Pioneer Anomaly discussion continued

Note: this is a continuation of the thread
http://groups.google.co.uk/group/sci...fb34db20b1af7f


On 5 Mar, 17:20, Craig Markwardt
wrote:

Since the analysis (and the anomaly) involve *neither* averaging *nor*
Fourier transformation, your speculations are still irrelevant. In
fact, a diurnal Doppler error signal due to incorrect station
positions would been readily visible in the residuals, and could have
been corrected by adjusting the station positions (along with any
corresponding biases, if any). No reasonable adjustment of the
station positions could resolve the anomaly (ref. Anderson et al.;
Markwardt 2002).

What I said was that *if* a Fourier transform is applied to the data,
then it would not only show an annual and diurnal residual (which *is*
present according to Anderson et al. (see page 40-42)) but also a
constant residual (i.e. the 'Pioneer anomaly'). Both Anderson et al.
and you arbitrarily ignore the periodic variations (in fact, you
appear to have filtered out the diurnal variations altogether) but
only consider the constant residual as relevant.

Regarding the station positions: you are writing in your paper that
treating these as free fit parameters would converge towards the
'correct' positions to within a few meters. Now this is by no means
sufficient. A change of the radial distance of the station from the
earth's center by just about 10 cm would fully absorb the Pioneer
anomaly (and presumably also the diurnal residuals).


But anyway, whatever your earth rotation model is, if you would change
the parameters such that it corresponds to a reduction of the
rotational acceleration of the observing station by about 5*10^-8 cm/
sec^2, then the anomaly must disappear.

This claim continues to be erroneous. First, earth orientation
parameters are nailed down by huge numbers of observations, so they
shouldn't be "changed" without invalidating all of those observations.
Second, any diddling of these numbers would produce distinct diurnal
Doppler signatures, which would *not* reflect a constant acceleration.

As I mentioned already, the parameters only need to changed within the
nominal errors as stated by the IERS (see http://hpiers.obspm.fr/eop-pc/models/constants.html
).


It *has* been caught in form of the Pioneer anomaly, and it is also
confirmed by the IERS data (seehttp://maia.usno.navy.mil/lod.gif)
where a constant offset of about 1 ms is apparent for the length of a
day (apart from fluctuations of a similar magnitude).

The plot you indicated is irrelevant. That plot shows the *measured
excess* of the length of day beyond the standard length. In other
words this is *not* an "unmodeled drift" since it is measured.

Perhaps you are arguing under the assumption that a standard
fixed-length day is used in the analysis. That assumption would be
false, as I have pointed out several times. In fact, the
instantaneous length of day, rotation speed/angles, etc. are used.
The very measurements you indicated, are used in the analysis.

For the present purpose, the 1ms/day drift *is* an unmodelled drift.
It appears to be essentially the difference between the UT1 and UTC
time scales, and as you may be aware, this is only corrected
occasionally (every 1-2 years) by inserting a leap second (see
http://en.wikipedia.org/wiki/Coordinated_Universal_Time ). So any data
that are not averaged over many years should show this drift, as the
latter is in fact continuous, and the insertion of the leap second is
thus not a proper modelling of the earth's rotation.

Thomas

Thomas Smid writes:
Note: this is a continuation of the thread
http://groups.google.co.uk/group/sci...fb34db20b1af7f


On 5 Mar, 17:20, Craig Markwardt
wrote:

Since the analysis (and the anomaly) involve *neither* averaging *nor*
Fourier transformation, your speculations are still irrelevant. In
fact, a diurnal Doppler error signal due to incorrect station
positions would been readily visible in the residuals, and could have
been corrected by adjusting the station positions (along with any
corresponding biases, if any). No reasonable adjustment of the
station positions could resolve the anomaly (ref. Anderson et al.;
Markwardt 2002).

What I said was that *if* a Fourier transform is applied to the data,
then it would not only show an annual and diurnal residual ... but also a
constant residual (i.e. the 'Pioneer anomaly').

And *if* I applied a light vinegrette, it could be a salad. But since
the premises of both *ifs* are false, the conclusions drawn are
irrelevant. The phenomenon you describe is a well-known property
specific to the Fourier transform when the signal is "windowed."
(namely, that artificial aliases can appear.)

However, since the Fourier transform is *not* used in the Doppler
analysis, and since the Doppler analysis technique *accounts* for
observational windowing, your scenario is irrelevant.

Finally, since it is the Doppler *frequency* which is actually
observed, one has to consider the velocity and not acceleration. Any
acceleration profile which has a half-wave "hump" would be integrated
to become an S-shaped profile with both positive and negative
excursions, which would (a) be easily detectable, and (b) have no DC
bias. So again, your claims are erroneous.


... [annual and diurnal residual ] (which *is*
present according to Anderson et al. (see page 40-42))

Yes, and it is clear from those figures that the residuals are (a)
sinusoidal, and (b) cover both positive and negative excursions from
peak to peak. I.e. no DC bias.

... Both Anderson et al.
and you arbitrarily ignore the periodic variations (in fact, you
appear to have filtered out the diurnal variations altogether) but
only consider the constant residual as relevant.

You are utterly in error. I note your complete lack of substantiation
of that claim. In fact, if Anderson discusses these residuals and
their systematic contribution to the "anomaly," it cannot be said that
they ignored it.[*] And in my analysis, I never performed any
filtering of diurnal residuals, and the fact that I tested for
station-dependent effects means that I could not have ignored them.
Why do you insist on making such ridiculously unsubstantiated
statements?

Simply put, the remaining sinusoidal Doppler residuals do have only a
very small net effect, after integrating over an integer number of
days, since they have a zero mean.[*]

[*] - this is true even if the station positions are incorrect by a
small amount.

Regarding the station positions: you are writing in your paper that
treating these as free fit parameters would converge towards the
'correct' positions to within a few meters. Now this is by no means
sufficient. A change of the radial distance of the station from the
earth's center by just about 10 cm would fully absorb the Pioneer
anomaly (and presumably also the diurnal residuals).

You presume incorrectly. Apparently you are having reading
comprehension problems. If adjustments in the station positions of a
few meters cannot improve the solution -- and cannot remove the
"anomaly" -- then a variation of 10 centimeters surely could not.


But anyway, whatever your earth rotation model is, if you would change
the parameters such that it corresponds to a reduction of the
rotational acceleration of the observing station by about 5*10^-8 cm/
sec^2, then the anomaly must disappear.

This claim continues to be erroneous. First, earth orientation
parameters are nailed down by huge numbers of observations, so they
shouldn't be "changed" without invalidating all of those observations.
Second, any diddling of these numbers would produce distinct diurnal
Doppler signatures, which would *not* reflect a constant acceleration.

As I mentioned already, the parameters only need to changed within the
nominal errors as stated by the IERS (see http://hpiers.obspm.fr/eop-pc/models/constants.html
).


Neither the mean earth radius, nor the mean earth rotation rate are
relevant parameters. Instead, the instantaneous rotation rate and
actual topocentric station positions are used. I note that you
conveniently deleted the portions of the discussion where those facts
were mentioned (many times). So no, the parameters do not "only need
to changed" since those values are irrelevant!


It *has* been caught in form of the Pioneer anomaly, and it is also
confirmed by the IERS data (seehttp://maia.usno.navy.mil/lod.gif)
where a constant offset of about 1 ms is apparent for the length of a
day (apart from fluctuations of a similar magnitude).

The plot you indicated is irrelevant. That plot shows the *measured
excess* of the length of day beyond the standard length. In other
words this is *not* an "unmodeled drift" since it is measured.

Perhaps you are arguing under the assumption that a standard
fixed-length day is used in the analysis. That assumption would be
false, as I have pointed out several times. In fact, the
instantaneous length of day, rotation speed/angles, etc. are used.
The very measurements you indicated, are used in the analysis.

For the present purpose, the 1ms/day drift *is* an unmodelled drift.
It appears to be essentially the difference between the UT1 and UTC
time scales, and as you may be aware, this is only corrected
occasionally (every 1-2 years) by inserting a leap second (see
http://en.wikipedia.org/wiki/Coordinated_Universal_Time ).

Huh? Since the UT1 time scale *is the one used* for Doppler analysis,
your point is totally irrelevant. In other words, the instantaneous
earth rotation properties are used, not the mean ones. Have you even
bothered to try to grasp this?

... So any data
that are not averaged over many years should show this drift, as the
latter is in fact continuous, and the insertion of the leap second is
thus not a proper modelling of the earth's rotation.

However, since the premise of your supposition is false (i.e. the true
UT1 timescale *is* used for determining earth rotation, contrary to
your assumption), your conclusions are utterly irrelevant.

I note that you continue to make totally unsubstantiated, erroneous
and irrelevant claims. Despite being informed multiple times of how
the actual Doppler analysis works, you continue to pretend that it's
done a different way in order to artificially substantiate your claims.

CM

On 9 Mar, 22:34, Craig Markwardt
wrote:

I note that you conveniently deleted the portions of the discussion
where those facts were mentioned (many times).

I am editing the previous posts as required so that we can concentrate
on the crucial arguments here. So I suggest you stick to what I am
saying, not what I am not saying.

Finally, since it is the Doppler *frequency* which is actually
observed, one has to consider the velocity and not acceleration. Any
acceleration profile which has a half-wave "hump" would be integrated
to become an S-shaped profile with both positive and negative
excursions, which would (a) be easily detectable, and (b) have no DC
bias.

We are not interested in the velocities but the accelerations. The
latter are obtained by differentiating the former, and if you do this
for instance for the diurnal velocity residuals shown in Fig.18 (page
41) in Anderson et al. (note that the caption incorrectly says
'acceleration residuals'), then you can see that the acceleration is
negative throughout as there are data points only in the declining
half of the sinusoidals (i.e. when the spacecraft was above the
horizon).

In fact, if Anderson discusses these residuals and
their systematic contribution to the "anomaly," it cannot be said that
they ignored it.

They did ignore it in the sense that they left the periodical
residuals unmodelled and thought they could consider the DC residual
independently of this. This is improper science, and it is indeed
erroneous here, as the acceleration residuals due to a mismatch of the
station acceleration would lead both to a diurnal and constant
anomaly as mentioned above.


And in my analysis, I never performed any
filtering of diurnal residuals,

So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

and the fact that I tested for
station-dependent effects means that I could not have ignored them.
Why do you insist on making such ridiculously unsubstantiated
statements?

According to your paper you didn't test for station dependent effects
at all, but had the station positions fixed to the nominal values as
used by Anderson et al., as you found that when you treated them as
free parameters, they converged to within a few meters of those.

But if you want to substantiate your claim, why don't you present some
numerical results which show the effect on the anomaly by changing the
geocentric distance of the stations in your model ? (if your algorithm
is not accurate enough to produce any difference in the results for a
radial position change of 10 cm or so, then change it by let's say 100
m and compare the result with the observed Pioneer anomaly)


Neither the mean earth radius, nor the mean earth rotation rate are
relevant parameters. Instead, the instantaneous rotation rate and
actual topocentric station positions are used.

First of all, the recorded positions and rotation angles are not
'instantaneous', but only daily values (at least this is what Anderson
et al. indicate in their paper (page 14), and I don't think the IERS
routinely provides the data more frequently anyway) . And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters. As mentioned, these errors account to about 1 ms/day
variations over a the space of year or so (and similar over longer
time scales) and are only 'modelled' by inserting a leap second when
the accumulated error exceeds a certain bound.

Having said this, it is actually not necessary to have an error in the
rotation rate to produce the Pioneer anomaly. The centrifugal
acceleration depends independently on the geocentric distance of the
observing station as well, and as mentioned, if you change the latter
by just 10 cm, the Pioneer anomaly could be accounted for anyway (but
the fact that the unmodelled UT1 drift of 1ms/day would about account
for the Pioneer anomaly, suggests at least that an error in the
rotation rate is relevant here as well).

Since the UT1 time scale *is the one used* for Doppler analysis,
your point is totally irrelevant. In other words, the instantaneous
earth rotation properties are used, not the mean ones.

As I indicated above already, the UT1 'timescale' consists of
theoretically unmodelled empirical data and should thus not be a
legitimate time scale if you are considering differences that fall
within the unmodelled variations (in the same sense as for instance
the observed Pioneer acceleration should not qualify as a legitimate
indicator of the sun's gravitational field to an accuracy better than
10^-7 as long as it is not fully theoretically modelled).

Anyway, if the UT1 time scale gives already the true rotation angle of
the earth, why do you (according to your paper) then apply a
correction UT1-UTC for the length of the day? You could compare the
rotation angle dphi directly with the receiver clock time dt, and dphi/
dt would then give you the true angular rotation rate without any
further corrections.

Thomas

On 10 Mar, 15:56, Thomas Smid wrote:
In the same sense as for instance
the observed Pioneer acceleration should not qualify as a legitimate
indicator of the sun's gravitational field to an accuracy better than
10^-7 as long as it is not fully theoretically modelled).

that should have been 'the sun's gravitational acceleration to an
accuracy better than 10^-7 cm/sec^2 '.

Thomas

3. Thomas Smid
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More options 10 Mar, 15:56
Newsgroups: sci.astro
From: Thomas Smid
Date: Mon, 10 Mar 2008 08:56:54 -0700 (PDT)
Local: Mon 10 Mar 2008 15:56
Subject: Pioneer Anomaly discussion continued
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On 9 Mar, 22:34, Craig Markwardt

wrote:

I note that you conveniently deleted the portions of the discussion
where those facts were mentioned (many times).

I am editing the previous posts as required so that we can concentrate
on the crucial arguments here. So I suggest you stick to what I am
saying, not what I am not saying.

Finally, since it is the Doppler *frequency* which is actually
observed, one has to consider the velocity and not acceleration. Any
acceleration profile which has a half-wave "hump" would be integrated
to become an S-shaped profile with both positive and negative
excursions, which would (a) be easily detectable, and (b) have no DC
bias.

We are not interested in the velocities but the accelerations. The
latter are obtained by differentiating the former, and if you do this
for instance for the diurnal velocity residuals shown in Fig.18 (page
41) in Anderson et al. (note that the caption incorrectly says
'acceleration residuals'), then you can see that the acceleration is
negative throughout as there are data points only in the declining
half of the sinusoidals (i.e. when the spacecraft was above the
horizon).

In fact, if Anderson discusses these residuals and
their systematic contribution to the "anomaly," it cannot be said that
they ignored it.

They did ignore it in the sense that they left the periodical
residuals unmodelled and thought they could consider the DC residual
independently of this. This is improper science, and it is indeed
erroneous here, as the acceleration residuals due to a mismatch of the
station acceleration would lead both to a diurnal and constant
anomaly as mentioned above.

And in my analysis, I never performed any
filtering of diurnal residuals,

So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

and the fact that I tested for
station-dependent effects means that I could not have ignored them.


According to your paper you didn't test for station dependent effects
at all, but had the station positions fixed to the nominal values as
used by Anderson et al., as you found that when you treated them as
free parameters, they converged to within a few meters of those.

But if you want to substantiate your claim, why don't you present some
numerical results which show the effect on the anomaly by changing the
geocentric distance of the stations in your model ? (if your algorithm
is not accurate enough to produce any difference in the results for a
radial position change of 10 cm or so, then change it by let's say 100
m and compare the result with the observed Pioneer anomaly)

Neither the mean earth radius, nor the mean earth rotation rate are
relevant parameters. Instead, the instantaneous rotation rate and
actual topocentric station positions are used.

First of all, the recorded positions and rotation angles are not
'instantaneous', but only daily values (at least this is what Anderson
et al. indicate in their paper (page 14), and I don't think the IERS
routinely provides the data more frequently anyway) . And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters. As mentioned, these errors account to about 1 ms/day
variations over a the space of year or so (and similar over longer
time scales) and are only 'modelled' by inserting a leap second when
the accumulated error exceeds a certain bound.

Having said this, it is actually not necessary to have an error in the
rotation rate to produce the Pioneer anomaly. The centrifugal
acceleration depends independently on the geocentric distance of the
observing station as well, and as mentioned, if you change the latter
by just 10 cm, the Pioneer anomaly could be accounted for anyway (but
the fact that the unmodelled UT1 drift of 1ms/day would about account
for the Pioneer anomaly, suggests at least that an error in the
rotation rate is relevant here as well).

Since the UT1 time scale *is the one used* for Doppler analysis,
your point is totally irrelevant. In other words, the instantaneous
earth rotation properties are used, not the mean ones.

As I indicated above already, the UT1 'timescale' consists of
theoretically unmodelled empirical data and should thus not be a
legitimate time scale if you are considering differences that fall
within the unmodelled variations (in the same sense as for instance
the observed Pioneer acceleration should not qualify as a legitimate
indicator of the sun's gravitational field to an accuracy better than
corresponding to an acceleration of 10^-7 cm/sec^2 as long as it is
not fully theoretically modelled).

Anyway, if the UT1 time scale gives already the true rotation angle of
the earth, why do you (according to your paper) then apply a
correction UT1-UTC for the length of the day? You could compare the
rotation angle dphi directly with the receiver clock time dt, and
dphi/
dt would then give you the true angular rotation rate without any
further corrections.

Thomas

On 9 Mar, 22:34, Craig Markwardt

wrote:

I note that you conveniently deleted the portions of the discussion
where those facts were mentioned (many times).

I am editing the previous posts as required so that we can concentrate
on the crucial arguments here. So I suggest you stick to what I am
saying, not what I am not saying.

Finally, since it is the Doppler *frequency* which is actually
observed, one has to consider the velocity and not acceleration. Any
acceleration profile which has a half-wave "hump" would be integrated
to become an S-shaped profile with both positive and negative
excursions, which would (a) be easily detectable, and (b) have no DC
bias.

We are not interested in the velocities but the accelerations. The
latter are obtained by differentiating the former, and if you do this
for instance for the diurnal velocity residuals shown in Fig.18 (page
41) in Anderson et al. (note that the caption incorrectly says
'acceleration residuals'), then you can see that the acceleration is
negative throughout as there are data points only in the declining
half of the sinusoidals (i.e. when the spacecraft was above the
horizon).

In fact, if Anderson discusses these residuals and
their systematic contribution to the "anomaly," it cannot be said that
they ignored it.

They did ignore it in the sense that they left the periodical
residuals unmodelled and thought they could consider the DC residual
independently of this. This is improper science, and it is indeed
erroneous here, as the acceleration residuals due to a mismatch of the
station acceleration would lead both to a diurnal and constant
anomaly as mentioned above.

And in my analysis, I never performed any
filtering of diurnal residuals,

So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

and the fact that I tested for
station-dependent effects means that I could not have ignored them.


According to your paper you didn't test for station dependent effects
at all, but had the station positions fixed to the nominal values as
used by Anderson et al., as you found that when you treated them as
free parameters, they converged to within a few meters of those.

But if you want to substantiate your claim, why don't you present some
numerical results which show the effect on the anomaly by changing the
geocentric distance of the stations in your model ? (if your algorithm
is not accurate enough to produce any difference in the results for a
radial position change of 10 cm or so, then change it by let's say 100
m and compare the result with the observed Pioneer anomaly)

Neither the mean earth radius, nor the mean earth rotation rate are
relevant parameters. Instead, the instantaneous rotation rate and
actual topocentric station positions are used.

First of all, the recorded positions and rotation angles are not
'instantaneous', but only daily values (at least this is what Anderson
et al. indicate in their paper (page 14), and I don't think the IERS
routinely provides the data more frequently anyway) . And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters. As mentioned, these errors account to about 1 ms/day
variations over a the space of year or so (and similar over longer
time scales) and are only 'modelled' by inserting a leap second when
the accumulated error exceeds a certain bound.

Having said this, it is actually not necessary to have an error in the
rotation rate to produce the Pioneer anomaly. The centrifugal
acceleration depends independently on the geocentric distance of the
observing station as well, and as mentioned, if you change the latter
by just 10 cm, the Pioneer anomaly could be accounted for anyway (but
the fact that the unmodelled UT1 drift of 1ms/day would about account
for the Pioneer anomaly, suggests at least that an error in the
rotation rate is relevant here as well).

Since the UT1 time scale *is the one used* for Doppler analysis,
your point is totally irrelevant. In other words, the instantaneous
earth rotation properties are used, not the mean ones.

As I indicated above already, the UT1 'timescale' consists of
theoretically unmodelled empirical data and should thus not be a
legitimate time scale if you are considering differences that fall
within the unmodelled variations (in the same sense as for instance
the observed Pioneer acceleration should not qualify as a legitimate
indicator of the sun's gravitational field to an accuracy better than
corresponding to an acceleration of 10^-7 cm/sec^2 as long as it is
not fully theoretically modelled).

Anyway, if the UT1 time scale gives already the true rotation angle of
the earth, why do you (according to your paper) then apply a
correction UT1-UTC for the length of the day? You could compare the
rotation angle dphi directly with the receiver clock time dt, and
dphi/
dt would then give you the true angular rotation rate without any
further corrections.

Thomas

My apologies for such a late reply.


Thomas Smid writes:

On 9 Mar, 22:34, Craig Markwardt
wrote:

I note that you conveniently deleted the portions of the discussion
where those facts were mentioned (many times).

I am editing the previous posts as required so that we can concentrate
on the crucial arguments here. So I suggest you stick to what I am
saying, not what I am not saying.

Oh, but I was focussing on what you were saying, and those things were
crucially incorrect.[*]

Do you understand now that the Doppler data are *not* averaged (daily
or multi-day)? [ and thus, your claims about half-daily signals being
averaged are erroneous? ]

Do you understand now that a Fourier transform is *not* used in the
Pioneer Doppler analysis? [ and thus, your claims about a DC
"constant offset" frequency are erroneous? ]
[*] Also, based on my experience from your previous discussions, I
am aware that you have a pattern of erasing previous discussion so that
you can re-introduce the same old points over again.

Finally, since it is the Doppler *frequency* which is actually
observed, one has to consider the velocity and not acceleration. Any
acceleration profile which has a half-wave "hump" would be integrated
to become an S-shaped profile with both positive and negative
excursions, which would (a) be easily detectable, and (b) have no DC
bias.

We are not interested in the velocities but the accelerations. The
latter are obtained by differentiating the former, ...

You are in error. The anomaly was "discovered" as an unaccounted-for
linear trend in the *frequency* residuals. We can *model* this trend
as an (approximately) constant acceleration, but that is only one
interpretation. Still, the "crucial" point is that it was the Doppler
*frequencies* that produced the anomaly -- not any kind of measured
accelerations. No differentiating was done.

... and if you do this
for instance for the diurnal velocity residuals shown in Fig.18 (page
41) in Anderson et al. (note that the caption incorrectly says
'acceleration residuals'), then you can see that the acceleration is
negative throughout as there are data points only in the declining
half of the sinusoidals (i.e. when the spacecraft was above the
horizon).

Again irrelevant. *No one* is claiming that the residuals shown in
that figure consitute the main "Pioneer anomaly." In fact, the main
anomaly is characterized by a nearly linear frequency increase over
about a decade. If the station positions were incorrect (among
several possibilities) then the diurnal sinusoidal amplitude would
increase, but the long term drift would be largely unaffected. While
the main Pioneer anomaly is a frequency increase corresponding to a
Doppler shift of about 200 mm/s over one decade, you are focussing
on a sinusoidal signal that has amplitude of ~0.15 mm/s and averages
to ~0 over a decade. I.e. you are not "concentrating on the crucial
arguments."


In fact, if Anderson discusses these residuals and
their systematic contribution to the "anomaly," it cannot be said that
they ignored it.

They did ignore it in the sense that they left the periodical
residuals unmodelled and thought they could consider the DC residual
independently of this. This is improper science, and it is indeed
erroneous here, as the acceleration residuals due to a mismatch of the
station acceleration would lead both to a diurnal and constant
anomaly as mentioned above.

Ummm, no. As noted in the same section of Anderson that you refer to,
the diurnal sinusoidal *Doppler* term has a miniscule net effect
compared to other effects, since it has both positive and negative
Doppler excursions about its mean. Meanwhile the true "anomaly" has a
long-term trend.


And in my analysis, I never performed any
filtering of diurnal residuals,

So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

How would you know? In fact, since the kinds of signals that Anderson
et al. found in their Fig 18 were very small (~0.1 mm/s) compared to
the true anomaly drift of ~200 mm/s, you wouldn't really see such
effects in my Fig 3. Furthermore, Anderson's Fig 18. is taken from
1996 data when the other noise terms were extremely small. The 1996
data was not available from the archive that I used. Were there very
small diurnal Doppler residuals? Probably, but as both Anderson and I
understand, these small sinusoidal frequency residuals do not make a
long term drift a thousand times larger!

and the fact that I tested for
station-dependent effects means that I could not have ignored them.
Why do you insist on making such ridiculously unsubstantiated
statements?

According to your paper you didn't test for station dependent effects
at all, but had the station positions fixed to the nominal values as
used by Anderson et al., as you found that when you treated them as
free parameters, they converged to within a few meters of those.

Apparently you are having difficulty comprehending your own sentence.
*If* I treated the station positions as free parameters, then I
obviously treated station-dependent effects. Sheesh. Since they had
no significant effect on the solution, I went ahead and fixed them.

But if you want to substantiate your claim, why don't you present some
numerical results which show the effect on the anomaly by changing the
geocentric distance of the stations in your model ? (if your algorithm
is not accurate enough to produce any difference in the results for a
radial position change of 10 cm or so, then change it by let's say 100
m and compare the result with the observed Pioneer anomaly)

Shifting the station positions by 100 meters makes a large
difference. It produces a hugely increased scatter on a decade
timescale (the r.m.s. of the Doppler residuals increases by a factor
of ~14 to about 58 mHz). When zoomed to a daily timescale, the
expected diurnal signature due to this station error is present.
There is no additional linear frequency drift. That is because your
initial suppositions were incorrect: the data are not averaged over
days; no Fourier transform is applied; and the "acceleration"
residuals are not examined.


Neither the mean earth radius, nor the mean earth rotation rate are
relevant parameters. Instead, the instantaneous rotation rate and
actual topocentric station positions are used.

First of all, the recorded positions and rotation angles are not
'instantaneous', but only daily values (at least this is what Anderson
et al. indicate in their paper (page 14), and I don't think the IERS
routinely provides the data more frequently anyway) . ...

It's not clear what your point is here. The offset (UT1-UTC) varies
only a few tens of microseconds per day, and it does so very smoothly.
Example: http://maia.usno.navy.mil/bullaprobt.gif
Thus, the earth rotation angle, UT1, can be calculated at any time by
knowing UTC (atomic clock time) and interpolating the very slowly
varying UT1-UTC offset correction. There is a proper way to do this
interpolation (IERS Gazette #13).

... And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters.

Huh? Can you describe in *any* way how these measurements are *not*
an accurate reflection of earth orientation? Since they are used
successfully in extremely high precision VLBI, GPS, SLR and LLR
observations, I doubt that you can.

... As mentioned, these errors account to about 1 ms/day
variations over a the space of year or so (and similar over longer
time scales) and are only 'modelled' by inserting a leap second when
the accumulated error exceeds a certain bound.

What you "mentioned" is irrelevant. As I noted several times -- but
you continue to delete and ignore -- the *excess* ~1 ms of the length
of day beyond 86400 seconds is *not* an error. It's a measurement!
The uncertainty is miniscule compared to that. [ And in any case, the
"length-of-day" is not used in the analysis, so your "concentration"
on that quantity is irrelevant. ]


Since the UT1 time scale *is the one used* for Doppler analysis,
your point is totally irrelevant. In other words, the instantaneous
earth rotation properties are used, not the mean ones.

As I indicated above already, the UT1 'timescale' consists of
theoretically unmodelled empirical data and should thus not be a
legitimate time scale if you are considering differences that fall
within the unmodelled variations ...

The UT1 "timescale" is *defined* as the rotation angle of the earth.
The only way to know the timescale then is to measure the earth
orientation. This exercise is done to exquisite precision by IERS
contributors, and the Doppler analysis uses the same results. I'm
sure it's quite convenient for you to summarily dismiss observations
that could show that your claims are erroneous, but the fact is, the
observations preclude the possibility that the earth rotation rate
could be mismeasured as grossly as you suggest.

Anyway, if the UT1 time scale gives already the true rotation angle of
the earth, why do you (according to your paper) then apply a
correction UT1-UTC for the length of the day?

Huh? You have it backwards. We know UTC from atomic clocks, and
UT1-UTC from tabulated values, so we can solve for UT1, which is
needed to calculate station orientation. [ And note that, the
analysis does not use the "length-of-day" values reported by the IERS,
only UT1-UTC. ]

Let's summarize.

1. No change in earth station positions by 10 cm (or even 100 m!)
will create the main Pioneer-type "anomaly". That is because
your suppositions regarding the analysis techniques were
incorrect.

2. We are not free to pretend that the earth rotation rate is
"wrong," since the earth rotation parameters are already
determined with high precision by many different observation
techniques. Your suppositions about the length of day having
"errors" of 1 ms are a total misinterpretation.

CM

On 23 Mar, 15:24, Craig Markwardt
wrote:


So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

How would you know? In fact, since the kinds of signals that Anderson
et al. found in their Fig 18 were very small (~0.1 mm/s) compared to
the true anomaly drift of ~200 mm/s, you wouldn't really see such
effects in my Fig 3. Furthermore, Anderson's Fig 18. is taken from
1996 data when the other noise terms were extremely small. The 1996
data was not available from the archive that I used. Were there very
small diurnal Doppler residuals? Probably, but as both Anderson and I
understand, these small sinusoidal frequency residuals do not make a
long term drift a thousand times larger!

The diurnal and long term acceleration residuals are virtually exactly
the same (0.1 mm/sec/day), so (as I said before) it is scientifically
improper to leave the former unmodelled and model the latter
independently of it. And it would be even more improper to sweep the
diurnal acceleration residuals under the carpet altogether (it is
quite obvious from Anderson et al.'s results that this term is present
throughout the data, even though it may be hidden in the noise most of
the time).

It is in fact straightforward to show that the diurnal term not only
leads to the observed acceleration residual, but also to the observed
long-term increase of the velocity residual in case of a mis-modelling
of the earth's rotation rate:
for simplicity let's take a one-dimensional oscillation x=x0*sin(wt)
(with the phase defined such that the sine function is positive when
the spacecraft is above the horizon); assuming there is a mis-
modelling of the rotation rate dw, we have then

x=x0*sin((w+dw)*t) = sin(wt)*cos(dw*t) + cos(wt)*sin(dw*t)

and thus

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


Now since dw is very small (dw/w = 10^-8), we can set cos(dw*t)=1 and
sin(dw*t)=dw*t, i.e.

dx/dt = x0*[ w*cos(wt) -dw^2*t*sin(wt) -dw*w*t*sin(wt) +dw*cos(wt) ]

The first term in the bracket is the modelled diurnal term, so it
disappears when forming the difference between the observed and model
data, the second can be neglected as it is quadratic in dw, so this
leaves then the residual velocity

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

Since there are no data when sin(wt) is negative (the spacecraft is
below the horizon then) we can thus replace sin(wt) by 0.5*|sin(wt)|
for our purposes, so

dx_r/dt = x0*[dw*cos(wt) -0.5*dw*w*t*|sin(wt)| ].

So the residual velocity consists not only of a true diurnal term but
also a term increasing linearly with t in the long term on average
(and both have, as observed, the same order of magnitude over the
space of one day).



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).


It's not clear what your point is here. The offset (UT1-UTC) varies
only a few tens of microseconds per day, and it does so very smoothly.
Example:http://maia.usno.navy.mil/bullaprobt.gif
Thus, the earth rotation angle, UT1, can be calculated at any time by
knowing UTC (atomic clock time) and interpolating the very slowly
varying UT1-UTC offset correction. There is a proper way to do this
interpolation (IERS Gazette #13).

... And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters.

Huh? Can you describe in *any* way how these measurements are *not*
an accurate reflection of earth orientation? Since they are used
successfully in extremely high precision VLBI, GPS, SLR and LLR
observations, I doubt that you can.


This plot is altogether inappropriate he it spans only a couple of
months and is not from the period in question here in the first place.
The point is that in the last few years there was hardly any
systematic drift in the earth's rotation rate (only one leap second
was inserted (in 2006) since the year 1999), but for the period of the
Pioneer data there was a strong systematic drift (a leap second was
inserted practically each year (8 between 1987 and 1998)). One can
thus say that the long term drift during the data period was roughly
seven times stronger than recently. And UT1-UTC would not show this
long term drift anyway, exactly because the leap seconds have been
introduced. As mentioned before, one should use the length of day
residuals (LODR) here instead (http://maia.usno.navy.mil/lplot1.gif )
and these show clearly a long-term drift of the order of 1-2 ms/day
for the period in question (which would explain the Pioneer anomaly in
the sense as shown above).

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). 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.


So to summarize: the unmodelled drift in the earth's rotation rate
is numerically consistent with the Pioneer anomaly (both with regard
to the diurnal as well as the long term drift). This is not proof that
it is associated with it (exactly because it is unmodelled), but I
feel it would otherwise be too much of a coincidence. So one should
rather look for corresponding underlying errors associated with the
determination of earth's rotation parameters and/or their
implementation in the data analysis.



Note: all this does obviously not apply to the 'flyby-anomaly', which
seems to be a completely different effect (the velocity changes are of
the order of 1 mm/sec within a few hours, rather than 0.1 mm/sec/day).
I am not sure yet how to explain these.

Thomas

On 26 Mar, 12:49, Thomas Smid wrote:

The point is that in the last few years there was hardly any
systematic drift in the earth's rotation rate (only one leap second
was inserted (in 2006) since the year 1999), but for the period of the
Pioneer data there was a strong systematic drift (a leap second was
inserted practically each year (8 between 1987 and 1998)).

I forgot to add the reference for this:
http://maia.usno.navy.mil/ser7/tai-utc.dat

See also http://tf.nist.gov/pubs/bulletin/leapsecond.htm for general
information regarding leap seconds.

Thomas

Thomas Smid writes:
On 23 Mar, 15:24, Craig Markwardt
wrote:

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

Returning to them:

1. Do you understand now that the Doppler data are *not* averaged (daily
or multi-day)? [ and thus, your claims about half-daily signals being
averaged are erroneous? ]

2. Do you understand now that a Fourier transform is *not* used in the
Pioneer Doppler analysis? [ and thus, your claims about a DC
"constant offset" frequency are erroneous? ]

3. Do you understand now that the "anomaly" was discovered a Doppler
frequency residual, and not as an "acceleration residual?"

4. Do you understand that varying the station positions produces no
improvement in the Doppler residuals, so your suppositions about
station position errors are incorrect?

5. Do you understand that by introducing deliberate station position
errors -- such as 100 meters, which you yourself suggested -- no
linear Doppler frequency drift is produced?

6. Do you understand that your claims about the variations in earth
length of day are irrelevant? Namely that, while it is true that the
length of day varies over time, these are *measured* very precisely
and can be accounted for. Your concentration on the length of day
issue is a canard: underlying it, is your assumption that Doppler
analysis models the earth rotation rate as constant. But since this
is an erroneous assumption, your conclusions are irrelevant.

7. Do you understand that the UT1 "timescale" is *defined* by the
earth rotation angle? The only way to determine UT1 is to measure it.
These measurements are done via observations of a large ensemble of
known, distant radio quasars -- and also to a constellation of
orbiting satellites -- which firmly tie earth rotation to a fixed
inertial frame.


So why does your analysis then not indicate any diurnal residuals? Or
don't you care about this obvious inconsistency with Anderson et al.'s
results?

How would you know? In fact, since the kinds of signals that Anderson
et al. found in their Fig 18 were very small (~0.1 mm/s) compared to
the true anomaly drift of ~200 mm/s, you wouldn't really see such
effects in my Fig 3. Furthermore, Anderson's Fig 18. is taken from
1996 data when the other noise terms were extremely small. The 1996
data was not available from the archive that I used. Were there very
small diurnal Doppler residuals? Probably, but as both Anderson and I
understand, these small sinusoidal frequency residuals do not make a
long term drift a thousand times larger!

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.

... so (as I said before) it is scientifically
improper to leave the former unmodelled and model the latter
independently of it. And it would be even more improper to sweep the
diurnal acceleration residuals under the carpet altogether (it is
quite obvious from Anderson et al.'s results that this term is present
throughout the data, even though it may be hidden in the noise most of
the time).

I note that you continue to latch onto minutiae. A sinusoidal
residual of amplitude 2000 times less than the long term drift
amplitude is largely negligible.


It is in fact straightforward to show that the diurnal term not only
leads to the observed acceleration residual, but also to the observed
long-term increase of the velocity residual in case of a mis-modelling
of the earth's rotation rate:
for simplicity let's take a one-dimensional oscillation x=x0*sin(wt)
(with the phase defined such that the sine function is positive when
the spacecraft is above the horizon); assuming there is a mis-
modelling of the rotation rate dw, we have then

x=x0*sin((w+dw)*t) = sin(wt)*cos(dw*t) + cos(wt)*sin(dw*t)

.... trim ...

dx_r/dt = x0*[dw*cos(wt) -0.5*dw*w*t*|sin(wt)| ].

So the residual velocity consists not only of a true diurnal term but
also a term increasing linearly with t in the long term on average
(and both have, as observed, the same order of magnitude over the
space of one day).

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.

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.

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.

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.

It's not clear what your point is here. The offset (UT1-UTC) varies
only a few tens of microseconds per day, and it does so very smoothly.
Example:http://maia.usno.navy.mil/bullaprobt.gif
Thus, the earth rotation angle, UT1, can be calculated at any time by
knowing UTC (atomic clock time) and interpolating the very slowly
varying UT1-UTC offset correction. There is a proper way to do this
interpolation (IERS Gazette #13).

... And in any case,
these are *unmodelled* empirical data (i.e. theoretically unexplained
in detail), and in this sense the details we are concerned about here
should be treated as random errors of the actually modelled
parameters.

Huh? Can you describe in *any* way how these measurements are *not*
an accurate reflection of earth orientation? Since they are used
successfully in extremely high precision VLBI, GPS, SLR and LLR
observations, I doubt that you can.


This plot is altogether inappropriate he it spans only a couple of
months and is not from the period in question here in the first place.
The point is that in the last few years there was hardly any
systematic drift in the earth's rotation rate (only one leap second
was inserted (in 2006) since the year 1999), but for the period of the
Pioneer data there was a strong systematic drift (a leap second was
inserted practically each year (8 between 1987 and 1998)).

Your discussion is still irrelevant. The point is *still* that the
difference UT1-UTC changes very slowly over time. Even a few
milliseconds per day is (a) routinely measurable, and (b) easily
accounted-for in the Pioneer Doppler analysis.

... One can
thus say that the long term drift during the data period was roughly
seven times stronger than recently. And UT1-UTC would not show this
long term drift anyway, exactly because the leap seconds have been
introduced. As mentioned before, one should use the length of day
residuals (LODR) here instead (http://maia.usno.navy.mil/lplot1.gif )
and these show clearly a long-term drift of the order of 1-2 ms/day
for the period in question (which would explain the Pioneer anomaly in
the sense as shown above).

Your claim is erroneous. One should not examine the "length of day"
since it is not used in the Pioneer Doppler analysis. UTC-UT1 is
used. See point 6 above.


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. ...

Huh? Are you really serious? An ensemble of distant radio quasars
ties earth rotation to a fixed inertial frame extremely precisely.
See point 7 above.

... 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.

... 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. See point 7 above. I'm sure it's
quite convenient for you to dismiss *all* VLBI observations because
they are not "fully theoretically modeled." The comment does not even
make sense. In fact, earth rotation is a combination of theory and
observation. The theory accounts for overall angular motion and the
observations provide small, slowly varying corrections.

The theory and measurements of earth orientation is of course directly
relevant, since this is precisely what is needed to perform spacecraft
Doppler analysis (i.e. to solve the station positions in inertial
space).

So to summarize: the unmodelled drift in the earth's rotation rate
is numerically consistent with the Pioneer anomaly (both with regard
to the diurnal as well as the long term drift). ...

"unmodelled drift" = another diversion. The changes in earth rotation
are in fact measured precisely, and applied to the Pioneer Doppler
analysis. Since the premise of your summary is erroneous, its further
conclusions are irrelevant.

My summary: you continue to offer up unsubstantiated and irrelevant
speculations.

CM