Pioneer 10 Anomaly solved with expanding wavelength

"Craig Markwardt" wrote in message
news

Hi George,

"George Dishman" writes:

Craig Markwardt wrote:
"George Dishman" writes:
As Craig has pointed out, and I wasn't clear in my earlier reply
so I guess I may have caused the confusion, the model was
initialised by setting the craft _velocity_ such that the modelled
frequency matched the observation at that time.

George, just to clarify, the spacecraft position and velocity in 1987
are initial conditions to the trajectory problem. During the analysis
we did not *intend* for the frequency residual to be zero in 1987, as
one might infer from your statement above. And indeed, the residual
would not need to be zero in 1987 (if the model would have been a poor
description of the data; or if the spacecraft initial conditions were
specified at a different epoch).

That's a useful clarification Craig, thanks. Looking at your
graph which John reproduces, it goes from zero anomaly
to about +18cm/s. It would be equally valid to have an
anomaly going from -18cm/s to zero but with a base model
that had an initial speed higher by 18cm/s. As I understand
the situation, up to the start of the study, the craft motion
was predicted using a shorter term model (50 days?) which
makes sense where effects like the planetary passes could
not be perfectly modelled. That suggests that if there had
been any anomalous force prior to 1987, its effect would have
been rolled up into the then current trajectory. Is my
understanding valid or am I missing something?

... It is that initial
velocity which is effectively a constant, the subsequent speed
being derived by modeling gravitational and other accelerations.

Also to clarify: the initial conditions (position & velocity) are
*varied* (not fixed) during the orbit determination process.

That I don't follow since I can't see how a uniform origin shift
of the anomaly can be distinguished from a change in initial
radial velocity.

What I was describing was the orbit determination procedure. It is
what it is. The origin of the "anomaly" was essentially held fixed at
the position origin of the solar system, for all but some diagnostic
analysis, and it is not well constrained. One can easily translate
the origin of the anomaly by a fraction of an AU without altering the
solution.

Sorry Craig, I guess I wasn't clear, by 'origin' I meant
the origin of the Y axis in the graph. What I was thinking
(using toy values) is that you could start on day one with
say a best fit of 12km/s and treat that equally as a craft
speed of 12000.00 m/s and zero anomaly or a craft speed of
12000.18 m/s and an anomaly of -0.18 m/s. So you could set
the anomaly at zero and fit the craft speed or set the
craft speed at the last known value and fit the anomaly
but you can't do a fit in which both are allowed to vary.
Am I missing something?

George

"George Dishman" writes:

"Craig Markwardt" wrote in message
news

Hi George,

"George Dishman" writes:

Craig Markwardt wrote:
"George Dishman" writes:
As Craig has pointed out, and I wasn't clear in my earlier reply
so I guess I may have caused the confusion, the model was
initialised by setting the craft _velocity_ such that the modelled
frequency matched the observation at that time.

George, just to clarify, the spacecraft position and velocity in 1987
are initial conditions to the trajectory problem. During the analysis
we did not *intend* for the frequency residual to be zero in 1987, as
one might infer from your statement above. And indeed, the residual
would not need to be zero in 1987 (if the model would have been a poor
description of the data; or if the spacecraft initial conditions were
specified at a different epoch).

That's a useful clarification Craig, thanks. Looking at your
graph which John reproduces, it goes from zero anomaly
to about +18cm/s. It would be equally valid to have an
anomaly going from -18cm/s to zero but with a base model
that had an initial speed higher by 18cm/s. As I understand
the situation, up to the start of the study, the craft motion
was predicted using a shorter term model (50 days?) which
makes sense where effects like the planetary passes could
not be perfectly modelled. That suggests that if there had
been any anomalous force prior to 1987, its effect would have
been rolled up into the then current trajectory. Is my
understanding valid or am I missing something?

... It is that initial
velocity which is effectively a constant, the subsequent speed
being derived by modeling gravitational and other accelerations.

Also to clarify: the initial conditions (position & velocity) are
*varied* (not fixed) during the orbit determination process.

That I don't follow since I can't see how a uniform origin shift
of the anomaly can be distinguished from a change in initial
radial velocity.

What I was describing was the orbit determination procedure. It is
what it is. The origin of the "anomaly" was essentially held fixed at
the position origin of the solar system, for all but some diagnostic
analysis, and it is not well constrained. One can easily translate
the origin of the anomaly by a fraction of an AU without altering the
solution.

Sorry Craig, I guess I wasn't clear, by 'origin' I meant
the origin of the Y axis in the graph. What I was thinking
(using toy values) is that you could start on day one with
say a best fit of 12km/s and treat that equally as a craft
speed of 12000.00 m/s and zero anomaly or a craft speed of
12000.18 m/s and an anomaly of -0.18 m/s. So you could set
the anomaly at zero and fit the craft speed or set the
craft speed at the last known value and fit the anomaly
but you can't do a fit in which both are allowed to vary.
Am I missing something?

No. The anomaly is zero at T0=1987 because the initial conditions of
the trajectory were determined at that time. If T0 were set to 1994,
then the anomaly would be zero then, by construction. My original
point was that the initial conditions must be varied to find the best
fit trajectory.

Craig

Craig Markwardt wrote:
John C. Polasek writes:

On 31 May 2006 10:52:02 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
But we are neglecting another reference frequency, nu_87 that is built
into the model. ...

No. Despite multiple corrections, and extensive discussions of the
actual procedures, you persist with this delusion. As the thread is
purely based on speculation, I no longer care to be involved.

CM
It would be helpfulif you would illuminate us on what steps were
followed to generate nu_model is so it could be subtracted from
nu_observed to get
(f_observ - f_model)DSN = -2fP*t (2)

It's not clear where you got this equation.

Equation 15 of Anderson et al (2002) is quite different. The text
around equation (15) describes generically how "nu_model" is found.
Note that as the sentence containing equation (15) states, the
"anomalous effect *can be expressed*" as that equation (emph added),
not that it *was* expressed that way in the analysis. In reality, the
anomalous term was absorbed into "nu_model".

Both Anderson et al (2002) and Markwardt (2002) describe how
"nu_model" was computed numerically, and how the orbit determination
was done.

But don't patronize me about definition of nu_0 etc. ...

Then don't make unsubstantiated and erroneous suppositions about how
the analysis was done.

CM

References
Anderson et al (2002, Phys Rev D, 65, 082004)
Markwardt 2002, gr-qc/0208046

Dear Craig Markwardt, please, look at:

http://groups.google.com/group/sci.p...e=source&hl=en

My arguments and interpretation of anomaly of "Pioneers" can change
your approach to interpretation of the problem.

John C. Polasek wrote:
On 30 May 2006 18:39:23 -0500, Craig Markwardt
wrote:

John C. Polasek writes:


On 30 May 2006 14:34:28 -0500, Craig Markwardt
wrote:
John C. Polasek writes:
...
As George said in his note above,
"The model was initialised in 1987 so at that time fmodel was set
equal to fobs."
The computer model clearly was so initialized as to time and
frequency. You can see there would be no motivationto readjust these.
...

You are incorrect. What was initialized in 1987 was the *trajectory*
model. Each tracking uplink provides a self contained coherent
frequency reference at the time of the session (not 1987). There are
no variables in the solution program which store the frequency as it
was in 1987.
If by trajectory you mean the orbital elements were determined in 1987
then, fine, but to produce actual ranges and velocities the
mathematical model has to include a good value of G to convert planet
distance into accelerations, to be integrated into real velocity. Then
to convert the velocity to frequency for comparison of Doppler phase
slippage, the program had to contain the multiplier f0/c as given in
Eq. 1 of Anderson, 10 Mar. 2005:
[ note incorrect citation ]
delta f(t) = f0*(1/c)*dr/dt
The conversion of dr/dt to delta f uses f0/c. Are you trying to tell
me that on initiation of each 5-day batch, they caused a re-setting of
f0 to match the current clock? It does not seem likely. ...

The equation you are citing is one that describes how DSN tracking
works in generic terms, and does not contain all of the technical
details. Still, if you had read the attached footnote (#38), you
would have found that "nu_0" is the "reference frequency." In fact,
the reference frequency is recorded at the moment of the tracking
session (it is the frequency standard of the station), and *NOT* in
1987. (see also eqn 13). It is not reset in "each 5-day batch,"
because it is recorded in each and every downlink record! [ and
several times per uplink. ] When will you get it into your head that
there are no variables in the program that store the "frequency" as of
1987?

CM
Firstly, #38 explains once again, only that "our frequency/velocity
convention is backwards", a receding craft getting a blue shift that
takes a bit of getting used to, but OK. No information is transmitted
there.

How is the reference frequency transcribed into the coefficients of
the mathematical computer program? As I pointed out there needs to be
a reliable G and a dependable f0, and of the latter, there was no
motivation in 1987 to assert that f0 is anything but constant.

What I have berought to your attention that is new is f0 increasing
with time as f = f0(1+Ht), and when compared to the static value in
the model, a linearly increasing disprepancy reveals itself.

The values f0 and c have to be in the program with no impetus to
change f0. Of course the ref frequency "is recorded at the moment of
the tracking session". Please clarify: is there a laboratory event
that causes one to change the equation constants?

I am talking about the construction of the model, against which all
these readings are taken. Is f0 a custom value for each shot?

John Polasek

Unfortunately you are wrong. It has nothing to do with the Hubble
expansion at all.

I have the answer.