Ranging and Pioneer

John (Liberty) Bell wrote:
wrote:

snip

Over 20 years the anomaly produces a displacement
of about 174000 km. An error in inital speed of just
0.276 m/s would produce the same displacement in
the same time.

There is similarly no ambiguity over the Doppler figures monitored
thereafter.

On the contrary, the usefulness of the range
measurements would be to distinguish whether
the frequency was shifted due to motion of the
craft via the Doppler effect or whether the
frequency was being directly affected in some
manner without matching displacement.

That was precisely my point in the first place.

Yes, I realise that.

However, I still
maintain that a single direct ranging observation (the later the
better) would have sufficed (and still might suffice) to answer that
question.

Well I think that depends on whether the radial speed
error of 0.276 m/s is credible. Given that thrusters were
used for ConScan manoeuvers two or three times a year,
incidental delta speed changes of the order of 10mm/s
average per manoeuver over 20 years are all that would
be required.

However I would agree partly in that an accurate range
shortly after a planetary encounter could act as a
baseline so perhaps just two range readings say in
1990 and 2000 using your method would have be
sufficient. An earlier range using your technique would
still have been preferable to provide confidence that the
method gave a comparable value to those obtained by
other methods, say imaging when passing through the
last planetary system encounter.

As I understand it, the basic principle of ranging using Doppler data
is as follows:
Measuring the Doppler shift gives an accurate figure of the radial
velocity of the probe relative to the observer, at any given time.

Yes, bearing in mind a number of other factors affect the
frequency which have to be estimated, for example solar
plasma and variation of ionospheric refraction.

Integrating that data over time gives an accurate figure for the total
radial distance travelled by the probe relative to that observer.

Integrating the speed inferred from that data, yes.

Looked at another way, the total difference between the number of
signal oscillations since launch, and the total number that would have
been observed in the same time if the probe remained on Earth, provides
a direct (Doppler) measure of the total radial distance travelled by
the probe, in that time.

If we had continuous contact that would be the case but
contacts were generally limited to 4 hours at any particular
site. The speed was estimated and propagated through the
periods between contacts to 'join the dots', then that speed
integrated. More specifically the trajectory was propagated
over periods of many days and fitted to a series of data
points.

Yes, we can jiggle our model of the exact trajectory somewhat to
modify both tangential relativistic corrections to Doppler shifts and
the predicted decelerations of our model due to gravity.

Relativistic Doppler and gravitational effects are inherent
in the modelling. The overall trajectory needs to be jiggled
for the non-gravitational external and internal forces. That
is the key to my point above. Assuming the speed
measured as you describe just before and just after a
ConScan gives an accurate measure of the delta, then
the initial trajectory velocity can be solved for to obtain a
best fit to al the data points. Unless they made an a priori
assumption of that velocity, it seems to me that three
range values are then needed to distingush an anomalous
acceleration from an incorrect initial radial speed.

However, the
reported anomaly is the _minimum_ anomaly that remains after all such
adjustments are taken into account, given e.g. the tight constraints
provided by observations performed during planetary catapaulting.

Yes, though note the anomaly was assessed on data
mainly long after the last encounter.

Such data indicates
a) that the probe has travelled less far than predicted
b) that the probe is travelling slower than predicted
c) that the probe is continuing to decelerate faster than predicted.

Consequently, all we need to do to test if the conclusions reached by
Doppler observations are physically meaningful is to test if the total
distance travelled is greater than the distance admitted by Doppler
ranging.

Yes. Just to avoid possible confusion, I'll just note
that by "Doppler ranging" you mean range infrerred
by integration of the speed obtained from Doppler
rather than the specific ranging measurement that
is normally used based on modulation of the carrier
and correlation with the downlink to which the term
'ranging' is usually applied.

The _minimum_ additional distance required for a round trip
signal (if Doppler conclusions are illusory) would already have been
greater than 1 light second (using your own figure for 1980 to the last
good signal), and would have been even larger if that Pioneer Doppler
effect was present (but unrecognised) prior to 1980.

That would only be true if the speed and range at some
point prior to 1980 and all subsequent speed changes
due to manoeuvers were known accurately but that is not
the case.

It is thus
completely irrelevant when the effect was first noticed, for the
purpose of testing that hypothesis.

True, what is important is the earliest point where the
speed and location were accurately measured and after
which all non-gravitational increments to the velocity can
be determined.

However, the point was that they were not in a position
to realise that such an inventive technique was needed
until they realised the anomaly could not be explained
simply as, for example, a bug in the software.

George

John (Liberty) Bell wrote:
wrote:

Finally you have perhaps the biggest problem of
measuring the switch-off of the signal with millisecond
accuracy through a receiver chain with a bandwidth of
less than 1 Hz which is what was needed to hold lock
on the carrier. That applies whichever method of timing
you use at the transmitter.

Notwithstanding my prior comment on this point, it is obvious that many
positions in this receiver chain have much higher frequency responses
than 1 Hz.

True but the siganl is far les than the noise prior to
the filter so not accessible. More below.

Ther frequency response you quote refers to a point in the
receiver chain and feedback loop(s) which behaves as an active low pass
filter. Whilst I am not familiar with the exact electronics used by
NASA, I do know from other active feedback circuits, that an active low
pass filter configuration can also be used as a band pass, high pass,
and even all pass circuit, depending on the point in the loop you
choose to define as output (and appropriately buffer).

Certainly, but if you tap off a high pass signal, you
get only the noise and you remove the signal so that's
not really useful.

In this context, it is pertinent to ask:- what do we mean by a
frequency responses of 1 Hz?

It is. There are documents describing the process in
considerable detail but I don't have the references here
so I'm going from memory (always a bad idea).

The system runs an FFT on a band where the signal is
expected That can have a very high resolution but is no
use for real-time reception. The highest peaks are then
checked and the receiver attempts to lock on with a
standard PLL technique (I believe it was implemented
digitally but the method is the same as an analogue
implementation). The low pass filter in that loop starts
at around 1Hz which means only a small amount of the
broadband noise but all the signal gets through. The
loop then locks onto the secular frequency, which
should be that of the signal, while the effect of the
remaining noise translates into phase jitter.

The output of the local oscillator is then a low-noise
copy of the signal so multiplying that by the filtered
signal gives a sin^2 term for the actual signal but
sin(a)*sin(b) for all noise components. The average
value of the output from that multiplier circuit is then
a measure of the amplitude of the signal since the
average of sin(a)*sin(b) is zero. Lock was declared
when that exceeded a predicted value based on the
craft transmitter power and approximate range.

Once lock was aquired, the filter bandwidth was further
reduced automatically to exclude the noise and hence
reduce phase jitter. How far it was reduced was
configurable so I can't say the exact value but IIRC it
could be as low as 0.01Hz.

What you wanted as an indication of the transmitter
going off would then be a sudden drop in the output
of the mean DC level from the multiplier circuit.

I suggest this merely means that we can be confident that the receiver
will remain locked on the last transmitted signal frequency for 1/2
second after that signal has terminated.

On loss of signal it would restart the search process
but even if it didn't, the local oscillator would just stop
being pulled to follow the signal which drifts due to
the varying Doppler from the Earth's rotation.

Far from being a disadvantage,
this is, therefore, an advantage, sice we can now monitor a higher
frequency output of the chain, (storing and subsequently analysing if
necessary), around, say, a 2 second window of the predicted turn off
time, with confidence that any observed sustained loss of signal is not
due to a loss of signal lock.

A software change could have been introduced to write
the last N seconds of data to a file for post-processing
(though other projects sharing the DSN might have
objected to the risk introduced) but the problem remains
of separating variations of amplitude due to atmospheric
scintillation, thermal noise getting through the loop
filter and actual reduction of signal when using such a
low bandwidth. The best would be to fit the filter response
to a step reduction in the presence of white noise to the
recorded output of the multiplier. At high SNR that would
work well but at low SNR the time uncertainty rises rapidly.

George

John (Liberty) Bell wrote:

snip

Some information on the command protocols is
available he

http://deepspace.jpl.nasa.gov/dsndoc...tationdata.cfm

In particular sections 208 and 205. Of course these
are current and may not reflect the condition of the
DSN as it was 20 years ago.

I'm still looking for the document describing the
receiver locking strategy.

HTH
George

wrote:
John (Liberty) Bell wrote:
wrote:

Finally you have perhaps the biggest problem of
measuring the switch-off of the signal with millisecond
accuracy through a receiver chain with a bandwidth of
less than 1 Hz which is what was needed to hold lock
on the carrier. That applies whichever method of timing
you use at the transmitter.

Notwithstanding my prior comment on this point, it is obvious that many
positions in this receiver chain have much higher frequency responses
than 1 Hz.

True but the siganl is far les than the noise prior to
the filter so not accessible. More below.

You are confusing me here. We seem to be talking about several filters
simultaneously. Furthermore, in a feedback loop, it is no longer
meaningful to discuss earlier and later, only physical points in the
loop.

Clearly, at one point we must have a high Q bandpass filter which is
tuned to the carrier frequency of ~ 2 gig. Its frequency response is,
presumably, the carrier frequency + - 1 Hz
Clearly at another point we must have a low pass filter providing a
control signal. Its effective frequency response is, presumably, 0 to
1Hz

I would be happy to stand corrected on this, but I don't think these
two 1Hz figures are the same thing.

John

wrote:
John (Liberty) Bell wrote:

snip

Some information on the command protocols is
available he

http://deepspace.jpl.nasa.gov/dsndoc...tationdata.cfm

In particular sections 208 and 205. Of course these
are current and may not reflect the condition of the
DSN as it was 20 years ago.

I'm still looking for the document describing the
receiver locking strategy.

HTH
George

Thanks.

There is also now an excellent explanation, and comments, on
appropriate technical details from George Dishman, only posted at
sci.astro.research. (I say this in case you are only monitoring this
discussion from sci.physics.research.{If so, you could have missed a
fair bit})

John Bell
http://global.accelerators.co.uk
(Change John to Liberty to respond by email)

wrote:
John (Liberty) Bell wrote:
wrote:

snip

Over 20 years the anomaly produces a displacement
of about 174000 km. An error in inital speed of just
0.276 m/s would produce the same displacement in
the same time.

There is similarly no ambiguity over the Doppler figures monitored
thereafter.

On the contrary, the usefulness of the range
measurements would be to distinguish whether
the frequency was shifted due to motion of the
craft via the Doppler effect or whether the
frequency was being directly affected in some
manner without matching displacement.

That was precisely my point in the first place.

Yes, I realise that.

However, I still
maintain that a single direct ranging observation (the later the
better) would have sufficed (and still might suffice) to answer that
question.

Well I think that depends on whether the radial speed
error of 0.276 m/s is credible. Given that thrusters were
used for ConScan manoeuvers two or three times a year,
incidental delta speed changes of the order of 10mm/s
average per manoeuver over 20 years are all that would
be required.

I have not put my maths head on for this, but this proposition seems
dubious to me. It looks like this would require not one but years of
misreadings of Doppler shifts by about 2 Hz. You might conceivably get
away with this, but for one thing. Considerable effort was expended in
attempting to make the anomaly disappear, without success. If what you
propose was permissible within the margins of uncertainty of the model,
I am sure they would have jumped at it with enthusiasm.


However I would agree partly in that an accurate range
shortly after a planetary encounter could act as a
baseline so perhaps just two range readings say in
1990 and 2000 using your method would have be
sufficient. An earlier range using your technique would
still have been preferable to provide confidence that the
method gave a comparable value to those obtained by
other methods, say imaging when passing through the
last planetary system encounter.

As I understand it, the basic principle of ranging using Doppler data
is as follows:
Measuring the Doppler shift gives an accurate figure of the radial
velocity of the probe relative to the observer, at any given time.

Yes, bearing in mind a number of other factors affect the
frequency which have to be estimated, for example solar
plasma and variation of ionospheric refraction.

Integrating that data over time gives an accurate figure for the total
radial distance travelled by the probe relative to that observer.

Integrating the speed inferred from that data, yes.

Looked at another way, the total difference between the number of
signal oscillations since launch, and the total number that would have
been observed in the same time if the probe remained on Earth, provides
a direct (Doppler) measure of the total radial distance travelled by
the probe, in that time.

If we had continuous contact that would be the case but
contacts were generally limited to 4 hours at any particular
site. The speed was estimated and propagated through the
periods between contacts to 'join the dots', then that speed
integrated. More specifically the trajectory was propagated
over periods of many days and fitted to a series of data
points.

Sure. I appreciated that considerable interpolation was involved in
practice. Just trying to get a baisc concept across ( and agreed)

Yes, we can jiggle our model of the exact trajectory somewhat to
modify both tangential relativistic corrections to Doppler shifts and
the predicted decelerations of our model due to gravity.

Relativistic Doppler and gravitational effects are inherent
in the modelling. The overall trajectory needs to be jiggled
for the non-gravitational external and internal forces. That
is the key to my point above. Assuming the speed
measured as you describe just before and just after a
ConScan gives an accurate measure of the delta, then
the initial trajectory velocity can be solved for to obtain a
best fit to al the data points. Unless they made an a priori
assumption of that velocity, it seems to me that three
range values are then needed to distingush an anomalous
acceleration from an incorrect initial radial speed.

However, the
reported anomaly is the _minimum_ anomaly that remains after all such
adjustments are taken into account, given e.g. the tight constraints
provided by observations performed during planetary catapaulting.

Yes, though note the anomaly was assessed on data
mainly long after the last encounter.

Such data indicates
a) that the probe has travelled less far than predicted
b) that the probe is travelling slower than predicted
c) that the probe is continuing to decelerate faster than predicted.

Consequently, all we need to do to test if the conclusions reached by
Doppler observations are physically meaningful is to test if the total
distance travelled is greater than the distance admitted by Doppler
ranging.

Yes. Just to avoid possible confusion, I'll just note
that by "Doppler ranging" you mean range infrerred
by integration of the speed obtained from Doppler
rather than the specific ranging measurement that
is normally used based on modulation of the carrier
and correlation with the downlink to which the term
'ranging' is usually applied.

Absolutely

The _minimum_ additional distance required for a round trip
signal (if Doppler conclusions are illusory) would already have been
greater than 1 light second (using your own figure for 1980 to the last
good signal), and would have been even larger if that Pioneer Doppler
effect was present (but unrecognised) prior to 1980.

That would only be true if the speed and range at some
point prior to 1980 and all subsequent speed changes
due to manoeuvers were known accurately but that is not
the case.

OK, I will try to explain the reasoning which led me to my conclusion.

1) Either the anomalous acceleration is real, or it isn't. If not, the
probe travels classically.
2) All other things being equal, if there is real anomalous
deceleration, the probe must travel less distance and at less mean
velocity. Conversely, if actually travelling classically, it must
travel more distance at greater mean velocity
3) Now, every effort was made to reconcile observation with classical
theory within the constraints and error margins of the theory (The
impossibility of achieving this objective only became apparent at 20
au.).

This means that if the anomalous acceleration was real the trajectory
model was pushed to the limits to make the elapsed distance and mean
velocity as large as possible, in order to fit as closely as possible
to theory.
Conversely, if the probe actually travelled classically, this means
that the trajectory model was pushed to the limits to make that
classical distance and mean velocity as small as possible, in order to
fit as closely as possible to observation.

Consequently we can use the same trajectory model for calculating the
distance elapsed if real, and if unreal, since this defines the
_absolute_ minimum distance discrepancy that results between these two
possibilities (This is all we need because the only purpose of the
experiment is to determine which of those divergent options is true.)

Hope this helps

John Bell
http://global.accelerators.co.uk
(Change John to Liberty to respond by email)

John (Liberty) Bell wrote:
wrote:
John (Liberty) Bell wrote:

snip

However, I still
maintain that a single direct ranging observation (the later the
better) would have sufficed (and still might suffice) to answer that
question.

Well I think that depends on whether the radial speed
error of 0.276 m/s is credible. Given that thrusters were
used for ConScan manoeuvers two or three times a year,
incidental delta speed changes of the order of 10mm/s
average per manoeuver over 20 years are all that would
be required.

I have not put my maths head on for this, but this proposition seems
dubious to me.

It is very dubious but cannot be excluded on principle
alone. That's why some measurements would be useful.

It looks like this would require not one but years of
misreadings of Doppler shifts by about 2 Hz.

No, let me give a toy example. Look at Fig 5 in the
paper which shows the effect of a manoeuvre. The
craft spin was of the order of 5 rpm. Suppose that
was halved by the manoeuvre and then spun up
after but the JPL team weren't aware. The RF signal
is circularly polarised so a spin change of 2.5 rpm
creates a frequency change of 41.7mHz on both
up- and down-links. The total is equivalent to an
error of 5.5mm/s delta V. The residual of -0.9 mm/s
makes that seem unlikely but do you see what I
mean?

You might conceivably get
away with this, but for one thing. Considerable effort was expended in
attempting to make the anomaly disappear, without success. If what you
propose was permissible within the margins of uncertainty of the model,
I am sure they would have jumped at it with enthusiasm.

Sure but there is an unknown cause so it is dangerous
to make an assumption as to whether it affects the
craft motion or just the received frequency. Another
example - we know the solar plasma affects the
frequency directly, perhaps this is where the problem
lies. Anyway, I agree a range measure would be
valuable but some of that value is lost if we assume
we only need to check one end of the track but not
the other. More below.

big snip

Such data indicates
The _minimum_ additional distance required for a round trip
signal (if Doppler conclusions are illusory) would already have been
greater than 1 light second (using your own figure for 1980 to the last
good signal), and would have been even larger if that Pioneer Doppler
effect was present (but unrecognised) prior to 1980.

That would only be true if the speed and range at some
point prior to 1980 and all subsequent speed changes
due to manoeuvers were known accurately but that is not
the case.

OK, I will try to explain the reasoning which led me to my conclusion.

1) Either the anomalous acceleration is real, or it isn't. If not, the
probe travels classically.

Agreed.

2) All other things being equal, if there is real anomalous
deceleration, the probe must travel less distance and at less mean
velocity. Conversely, if actually travelling classically, it must
travel more distance at greater mean velocity

Agreed.

3) Now, every effort was made to reconcile observation with classical
theory within the constraints and error margins of the theory (The
impossibility of achieving this objective only became apparent at 20
au.).

OK, I think they finally realised other mundane
explanations couldn't explain it later but no matter.

This means that if the anomalous acceleration was real the trajectory
model was pushed to the limits to make the elapsed distance and mean
velocity as large as possible, in order to fit as closely as possible
to theory.
Conversely, if the probe actually travelled classically, this means
that the trajectory model was pushed to the limits to make that
classical distance and mean velocity as small as possible, in order to
fit as closely as possible to observation.

Not quite. The trajectory model was not pushed one
way or the other, the examination of influences on the
motion were extended to include everything that could
be dreampt up and lot of work then went into replacing
rough estimates with more accurate versions. Eventually
they got the uncertainty down to an order of magnitude
less than the anomaly. At that point no assumption was
being made about whether the motion was affected or
not.

In fact it is quite likely that there is a bit of both involved
since the solar plasma effect on the transmission can
only be estimated and the exact reaction force from the
radio beam which accelerates the craft isn't known to
better than 10%.

Consequently we can use the same trajectory model for calculating the
distance elapsed if real, and if unreal, since this defines the
_absolute_ minimum distance discrepancy that results between these two
possibilities (This is all we need because the only purpose of the
experiment is to determine which of those divergent options is true.)

Yes we can, but it doesn't resolve the question. If we
find that the craft is distance D (= 1/2 * a_P * t^2) closer
than we expected from the 'classical' prediction, how do
we tell whether it is because a_P is real or the craft was
D closer when we started the calculation? If we are
confident of the range at both start and end, how do we
know it wasn't because the inital speed was D/t lower
than we thought due to the anomaly producing an error
in that.

If we try to find a classical solution using _only_ range
measurements then we need a minimum of three. If
we merge both then there may be a discernible
difference in the residuals with fewer.

Hope this helps

I think it does but I think you also need to think carefully
about what a priori data you are going to trust.

George

wrote:
John (Liberty) Bell wrote:
wrote:
John (Liberty) Bell wrote:

snip

However, I still
maintain that a single direct ranging observation (the later the
better) would have sufficed (and still might suffice) to answer that
question.

Well I think that depends on whether the radial speed
error of 0.276 m/s is credible. Given that thrusters were
used for ConScan manoeuvers two or three times a year,
incidental delta speed changes of the order of 10mm/s
average per manoeuver over 20 years are all that would
be required.

I have not put my maths head on for this, but this proposition seems
dubious to me.

It is very dubious but cannot be excluded on principle
alone. That's why some measurements would be useful.

It looks like this would require not one but years of
misreadings of Doppler shifts by about 2 Hz.

No, let me give a toy example. Look at Fig 5 in the
paper which shows the effect of a manoeuvre. The
craft spin was of the order of 5 rpm. Suppose that
was halved by the manoeuvre and then spun up
after but the JPL team weren't aware. The RF signal
is circularly polarised so a spin change of 2.5 rpm
creates a frequency change of 41.7mHz on both
up- and down-links. The total is equivalent to an
error of 5.5mm/s delta V. The residual of -0.9 mm/s
makes that seem unlikely but do you see what I
mean?

You might conceivably get
away with this, but for one thing. Considerable effort was expended in
attempting to make the anomaly disappear, without success. If what you
propose was permissible within the margins of uncertainty of the model,
I am sure they would have jumped at it with enthusiasm.

Sure but there is an unknown cause so it is dangerous
to make an assumption as to whether it affects the
craft motion or just the received frequency. Another
example - we know the solar plasma affects the
frequency directly, perhaps this is where the problem
lies. Anyway, I agree a range measure would be
valuable but some of that value is lost if we assume
we only need to check one end of the track but not
the other. More below.

big snip

Such data indicates
The _minimum_ additional distance required for a round trip
signal (if Doppler conclusions are illusory) would already have been
greater than 1 light second (using your own figure for 1980 to the last
good signal), and would have been even larger if that Pioneer Doppler
effect was present (but unrecognised) prior to 1980.

That would only be true if the speed and range at some
point prior to 1980 and all subsequent speed changes
due to manoeuvers were known accurately but that is not
the case.

OK, I will try to explain the reasoning which led me to my conclusion.

1) Either the anomalous acceleration is real, or it isn't. If not, the
probe travels classically.

Agreed.

2) All other things being equal, if there is real anomalous
deceleration, the probe must travel less distance and at less mean
velocity. Conversely, if actually travelling classically, it must
travel more distance at greater mean velocity

Agreed.

3) Now, every effort was made to reconcile observation with classical
theory within the constraints and error margins of the theory (The
impossibility of achieving this objective only became apparent at 20
au.).

OK, I think they finally realised other mundane
explanations couldn't explain it later but no matter.

This means that if the anomalous acceleration was real the trajectory
model was pushed to the limits to make the elapsed distance and mean
velocity as large as possible, in order to fit as closely as possible
to theory.
Conversely, if the probe actually travelled classically, this means
that the trajectory model was pushed to the limits to make that
classical distance and mean velocity as small as possible, in order to
fit as closely as possible to observation.

Not quite. The trajectory model was not pushed one
way or the other, the examination of influences on the
motion were extended to include everything that could
be dreampt up and lot of work then went into replacing
rough estimates with more accurate versions. Eventually
they got the uncertainty down to an order of magnitude
less than the anomaly. At that point no assumption was
being made about whether the motion was affected or
not.

In fact it is quite likely that there is a bit of both involved
since the solar plasma effect on the transmission can
only be estimated and the exact reaction force from the
radio beam which accelerates the craft isn't known to
better than 10%.

Consequently we can use the same trajectory model for calculating the
distance elapsed if real, and if unreal, since this defines the
_absolute_ minimum distance discrepancy that results between these two
possibilities (This is all we need because the only purpose of the
experiment is to determine which of those divergent options is true.)

Yes we can, but it doesn't resolve the question. If we
find that the craft is distance D (= 1/2 * a_P * t^2) closer
than we expected from the 'classical' prediction, how do
we tell whether it is because a_P is real or the craft was
D closer when we started the calculation? If we are
confident of the range at both start and end, how do we
know it wasn't because the inital speed was D/t lower
than we thought due to the anomaly producing an error
in that.

If we try to find a classical solution using _only_ range
measurements then we need a minimum of three. If
we merge both then there may be a discernible
difference in the residuals with fewer.

Hope this helps

I think it does but I think you also need to think carefully
about what a priori data you are going to trust.

I do see your point in principle, particularly in view of the latest
paper by Anderson et al. Here they suggest the anomaly could have been
caused by an unmodelled difference in dynamics during planetary
catapaulting. That is ironic since earlier in the discussion most
seemed in agreement that a close planetary encounter helped to pin down
where the probe was at a given time. We now find that this may have
done precisely the opposite, for the subsequent trajectory.

John Bell
http://accelerators.co.uk
(Change John to Liberty to respond by email)

"John (Liberty) Bell" wrote in message
oups.com...
wrote:

snip

If we try to find a classical solution using _only_ range
measurements then we need a minimum of three. If
we merge both then there may be a discernible
difference in the residuals with fewer.

Hope this helps

I think it does but I think you also need to think carefully
about what a priori data you are going to trust.

I do see your point in principle, particularly in view of the latest
paper by Anderson et al. Here they suggest the anomaly could have been
caused by an unmodelled difference in dynamics during planetary
catapaulting. That is ironic since earlier in the discussion most
seemed in agreement that a close planetary encounter helped to pin down
where the probe was at a given time. We now find that this may have
done precisely the opposite, for the subsequent trajectory.

Excellent. In practice it is simpler, different methods
of making the same measurement will often produce different
results since different error mechanisms come into play. To
confirm a_P is physical we really want three range measures
using the same technique. Their 'confidence check' on other
craft where they compared integrated Doppler speed with delta
range showed discrepancies at about the same level as a_P
over a day.

To add an alternative perspective to your proposal, I would
like to add a comment on an alternative methods for finding
the range using existing data. The existing software does
this but as an integral part of finding the best overall fit
rather than extracting a specific range value.

Firstly note that the speed of rotation of the Earth at the
equator is around 465m/s which introduces a Doppler shift of
about 3555 Hz on the signal, both on the up-link and down-
link. The rate of change for each link is about 15.5Hz/minute
at the equator.

For each DSN site, that is reduced by a factor of cos(latitude).
The exact time of receipt of the signal is known hence the
Doppler at the receiving site and the effect of the orbital
motion of the Earth can be removed, as can the orbital motion
at the transmit site since this changes by a negligible amount
over times of a minute or less which is the basic uncertainty
in the transmit time.

The remaining diurnal component is that due to the rotational
speed of the transmit site. We can fit a sine wave to that and
the phase then gives the exact transmit time. The difference
between transmit and receive times then provides the range.

Given that Markwardt's paper shows final residuals of the order
of 4.2mHz, the uncertainty in the transmit time is around 16ms
or perhaps 20ms to 25ms rms allowing for latitude. Your method
would have to provide better accuracy than that. See figure 2
of:

http://www.arxiv.org/abs/gr-qc/0208046

I think a degree of isolation of the range value from speed
could be obtained by taking a second derivative of the Doppler
values which has the effect of magnifying the diurnal variation
by 365^2 compared to the annual sine variation and almost
constant craft speed.

If the range were calculated on a contact-by-contact basis in
that manner and compared with the integral of the direct Doppler
speed then there should be a quadratic difference if the anomaly
affects the RF signal but no difference if it affects the craft
motion.

Actually this is a simplification of something I have been
considering for some time where the time of zero diurnal
variation gives the Right Ascension of the craft and might
allow a crude parallax measure of range. Unfortunately the
numbers don't seem to give a benefit using that method.

George

"Oh No" wrote in message
...

The position of Pioneer was calculated from Doppler information. Ranging
was not available. Can anyone explain why ranging could not be used? Is
this just a limit on available technology, or is there a more
fundamental reason?

To get a range measure, the DSN applies a "ramp" to the
uplink. I believe that means very slow sawtooth FM. The
time delay to the corresponding downlink modulation via
the transponder gives the range. Because of the extreme
distance and low signal levels, the bandwidth had to be
very narrow both at the craft and the DSN. From personal
emails from one of the team, I believe that they did
attempt to apply the modulation soon after the Jupiter
flyby but it always caused the spacecraft to loose lock
with the uplink.

George