Ranging and Pioneer

Oh No wrote:
Sorry for the delay in my response to this which got overlooked due to
other distractions.

OK, I just glad you hadn't dismissed me as a crank ;-)

Thus spake "
Oh No wrote:
....
I don't think Anderson actually says how frequent cycle slips were, just
that some were examined by an analyst. They did exclude the data.

The samples are generally once per minute and
few are missing in the small sample of days I
have examined. That may give you an upper
limit of a few per hour at most, possibly much
lower, that you could compare with your predicted
rate.

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

In the instance of Mars I calculate a maximum shift
equivalent to a velocity 0.34m/s, which I believe should be detectable
in principle at optical frequencies, although is actually two orders of
magnitude smaller than the resolution of HIRES, the most accurate
echelle spectrometer. This equates to a proportional shift of 0.34/c, or
10^-9. That does not translate directly into a rate for cycle slip,
because the disparity between Doppler and ranging should only be
detectable at the frequency corresponding to measurement accuracy.

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

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?

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.

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 not quite sure where the 15000 increase is, or what the equation
a_H = 2 Hv refers to.

snip derivations

... giving an apparent acceleration
of 5.50e-14 m/s^2. Compare that with the anomaly
of 8.74e-10 m/s^2.

Did that clarify my comment and show how the
speed of the craft comes into the equation?

Can you now explain why your result is so much
higher for Pioneer

As I think I said elsewhere, this is not the calculation I am doing. In
quantum coordinates the time coordinate shows an acceleration in time
which leads to prediction of a shift equivalent to uniform acceleration,
independent of the motion of the spacecraft. Radar uses measured time in
classical coordinates, so should not show any such acceleration.

Well it is still a measurement against a local clock
so I would expect it would but let's drop that, if
your calculation is purely a time acceleration I need
to study Anderson's phenomenological time models
before commenting.

yet that doesn't translate to
extra-galactic redshift measurements?

Ah, but it does. Actually my arguments, and results, are much clearer
for extra galactic red shift measurements. Translating them into results
for Pioneer I find much harder.

OK, it is really the Pioneer effect I am focussing
on so since I have been studying for some time
so I'll snip your comments on red shift.

Yes. I think really though that a new mission is required, preferably
one which allows both Doppler and ranging measurements in the outer
solar system.

I have a few ideas on that myself, probably not practical
though :-(

George