Re: Pioneer Anomaly discussion continued

On 9 Mar, 22:34, Craig Markwardt
<craigm...@xxxxxxxxxxxxxxxxxxxxxxxxxx> 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



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Relevant Pages

  • Re: Pioneer Anomaly discussion continued
    ... one has to consider the velocity and not acceleration. ... for instance for the diurnal velocity residuals shown in Fig.18 (page ... According to your paper you didn't test for station dependent effects ... rotation rate to produce the Pioneer anomaly. ...
    (sci.astro)
  • Re: Pioneer Anomaly discussion continued
    ... one has to consider the velocity and not acceleration. ... for instance for the diurnal velocity residuals shown in Fig.18 (page ... According to your paper you didn't test for station dependent effects ... rotation rate to produce the Pioneer anomaly. ...
    (sci.astro)
  • Re: Pioneer Anomaly discussion continued
    ... one has to consider the velocity and not acceleration. ... for instance for the diurnal velocity residuals shown in Fig.18 (page ... If the station positions were incorrect (among ... but had the station positions fixed to the nominal values as ...
    (sci.astro)
  • Re: Pioneer Anomaly Caused by Earths Rotation?
    ... residuals. ... deg out of phase with the acceleration and thus has, ... velocity residuals will therefore average to zero with time (as the ... Is the angular rotation of the earth actually not part of the ...
    (sci.astro)
  • Re: Pioneer Anomaly discussion continued
    ... only difference is that the first is a circular acceleration, ... In terms of the earth motion, the spacecraft rises in the east ... to does *not* show sinusoidal residuals whose amplitude grows linearly ... Furthermore, the ionosphere is more complicated than you suggest, ...
    (sci.astro)
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