Ranging and Pioneer

Thus spake "

Of course where there is a drift the rate should be increasing. I am not
clear that a rate for cycle slip is calculable for Pioneer, as it should
only be detected when we are able to perform direct measurements of
position, and hence find a conflict between ranging and Doppler.

This is getting really confusing.

I don't deny that the effect is confusing.

I would ask how performing
a range measurement could affect the Doppler measurement
but since they share the carrier there is an obvious link.

The idea is that whenever a direct measurement of position is done (in
this instance ranging) the quantum theory gets renormalised. The reason
being that quantum theory is formulated between initial and final
states, and with each classical measurement a final state is
reinterpreted as an initial state in a quantum theory formulated on an
expanded universe. When measurement of position can be regarded
continuous the effect is a continuous renormalisation of the quantum
theory, which then yields classical results for Doppler. The "new
physics" stuff happens when measurement of position cannot be regarded
as continuous.

In an ideal measurement with instantaneous return of the ranging signal
the theory would effectively be renormalised more rapidly than one cycle
of the Doppler signal, giving the classical Doppler result. But for
Pioneer we do not have that. I feel handicapped by not understanding
enough of the practicalities of measurement to understand exactly how
when and why ranging for Pioneer breaks down. However, so long as it
does break down and we cannot do a direct measurement of position I
think we are looking at Doppler between measurements, and therein lies
the source of the anomaly.

What I don't see is why cycle slips would occur if a range
measurement was in progress but not if only the Doppler
was being used on pysical grounds, though it is clear why
the range modulation sweep rate might exceed the ability
of the PLLs to follow in lock at a practical level.

I am
hoping that in attempting to answer your points things will become
clearer to me.

Yes, I hope I can act as a test for your explanation.

I appreciate it.

I haven't a clue what you mean so I'm going to take a
Devil's Advocate stance and throw up something for
you to knock down.

Assuming a carrier of 2.291GHz, the two-way Doppler
at 12.5km/s would be about 191048.836 Hz. An error
of 0.34m/s would produce a further shift of 5.196Hz
giving 191054.032 Hz.

Are you say that the signal would consist of short
sections at 191048.836 Hz separated by phase
discontinuities such that the mean phase rate was
191054.032 Hz ?

That is the idea.

Even so, why would that cause
cycle slips? Surely it would just give a sawtooth
modulation on the PLL control voltage?

I expect you are right. I feel I am handicapped by a lack of knowledge
of the practical engineering principles according to which these things
work. Can you give me, or point me at, a simple explanation.

And then how is the rate of slips influenced by the
theoretical resolution of a range measurement which
was not actually being performed at the time?

There is definitely an issue here to do with measurement in principle. I
don't think it is necessary that we actually take readings for a
measurement, but if it is possible to infer the results of a quantum
measurement in principle from readings which could be taken, that is
enough to cause wave function collapse and renormalisation of the
quantum theory.

Sorry, I guess I have completely misunderstood your
explanation but hopefully you will see where I am
going wrong and point me in the right direction.

It may be the other way about. I would like to look more carefully at
what you mean by "sawtooth modulation on the PLL control voltage". Can
you put this in context.

Thus,
if we can measure Mars to an accuracy of 12m (Anderson's figure), then
intermediate positions calculated from high frequency Doppler (if we
could resolve them with sufficient accuracy) would have to be corrected
every 12/c secs.

Well the ranging system as I said was theoretically
capable of better than cm resolution, it just wasn't
working. For other spacecraft it did but why that
would create cycle slips in the frequency measuring
system is unclear to me.

I am unclear about this. Anderson talks of it taking minutes to resolve
and return a ranging signal. Does this time period not gradually
increase with distance, or is there something more fundamental I have
not understood?




Regards

--
Charles Francis
substitute charles for NotI to email