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).

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.

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.

Note: this is a continuation of the thread
http://groups.google.co.uk/group/sci.astro/browse_frm/thread/87fb34db20b1af7f


On 5 Mar, 17:20, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> 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').

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

... 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.

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

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.

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?

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.

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.

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).

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

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.

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.

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.

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.

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

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.

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.

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.

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.

On 9 Mar, 22:34, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> 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.

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 ...

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?

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!

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.

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)).

On 23 Mar, 15:24, Craig Markwardt
craigm...@REMOVEcow.physics.wisc.edu> 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)

.... 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).

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 here: 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). ...

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

Correct me if I'm wrong, but wasn't the spacecraft observed from more than

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

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.

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.

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.

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.

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.

... 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.

Thomas Smid (thomas.s...@gmail.com) writes:

[...]

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

Correct me if I'm wrong, but wasn't the spacecraft observed from more than
one site, meaning that it would only rarely be below the horizon from
everyone?

On 26 Mar, 18:39, af...@FreeNet.Carleton.CA (John Park) wrote:
Thomas Smid (thomas.s...@gmail.com) writes:

[...]

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

Correct me if I'm wrong, but wasn't the spacecraft observed from more than
one site, meaning that it would only rarely be below the horizon from
everyone?

By definition, the space craft always must be above the horizon when
observed from any station. A switch of station would just mean a
sudden phase shift in the sine function, but this is (hopefully) being
taken into account in the data analysis, so technically we can for
this purpose just as well pretend that only one station is being
used.

However, additionally we would have to account for the fact that the
signals are emitted and received at different local times, so we would
actually be dealing with an average (|sin(wt)|+|sin(wt+phi)|))/2,
where phi is the angle corresponding to this difference in local time.

Thomas Smid (thomas.smid@gmail.com) writes:
On 26 Mar, 18:39, af...@FreeNet.Carleton.CA (John Park) wrote:
Thomas Smid (thomas.s...@gmail.com) writes:

[...]

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

Correct me if I'm wrong, but wasn't the spacecraft observed from more than
one site, meaning that it would only rarely be below the horizon from
everyone?

By definition, the space craft always must be above the horizon when
observed from any station. A switch of station would just mean a
sudden phase shift in the sine function, but this is (hopefully) being
taken into account in the data analysis, so technically we can for
this purpose just as well pretend that only one station is being
used.

Don't understand. If, to take an extreme case, two stations, 180 degrees
apart in longitude, monitored the satellite and combined their data, the
satellite would always be above someone's horizon, and under continuous
observation. So where would your half-wave-rectified-sinusoid problem come
from?

However, additionally we would have to account for the fact that the
signals are emitted and received at different local times, so we would
actually be dealing with an average (|sin(wt)|+|sin(wt+phi)|))/2,
where phi is the angle corresponding to this difference in local time.

And if phi = pi, you have the equivalent of full-wave rectification.