Perhaps in percentage terms, ranging using
the corner refectors on the Moon achieves cm
accuracy.

....
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.

You can think of Doppler giving a plot of speed
over time while the ranging system intergrated
hence gives something like an average ignoring
acceleration. It is just a practical difficulty.

... 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.

Take the Hubble constant H as 71km/s per MPc.
A parsec is 3.09e16 m and an AU is 1.5e11 m
so changing units H = 3.44e-7 m/s per AU.

In Jan 1987 the craft was at 40 AU so the signal
had to travel 80 AU giving a redshift due to the
Hubble constant equivalent to a speed of
2.75e-5 m/s. Similarly in Dec 1994 at the end
of the period analysed for Pioneer 10, the range
was 60 AU and the round trip 120 AU which
gives an apparent speed from the Hubble Law of
4.13e-5 m/s.

That's a change of 1.38e-5 m/s in a time of 2921
days or 2.51e8 s giving an apparent acceleration
of 5.50e-14 m/s^2. Compare that with the anomaly
of 8.74e-10 m/s^2.

The equation that summarises that is a = 2 H v
where H is the Hubble constant, v is the radial
speed of the craft, a is the resulting apparent
acceleration and the factor of 2 is due to the
double trip.

I have it that quantum coordinates introduce an
acceleration in time which can be shown by a coordinate transformation
equivalent to an acceleration Hc.

If it is an effect in time, that could be quite different
to the ranging analysis and might explain why the
numbers differ so much. Of the phenomenological
time models considered by Anderson et al, do any
of their equations (60) through (65) match? See
page 46 of gr-qc/0104064 for details.

George