On 26 Mar, 18:31, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

I note that you continue to delete "crucial" components to the debate.

They are not crucial. I only leave out those parts of your posts in my
reply that are either related to your habit of inserting comments
without even having read the next sentence (let alone the whole post),
or because I have addressed the particular point elsewhere in my
reply. So if you would read my whole post before deciding where to set
your comments, you could save yourself a lot of writing, and me a lot
of editing.

The diurnal and long term acceleration residuals are virtually exactly
the same (0.1 mm/sec/day), ...

Your units are incorrect. The diurnal residuals noted by Anderson in
their Figure 18 are sinusoidal with an *amplitude* of 0.1 mm/s, not a
drift of 0.1 mm/s/day.

The units are correct. As you can see from the figure, the magnitude
of the diurnal residual velocity changes are of the order of 0.1 mm/
sec/day (i.e. corresponding to an acceleration of 10^-7 cm/sec^2). The
only difference is that the first is a circular acceleration, but the
second apparently a linear one ...

... (I am saying 'apparently' because from
my above derivation it should be evident that it could just as well be
a circular acceleration with a very long period (corresponding to the
drift of a possible rotation rate error in this case)) .

Your derivation is fascinating but irrelevant. You have introduced a
model earth that rotates at a constant angular speed difference than
an actual earth. *Of course*, in that scenario, diurnal residuals
will grow as the phase difference between the model earth and the true
earth grows.
....
Also, it's worth noting that the term,
-0.5*dw*w*t*|sin(wt)|
is *not* a linear drift in time, but still a diurnal sinusoid with
growing amplitude. This is *not* what is observed, so in any case,
your derivation fails to match the actual observations. Also, see
points 1 and 2 above.

It isn't a sinusoid, but only the upper half of a sinusoid (which I
schematically approximated here by taking the absolute value), so the
daily average would increase linearly. ...

However, you have assumed an unsubstantiated rotation-rate error. In
fact, the orientation rotation *angles* are measured and constrained
on a daily basis by many IERS contributors, so the "model earth" could
never become out of phase as grossly as you suggest. Since the
premise of your argument is false, your conclusions are thus
irrelevant.

The assumption of a rotation rate error is not unsubstantiated. It is
exactly substantiated by the Pioneer anomaly. ...

I admit that there is no corresponding long term velocity residual if
the radial position of the observing station is assumed as incorrect
(rather than the rotation rate), but still it yields a diurnal term
(dx_r/dt= dr*w*cos(wt), if dr is the radius mis-match) which could be
significant here for the modelling for dr as small as a few
centimeters).

True, but see point 4 above.

How would you know if your algorithm is only accurate to within a few
meters (as you state in your paper), ...

... and indeed you don't obtain any
diurnal variations at all?

Your argument is that these fluctuations would be taken into account
automatically, but this assumes that they are actually related to the
earth's rotation. You can not substantiate this assumption as you
don't have any reference point regarding the true rotation angle. ...
.. The 'observed' values could be affected by any number of errors associated
with incorrect modelling of other physical effects (e.g. ionospheric
refraction). ...

They could be? By what mechanism? By how much? What is the basis
for your claim? Could these effects really mimic a rotation rate
error? I note that you did not substantiate your claim; you basically
threw it out there as a diversion. In fact, multi-frequency
observations can straightforwardly correct for ionospheric effects.

By what mechanism do you explain in detail the variations in the
earth's rotation data? Do you have any quantitative theory for this?
...

I have some vague ideas that I could follow up (e.g. the ionosphere/
magnetosphere is likely not to fully co-rotate with the earth, as the
magnetic field is not coupled to the surface but to somewhere in the
interior, and thus light might be dragged according to the
differential rotation), but I would really need to know exact details
how ionospheric and other potential error sources are being covered in
the VLBI data analysis.

... The fact that VLBI data are 'exact' (i.e. consistent) to
a certain degree doesn't mean they are correct. It all depends on the
model used for obtaining these data.
As I said before, unless the apparent variations in the earth's
rotation rate can be fully theoretically modelled, it is not
appropriate to use them as a physical standard.

This is another diversion by you.

It isn't a diversion. I am just trying to point out the inconsistency
in your attitude here: you are bothering about unmodelled terms at the
10^-8 level in the Pioneer Doppler data, but you are not bothering
about unmodelled terms of an identical magnitude in the earth's
rotation data. Common sense would suggest that you sort out the latter
first before using them as given elements in the analysis of the
former (if not you shouldn't be surprised if inconsistencies pop up).
Reversely, if you accept the earth rotation data as given empirical
facts, you might just as well accept the Pioneer Doppler data as given
empirical facts and not bother about them any further.

The units are correct. As you can see from the figure, the magnitude
of the diurnal residual velocity changes are of the order of 0.1 mm/
sec/day (i.e. corresponding to an acceleration of 10^-7 cm/sec^2). The
only difference is that the first is a circular acceleration, but the
second apparently a linear one ...

That's an interesting clarification. It's also entirely erroneous
since the difference between a one-day sinusoid and a decade-long
linear drift is a *huge* difference.

Incidentally, your truncated sinusoid term, |sin(wt)|, is incorrect.
In terms of the earth motion, the spacecraft rises in the east
(station moving toward the spacecraft, so a blueshift), and then sets
in the west (station moving away from the spacecraft, so a redshift).

While the actual behavior of the Doppler signal during tracking passes
is indeed a "half" of a sine-wave, it is *not* just the positive half,
but rather the half from 90 to 270 degrees, which has both positive
and negative excursions. You erroneously took the absolute value
without considering the proper phasing.

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.

It isn't a sinusoid, but only the upper half of a sinusoid (which I
schematically approximated here by taking the absolute value), so the
daily average would increase linearly. ...

A fascinating claim, but since daily averages were *not* used in the
analysis (see point 1 above) your conclusions are irrelevant.

Furthermore, the IERS contributors come from hundreds of earth
stations, measuring tens of satellites and hundreds of quasars, with
thousands of observations per day. Some of the techniques use the
same receiver technology as spacecraft Doppler tracking (GPS, VLBI),
and some even use the same solution algorithms (GPS). All of these
observations produce at a single consistent picture of how the earth
orientation is tied to an inertial frame.

An "unmodeled" error in earth rotation {rate} would indeed show up in
these (GPS,VLBI,SLR,LLR) observations as a sinusoid with growing
amplitude. But then the model value of UT1-UTC {rate} would need be
adjusted to remove such a residual. It is these adjusted UT1-UTC
values which are used for spacecraft Doppler analysis.

I have some vague ideas that I could follow up (e.g. the ionosphere/
magnetosphere is likely not to fully co-rotate with the earth, as the
magnetic field is not coupled to the surface but to somewhere in the
interior, and thus light might be dragged according to the
differential rotation), but I would really need to know exact details
how ionospheric and other potential error sources are being covered in
the VLBI data analysis.

OK, so I note that your vague ideas are not a substantiation of a
problem with ionosphere modeling.

Furthermore, the ionosphere is more complicated than you suggest,
since the dynamics are driven by an interaction between solar UV
radiation and the magnetosphere. It's all very fascinating, but again
irrelevant, since (a) the ionosphere is well understood after decades
of study,

and (b) the ionospheric effect can be accounted for
precisely for both GPS and VLBI analysis when data is taken at
multiple wavelengths.

What you still don't seem to get, is that the earth *orientation* is
measured, i.e. the actual rotation *angles*, and not the rotation
rate.

On 30 Mar, 09:20, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

The units are correct. As you can see from the figure, the magnitude
of the diurnal residual velocity changes are of the order of 0.1 mm/
sec/day (i.e. corresponding to an acceleration of 10^-7 cm/sec^2). The
only difference is that the first is a circular acceleration, but the
second apparently a linear one ...

That's an interesting clarification. It's also entirely erroneous
since the difference between a one-day sinusoid and a decade-long
linear drift is a *huge* difference.

It only becomes a huge difference as one acceleration integrates up,
but the other not. The absolute value of the acceleration is the same
in both cases, which on its own suggests that their cause might be a
common one.

Incidentally, your truncated sinusoid term, |sin(wt)|, is incorrect.
In terms of the earth motion, the spacecraft rises in the east
(station moving toward the spacecraft, so a blueshift), and then sets
in the west (station moving away from the spacecraft, so a redshift).

While the actual behavior of the Doppler signal during tracking passes
is indeed a "half" of a sine-wave, it is *not* just the positive half,
but rather the half from 90 to 270 degrees, which has both positive
and negative excursions. You erroneously took the absolute value
without considering the proper phasing.

The phasing is correct: x=x0*sin((w+dw)t) describes the location of
the spacecraft (defined as positive if the spacecraft is above the
horizon), which after differentiation, Taylor expansion, and
subtraction of the modelled oscillation leads to (see a couple of
posts above)

dx_r/dt = x0*[dw*cos(wt) -dw*w*t*sin(wt) ]

The first term in the bracket does indeed both result in a red- and
blue shift during a 'spacecraft day', but the second, with its phase
shifted by 90 deg, results only in either a redshift or a blueshift
(depending on the sign of dw).

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.

Yes, that's because evidently the long term drift has been subtracted
here. ...

It isn't a sinusoid, but only the upper half of a sinusoid (which I
schematically approximated here by taking the absolute value), so the
daily average would increase linearly. ...

A fascinating claim, but since daily averages were *not* used in the
analysis (see point 1 above) your conclusions are irrelevant.


I would actually question this. I had another look at Anderson's
paper, and from what I understand, all plots displaying the long term
residuals (e.g. Fig. where obtained by averaging the data over
blocks ranging from 1-200 days. ...

Furthermore, the IERS contributors come from hundreds of earth
stations, measuring tens of satellites and hundreds of quasars, with
thousands of observations per day. Some of the techniques use the
same receiver technology as spacecraft Doppler tracking (GPS, VLBI),
and some even use the same solution algorithms (GPS). All of these
observations produce at a single consistent picture of how the earth
orientation is tied to an inertial frame.

An "unmodeled" error in earth rotation {rate} would indeed show up in
these (GPS,VLBI,SLR,LLR) observations as a sinusoid with growing
amplitude. But then the model value of UT1-UTC {rate} would need be
adjusted to remove such a residual. It is these adjusted UT1-UTC
values which are used for spacecraft Doppler analysis.

But the unmodelled error does show up. It is the reason why a leap
second is introduced occasionally into UTC (which brings the latter in
synch again with the earth's rotation). And this error had the same
magnitude as the Pioneer anomaly over the period from 1987-1998.

I have some vague ideas that I could follow up (e.g. the ionosphere/
magnetosphere is likely not to fully co-rotate with the earth, as the
magnetic field is not coupled to the surface but to somewhere in the
interior, and thus light might be dragged according to the
differential rotation), but I would really need to know exact details
how ionospheric and other potential error sources are being covered in
the VLBI data analysis.

OK, so I note that your vague ideas are not a substantiation of a
problem with ionosphere modeling.

It is in the nature of ideas that they are not substantiated (not
conclusively anyway). But they could be substantiated if one would
look closer into the matter.

Furthermore, the ionosphere is more complicated than you suggest,
since the dynamics are driven by an interaction between solar UV
radiation and the magnetosphere. It's all very fascinating, but again
irrelevant, since (a) the ionosphere is well understood after decades
of study,

You can understand everything well if you don't bother about obvious
inconsistencies, and in case of ionospheric physics there are many. I
showed for instance by means of a detailed numerical model that
ionospheric photoelectrons can not possibly (as is generally assumed)
thermalize by means of elastic collisions with ions and neutrals, as
the energy transfer in an elastic collision is much too small (see
http://www.plasmaphysics.org.uk/research/elspec.htm ). I have also
shown that the scattering (and refraction) or radio waves could (or
rather should) be due to high atomic Rydberg states rather than
electrons (see http://www.plasmaphysics.org.uk/papers/radscat2.htm ).
There are about half a dozen other points I could address here. These
may not all be relevant in this context, but some may be, and there
may be other issues I have not considered in detail before, like the
suggested dragging of light by the earth's magnetic field. In any
case, the latter would only be a very small effect, and unlike some of
the other points addressed here, it would not imply a radically new
view of things.

and (b) the ionospheric effect can be accounted for
precisely for both GPS and VLBI analysis when data is taken at
multiple wavelengths.

This all stands or falls with the correctness of the corresponding
physical models used. There would be no reason to question the latter
if everything would be consistent, but after all, we *are* dealing
with observed inconsistencies in case of the Pioneer and flyby
anomalies.

What you still don't seem to get, is that the earth *orientation* is
measured, i.e. the actual rotation *angles*, and not the rotation
rate.

Your position seems to be one of blind faith, i.e. to assume that
everything is the way it is claimed to be. I doubt that the Pioneer
(or any other) anomaly can be resolved this way.

In any case, the earth orientation is, as far as I am aware, only
being measured (or at least distributed) once a day, i.e. diurnal
variations could not be modelled with this at all

Incidentally, your truncated sinusoid term, |sin(wt)|, is incorrect.
In terms of the earth motion, the spacecraft rises in the east
(station moving toward the spacecraft, so a blueshift), and then sets
in the west (station moving away from the spacecraft, so a redshift).

While the actual behavior of the Doppler signal during tracking passes
is indeed a "half" of a sine-wave, it is *not* just the positive half,
but rather the half from 90 to 270 degrees, which has both positive
and negative excursions. You erroneously took the absolute value
without considering the proper phasing.

The phasing is correct: x=x0*sin((w+dw)t) describes the location of
the spacecraft (defined as positive if the spacecraft is above the
horizon), which after differentiation, Taylor expansion, and
subtraction of the modelled oscillation leads to (see a couple of
posts above)

dx_r/dt = x0*[dw*cos(wt) -dw*w*t*sin(wt) ]

The first term in the bracket does indeed both result in a red- and
blue shift during a 'spacecraft day', but the second, with its phase
shifted by 90 deg, results only in either a redshift or a blueshift
(depending on the sign of dw).

As you wish.

I note that the residuals you point out in Anderson et
al's Fig 18 (a) do not have a growing amplitude, and (b) are not the
sinusoidal "upper half" which you predicted, but rather both positive
and negative quadrants.

Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.

Furthermore, as a test, I can and did change the the earth rotation
"rate" in the Doppler analysis algorithm (by artificially adjusting
the formula for Greenwich Mean Sidereal Time by a small but
significant amount), and it does *not* produce a linear Doppler drift
in the Pioneer analysis.

A fascinating claim, but since daily averages were *not* used in the
analysis (see point 1 above) your conclusions are irrelevant.

I would actually question this. I had another look at Anderson's
paper, and from what I understand, all plots displaying the long term
residuals (e.g. Fig. where obtained by averaging the data over
blocks ranging from 1-200 days. ...

You understand incorrectly. See summary point 1 above. Neither least
squares (Anderson et al. or Markwardt) nor batch-sequential analysis
(Anderson et al.) involve averaging the Doppler data. I can tell you
umambiguously: I never averaged any Doppler data during my Pioneer analysis

You can understand everything well if you don't bother about obvious
inconsistencies, and in case of ionospheric physics there are many. I
showed for instance by means of a detailed numerical model that
ionospheric photoelectrons can not possibly (as is generally assumed)
thermalize by means of elastic collisions with ions and neutrals, as
the energy transfer in an elastic collision is much too small (see
http://www.plasmaphysics.org.uk/research/elspec.htm). I have also
shown that the scattering (and refraction) or radio waves could (or
rather should) be due to high atomic Rydberg states rather than
electrons (see http://www.plasmaphysics.org.uk/papers/radscat2.htm).
There are about half a dozen other points I could address here. These
may not all be relevant in this context, but some may be, and there
may be other issues I have not considered in detail before, like the
suggested dragging of light by the earth's magnetic field. In any
case, the latter would only be a very small effect, and unlike some of
the other points addressed here, it would not imply a radically new
view of things.

You are making a mountain out of a mole-hill. The ionospheric effects
at the frequencies at issue (1.5-3 GHz) are small, and behave
predictably. Furthermore, they have been verified by measurement of
frequency-dependent phase and group delays, Faraday rotation, and
angular deflection; as measured by ionogram, sounding rocket, GPS
tomography, VLBI, radio astronomy observations, and radio occultation.
And of course those same observations have been combined into
successful models which can predict ionosphere and thermosphere
densities and behaviors (which, incidentally, also successfully
explain drag effects on orbiting spacecraft). The small effects
ionospheric are easily accounted for, and thus there is no need for a
"new" (and unsubstantiated) theory of the ionosphere by you.

Furthermore, as noted already, many of the earth orientation
observations are taken at similar wavelengths (microwave), with
similar receiver technologies, as spacecraft navigation techniques.
That your ionosphere "idea" would need to affect Pioneer and the earth
orientation observations dissimilarly is another strike against it.

On 8 Apr, 10:33, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

Incidentally, your truncated sinusoid term, |sin(wt)|, is incorrect.
In terms of the earth motion, the spacecraft rises in the east
(station moving toward the spacecraft, so a blueshift), and then sets
in the west (station moving away from the spacecraft, so a redshift).

While the actual behavior of the Doppler signal during tracking passes
is indeed a "half" of a sine-wave, it is *not* just the positive half,
but rather the half from 90 to 270 degrees, which has both positive
and negative excursions. You erroneously took the absolute value
without considering the proper phasing.

The phasing is correct: x=x0*sin((w+dw)t) describes the location of
the spacecraft (defined as positive if the spacecraft is above the
horizon), which after differentiation, Taylor expansion, and
subtraction of the modelled oscillation leads to (see a couple of
posts above)

dx_r/dt = x0*[dw*cos(wt) -dw*w*t*sin(wt) ]

The first term in the bracket does indeed both result in a red- and
blue shift during a 'spacecraft day', but the second, with its phase
shifted by 90 deg, results only in either a redshift or a blueshift
(depending on the sign of dw).

As you wish.

It's not my wish. It's a hard fact that a small mismatch of the
earth's rotation rate will result in a term representing either a net
redshift or blueshift over the course of a day.

I note that the residuals you point out in Anderson et
al's Fig 18 (a) do not have a growing amplitude, and (b) are not the
sinusoidal "upper half" which you predicted, but rather both positive
and negative quadrants.

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.

Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.


There is no evidence in Anderson's paper to support your assumption
that a linear drift was subtracted to obtain this figure. It is only
clear that *something* must have been subtracted, as otherwise there
would be a large systematic drift of some sort over the 30 days.

Furthermore, as a test, I can and did change the the earth rotation
"rate" in the Doppler analysis algorithm (by artificially adjusting
the formula for Greenwich Mean Sidereal Time by a small but
significant amount), and it does *not* produce a linear Doppler drift
in the Pioneer analysis.

Well, what does it produce then? It certainly must have produced
something, otherwise one would have to question your algorithm. So you
should substantiate this point with concrete data.

A fascinating claim, but since daily averages were *not* used in the
analysis (see point 1 above) your conclusions are irrelevant.

I would actually question this. I had another look at Anderson's
paper, and from what I understand, all plots displaying the long term
residuals (e.g. Fig. where obtained by averaging the data over
blocks ranging from 1-200 days. ...

You understand incorrectly. See summary point 1 above. Neither least
squares (Anderson et al. or Markwardt) nor batch-sequential analysis
(Anderson et al.) involve averaging the Doppler data. I can tell you
umambiguously: I never averaged any Doppler data during my Pioneer analysis

Well, if you didn't average the data, then they must have been
averaged already when you received them. ...

... Otherwise I can't see a way
how you get this small statistical error for the acceleration
residual, which is almost identical to that in Anderson's CHASMP
analysis. ...

... And as mentioned on page 20 in Anderson's paper, for this
analysis the *raw data* where already averaged, not just the residuals
resulting from the difference with the model data. The possibility
that you used the same data set is also indicated by the fact that it
covers the same period (1987-1994).

You can understand everything well if you don't bother about obvious
inconsistencies, and in case of ionospheric physics there are many. I
showed for instance by means of a detailed numerical model that
ionospheric photoelectrons can not possibly (as is generally assumed)
thermalize by means of elastic collisions with ions and neutrals, as
the energy transfer in an elastic collision is much too small (see
http://www.plasmaphysics.org.uk/research/elspec.htm). I have also
shown that the scattering (and refraction) or radio waves could (or
rather should) be due to high atomic Rydberg states rather than
electrons (see http://www.plasmaphysics.org.uk/papers/radscat2.htm).
There are about half a dozen other points I could address here. These
may not all be relevant in this context, but some may be, and there
may be other issues I have not considered in detail before, like the
suggested dragging of light by the earth's magnetic field. In any
case, the latter would only be a very small effect, and unlike some of
the other points addressed here, it would not imply a radically new
view of things.

You are making a mountain out of a mole-hill. The ionospheric effects
at the frequencies at issue (1.5-3 GHz) are small, and behave
predictably. Furthermore, they have been verified by measurement of
frequency-dependent phase and group delays, Faraday rotation, and
angular deflection; as measured by ionogram, sounding rocket, GPS
tomography, VLBI, radio astronomy observations, and radio occultation.
And of course those same observations have been combined into
successful models which can predict ionosphere and thermosphere
densities and behaviors (which, incidentally, also successfully
explain drag effects on orbiting spacecraft). The small effects
ionospheric are easily accounted for, and thus there is no need for a
"new" (and unsubstantiated) theory of the ionosphere by you.

I pointed out a number of inconsistencies in the theory of the
ionosphere above, so my suggestion isn't unsubstantiated. You are just
discrediting it as such without any concrete counter arguments.

Furthermore, as noted already, many of the earth orientation
observations are taken at similar wavelengths (microwave), with
similar receiver technologies, as spacecraft navigation techniques.
That your ionosphere "idea" would need to affect Pioneer and the earth
orientation observations dissimilarly is another strike against it.

You seem to be missing the point here. The Pioneer anomaly is so
miniscule that it can only be discovered if the spacecraft is far
enough from the sun (and earth) so that the physical influence of the
latter becomes secondary. At closer distance the effect will simply
disappear under the data noise (or be apparently absorbed into any
number of other physical forces).

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.
Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.

There is no evidence in Anderson's paper to support your assumption
that a linear drift was subtracted to obtain this figure. It is only
clear that *something* must have been subtracted, as otherwise there
would be a large systematic drift of some sort over the 30 days.

Since the Figure you refer to shows residuals, the "something" that
was subtracted was the *best-fit model* -- which includes a linear
frequency drift. It is *you* that supposed that a long-term drift was
subtracted.

... And as mentioned on page 20 in Anderson's paper, for this
analysis the *raw data* where already averaged, not just the residuals
resulting from the difference with the model data. The possibility
that you used the same data set is also indicated by the fact that it
covers the same period (1987-1994).

You've discovered an ambiguity of passive voice in the English
language. The phrase in the Anderson paper, "[t]he raw data set was
averaged to 7560 data points..." is not a comment about the state of
the "raw" data, but rather a statement about how their data reduction
process operated on the raw data. It could be rephrased to the active
voice as, "we averaged the raw data to produce 7560 data points..."

Let's return to your original speculation that somehow the mean earth
rotation rate were relevant, and that it was mis-measured. According
to your inspection of the IERS website, the error in the mean rate is
about 1e-12 rad/s. Such an error would produce apparent shifts in
station positions in the East-West direction, with typical magnitudes
of about 200 meters per year. For the ~20-30 years that high
precision GPS and VLBI have been available, that would produce 4-5
kilometer shifts in station positions! Such shifts are simply not
occurring. Typical GPS and VLBI accuracies today are in the few
millimeter range. Thus, your speculation simply does not hold water.
But the shifts due to deviations from the mean rate *are* occurring.

You seem to be missing the point here. The Pioneer anomaly is so
miniscule that it can only be discovered if the spacecraft is far
enough from the sun (and earth) so that the physical influence of the
latter becomes secondary. At closer distance the effect will simply
disappear under the data noise (or be apparently absorbed into any
number of other physical forces).

Actually, the Pioneer anomaly is not *so* miniscule. An anomaly of
8e-8 cm/s^2 is equal to 2.4 cm/s per year. Such an acceleration would
produce 5-10 meter offsets in station positions over the 20-30 year
lifetimes of VLBI and GPS stations. These offsets are simply not
seen. GPS observations in particular are actually *more* sensitive
than deep space Doppler because the GPS signals are stronger.

On 14 Apr, 22:29, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.
Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.

There is no evidence in Anderson's paper to support your assumption
that a linear drift was subtracted to obtain this figure. It is only
clear that *something* must have been subtracted, as otherwise there
would be a large systematic drift of some sort over the 30 days.

Since the Figure you refer to shows residuals, the "something" that
was subtracted was the *best-fit model* -- which includes a linear
frequency drift. It is *you* that supposed that a long-term drift was
subtracted.

It wouldn't be permissible to subtract the 'best-fit' model here, as
the latter has been obtained from a completely different data set
(involving long-term batch averages). As the authors don't say what
has been subtracted in their Fig.18, it is thus everybody's guess.

... And as mentioned on page 20 in Anderson's paper, for this
analysis the *raw data* where already averaged, not just the residuals
resulting from the difference with the model data. The possibility
that you used the same data set is also indicated by the fact that it
covers the same period (1987-1994).

You've discovered an ambiguity of passive voice in the English
language. The phrase in the Anderson paper, "[t]he raw data set was
averaged to 7560 data points..." is not a comment about the state of
the "raw" data, but rather a statement about how their data reduction
process operated on the raw data. It could be rephrased to the active
voice as, "we averaged the raw data to produce 7560 data points..."

That's how I understood it, and that means that the Doppler shifts
were already averaged before the residuals were calculated (obviously,
the model Doppler shifts would then have to be averaged in exactly the
same way).

With regard to the statistical error given in your paper as 0.03*10^-8
cm/sec^2, this means that we are dealing with a batch average over
(2/0.03)^2*600 sec = 2.66*10^6 sec = 30.8 days, so this appears to be
the 30-day batch average (the batch sizes used by Anderson et al. were
0,1,5,10,30,200 days (p.17)).
So your claim that you didn't use averaged data is not consistent with
the statistical error you give.

Anderson's mentioning of the 7560 points for the CHASMP analysis is by
the way not consistent with any of the integration or batch periods,
as it would correspond to about 1 point every 8 hours. So one would
have to conclude that actually a sliding average (every 8 hours in
this case) with a 30-day window was performed.

Let's return to your original speculation that somehow the mean earth
rotation rate were relevant, and that it was mis-measured. According
to your inspection of the IERS website, the error in the mean rate is
about 1e-12 rad/s. Such an error would produce apparent shifts in
station positions in the East-West direction, with typical magnitudes
of about 200 meters per year. For the ~20-30 years that high
precision GPS and VLBI have been available, that would produce 4-5
kilometer shifts in station positions! Such shifts are simply not
occurring. Typical GPS and VLBI accuracies today are in the few
millimeter range. Thus, your speculation simply does not hold water.
But the shifts due to deviations from the mean rate *are* occurring.
As mentioned before, they are the reason why a leap second is
introduced into UTC occasionally ...

You seem to be missing the point here. The Pioneer anomaly is so
miniscule that it can only be discovered if the spacecraft is far
enough from the sun (and earth) so that the physical influence of the
latter becomes secondary. At closer distance the effect will simply
disappear under the data noise (or be apparently absorbed into any
number of other physical forces).

Actually, the Pioneer anomaly is not *so* miniscule. An anomaly of
8e-8 cm/s^2 is equal to 2.4 cm/s per year. Such an acceleration would
produce 5-10 meter offsets in station positions over the 20-30 year
lifetimes of VLBI and GPS stations. These offsets are simply not
seen. GPS observations in particular are actually *more* sensitive
than deep space Doppler because the GPS signals are stronger.

I am not quite sure why you are getting just 5-10 m offsets in 20-30
years here, when above you got a few kilometers ...

Anyway, location or velocity offsets are not really physically
meaningful here. What is relevant for the dynamical development of a
physical system is only the acceleration. ...

... Now a satellite in earth
orbit will have an acceleration of the order of 1-10 m/sec^2 =100-1000
cm/sec^2. The 'Pioneer anomaly' only amounts to 10^-7 cm/sec^2, which
is merely a fraction 10^-10 -10^-9 of the orbital satellite
acceleration. Now if you have another look at the IERS data (http://
hpiers.obspm.fr/eop-pc/models/constants.html ) you can find that the
'Geocentric constant of gravitation' GM has a nominal error of
2*10^-9, which means that the 'Pioneer effect' should be irrelevant
for earth-bound satellites (one could as well change the mass of the
earth by the same amount without that it should be noticeable).

Apart from my suggested ionospheric/magnetospheric 'light drag'
mechanism contributing to the earth's apparent rotation rate, I would
however also like to suggest again that the earth orientation data may
simply have been installed incorrectly for the Pioneer data analysis:
as indicated before for instance, the UT1-UTC correction applied both
by Anderson and you, would, (unless it means that simply the leap
seconds are taken out again), either reduce the 'true' rotation rate
again to a uniform rotation, or the deviation from a uniform rate
would effectively be applied twice (depending on which way the
correction goes).

As usual, you continue to make unsubstantiated and erroneous remarks,
as summarized at the end of this message.



Thomas Smid <thomas.s...@gmail.com> writes:
On 14 Apr, 22:29, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.
Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.

There is no evidence in Anderson's paper to support your assumption
that a linear drift was subtracted to obtain this figure. It is only
clear that *something* must have been subtracted, as otherwise there
would be a large systematic drift of some sort over the 30 days.

Since the Figure you refer to shows residuals, the "something" that
was subtracted was the *best-fit model* -- which includes a linear
frequency drift. It is *you* that supposed that a long-term drift was
subtracted.

It wouldn't be permissible to subtract the 'best-fit' model here, as
the latter has been obtained from a completely different data set
(involving long-term batch averages). As the authors don't say what
has been subtracted in their Fig.18, it is thus everybody's guess.

You are incorrect. The best-fit model makes a prediction for each
data point, which can then be subtracted. This is the standard
definition of "residuals." Since you continue to mis-interpret the
term "batch" as meaning "batch average," (see summary points 1 and 14)
your conclusions are irrelevant.



... And as mentioned on page 20 in Anderson's paper, for this
analysis the *raw data* where already averaged, not just the residuals
resulting from the difference with the model data. The possibility
that you used the same data set is also indicated by the fact that it
covers the same period (1987-1994).

You've discovered an ambiguity of passive voice in the English
language. The phrase in the Anderson paper, "[t]he raw data set was
averaged to 7560 data points..." is not a comment about the state of
the "raw" data, but rather a statement about how their data reduction
process operated on the raw data. It could be rephrased to the active
voice as, "we averaged the raw data to produce 7560 data points..."

That's how I understood it, and that means that the Doppler shifts
were already averaged before the residuals were calculated (obviously,
the model Doppler shifts would then have to be averaged in exactly the
same way).

However, that amount of averaging is not relevant (see summary points
1 and 14). Your claim about the "raw data" being averaged is still
incorrect.

...

With regard to the statistical error given in your paper as 0.03*10^-8
cm/sec^2, this means that we are dealing with a batch average over
(2/0.03)^2*600 sec = 2.66*10^6 sec = 30.8 days, so this appears to be
the 30-day batch average (the batch sizes used by Anderson et al. were
0,1,5,10,30,200 days (p.17)).
So your claim that you didn't use averaged data is not consistent with
the statistical error you give.

This is all fascinating, but you continue to ignore the absolute fact
that my Doppler analysis did not perform daily or multi-day averaging.
There simply were no 30 day batches. Your "calculation" makes several
unsubstantiated assumptions about the contiguity of the tracking (it
actually was not contiguous), or the data filtering strategy (the data
were decimated).

Anderson's mentioning of the 7560 points for the CHASMP analysis is by
the way not consistent with any of the integration or batch periods,
as it would correspond to about 1 point every 8 hours. So one would
have to conclude that actually a sliding average (every 8 hours in
this case) with a 30-day window was performed.

Again, you are making unsubstantiated assumptions about the contiguity
of the data (i.e. the correspondence between calendar date and
accumulated tracking time). Thus, your conclusions are irrelevant.

On 20 Apr, 02:29, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:
As usual, you continue to make unsubstantiated and erroneous remarks,
as summarized at the end of this message.



Thomas Smid <thomas.s...@gmail.com> writes:
On 14 Apr, 22:29, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> wrote:

Finally, it's worth noting that the same Figure 18 you keep referring
to does *not* show sinusoidal residuals whose amplitude grows linearly
with time, but rather a sinusoid with a nearly constant amplitude.
Thus, your "derivation" does not match the data.
Yes, that's because evidently the long term drift has been subtracted
here. ...

It is impossible to compute (sinusoid with growing amplitude) minus
(linear drift) and arrive at (sinusoid with constant amplitude).
There is simply no way to do it. Thus, there is no way for your claim
to be correct, and any conclusions you draw from it are irrelevant.

There is no evidence in Anderson's paper to support your assumption
that a linear drift was subtracted to obtain this figure. It is only
clear that *something* must have been subtracted, as otherwise there
would be a large systematic drift of some sort over the 30 days.

Since the Figure you refer to shows residuals, the "something" that
was subtracted was the *best-fit model* -- which includes a linear
frequency drift. It is *you* that supposed that a long-term drift was
subtracted.

It wouldn't be permissible to subtract the 'best-fit' model here, as
the latter has been obtained from a completely different data set
(involving long-term batch averages). As the authors don't say what
has been subtracted in their Fig.18, it is thus everybody's guess.

You are incorrect. The best-fit model makes a prediction for each
data point, which can then be subtracted. This is the standard
definition of "residuals." Since you continue to mis-interpret the
term "batch" as meaning "batch average," (see summary points 1 and 14)
your conclusions are irrelevant.

... And as mentioned on page 20 in Anderson's paper, for this
analysis the *raw data* where already averaged, not just the residuals
resulting from the difference with the model data. The possibility
that you used the same data set is also indicated by the fact that it
covers the same period (1987-1994).

You've discovered an ambiguity of passive voice in the English
language. The phrase in the Anderson paper, "[t]he raw data set was
averaged to 7560 data points..." is not a comment about the state of
the "raw" data, but rather a statement about how their data reduction
process operated on the raw data. It could be rephrased to the active
voice as, "we averaged the raw data to produce 7560 data points..."

That's how I understood it, and that means that the Doppler shifts
were already averaged before the residuals were calculated (obviously,
the model Doppler shifts would then have to be averaged in exactly the
same way).

However, that amount of averaging is not relevant (see summary points
1 and 14). Your claim about the "raw data" being averaged is still
incorrect.

...

With regard to the statistical error given in your paper as 0.03*10^-8
cm/sec^2, this means that we are dealing with a batch average over
(2/0.03)^2*600 sec = 2.66*10^6 sec = 30.8 days, so this appears to be
the 30-day batch average (the batch sizes used by Anderson et al. were
0,1,5,10,30,200 days (p.17)).
So your claim that you didn't use averaged data is not consistent with
the statistical error you give.

This is all fascinating, but you continue to ignore the absolute fact
that my Doppler analysis did not perform daily or multi-day averaging.
There simply were no 30 day batches. Your "calculation" makes several
unsubstantiated assumptions about the contiguity of the tracking (it
actually was not contiguous), or the data filtering strategy (the data
were decimated).

Anderson's mentioning of the 7560 points for the CHASMP analysis is by
the way not consistent with any of the integration or batch periods,
as it would correspond to about 1 point every 8 hours. So one would
have to conclude that actually a sliding average (every 8 hours in
this case) with a 30-day window was performed.

Again, you are making unsubstantiated assumptions about the contiguity
of the data (i.e. the correspondence between calendar date and
accumulated tracking time). Thus, your conclusions are irrelevant.

On the contrary, it is your claim that unaveraged data were used which
is unsubstantiated. Unless you have an alternative explanation for the
small statistical error in your analysis (as well as Anderson's), one
has to conclude that averaged data were used (and the figures are
consistent in this respect with the batch periods mentioned in
Anderson's paper).

As should be evident from what I mentioned earlier, the numerical
figures clearly suggest that the anomaly is in some way related to an
incorrect modelling of the earth's rotation (either because the latter
itself has not been correctly measured, or because it has been
incorrectly implemented in the data analysis).