Pioneer : Anomaly Still Anonymous

Craig Markwardt wrote:
"GSS" writes:
Craig Markwardt wrote:
"GSS" writes:
...
DNu_mod/Nu_0 = 2 v_mod/c ..... (4)
And
2 v_obs/c = DNu_obs/Nu_0 ..... (5)
...

It has been mentioned in the above quoted reference that *all
relativistic corrections* have been incorporated in the model. In this
regard kindly give your opinion whether it is possible that the so
called relativistic corrections themselves could be the source of the
Anomalous effect??

No. Switching from relativistic to classical physics only worsens the
solution, not improves.

Has this been tried out? If so by whom and what is the quantitative
difference in the Anomalous effect?

Yes, by me. Changing from relativistic to classical Doppler shifts
essentially adds noise to the solution, which is of order a few Hz.
This is appropriate since the difference between the two kinds of
Doppler shifts occurs at second order in (v/c). It's also
understandable since the dominant Doppler shifts are the earth's
motion and rotation (factor of 2-3 times larger than the spacecraft
speed w.r.t. the sun). The anomaly itself is still present with both
methods, just noisier with classical Doppler shifts.

From the above quoted reference [arXiv:gr-qc/0104064 v5] it appears
that the Relativity corrections have been used both for improving
accuracy of the model and to use such an improved model for testing the
Relativity Theories. Quoting from pages 12 and 14 of this reference -

"Responding to the increasing demand of the navigational accuracy, the
gravitational field in the solar system is modeled to include a number
of relativistic effects that are predicted by the different metric
theories of gravity. Thus, within the accuracy of modern experimental
techniques, the parameterized post-Newtonian (PPN) approximation of
modern theories of gravity provides a useful starting point not only
for testing these predictions, but also for describing the motion of
selfgravitating bodies and test particles."

"Indeed, this dynamical model has been good enough to perform tests of
general relativity."

Or, from the above quoted reference [arxiv.org/gr-qc/0208046],

"The equations of motion I used [... included ... ] aN ... due to
Newtonian gravity"

and

"[Anderson et al 2002] considers additional terms for the
acceleration which allow for alternate theories of gravity (their
equation 3). I find that over the span of the data, these terms are
always smaller than 3x10^{-12} cm/s^2 and thus I neglect them for
the purposes of Doppler tracking analysis.

So, despite using Newtonian gravity, the anomaly was the same. Adding
the relativistic terms to the equation of motion did not change the
solution appreciably.

Thanks for the clarification.

Doesn't it appear to be fundamentally illogical to first use Relativity
to perfect the model and then to use that model to test Relativity. If
the Relativity does need to be tested then why use it till its
clearance through authentic testing?

Ignoring for the moment that your question is moot -- given the above
description -- the first "P" in the PPN theory of gravity is
"parameterized." The PPN theory is parameterized family of gravity
models, *not* just GR.

And is it also possible that some theoretical error in the Doppler
relations (4) and (5) could lead to the observed Anomalous effect?

Relations 4 and 5 are inexact representations of the Doppler shift.
The exact relativistic formulation improves the solution.

Craig

Kindly provide the ' exact relativistic formulation ' in place of
relations (4) and (5) or atleast provide a reference for the same.

Kindly consult the referred-to papers, for example, gr-qc/0208046 eq 2.

CM

Let me try to reproduce equation 2 from your paper gr-qc/0208046 since
I intend to have a detailed discussion on this issue.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ˆr12 · v2/c^2)/(1 - ˆr12 · v1/c^2)] ............. (2)
The unit vector ˆr12 points from the transmitting station to the
spacecraft,
i.e., ˆr12 = r12/r12.

This equation appears to be wrong since it is not dimensionally
balanced. Perhaps it should have been as given below.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ˆr12 · v2/c)/(1 - ˆr12 · v1/c)] ............. (2')

Kindly confirm.

GSS

"GSS" writes:
Craig Markwardt wrote:
"GSS" writes:
Craig Markwardt wrote:
"GSS" writes:
...
DNu_mod/Nu_0 = 2 v_mod/c ..... (4)
And
2 v_obs/c = DNu_obs/Nu_0 ..... (5)
...

It has been mentioned in the above quoted reference that *all
relativistic corrections* have been incorporated in the model. In this
regard kindly give your opinion whether it is possible that the so
called relativistic corrections themselves could be the source of the
Anomalous effect??

No. Switching from relativistic to classical physics only worsens the
solution, not improves.

Has this been tried out? If so by whom and what is the quantitative
difference in the Anomalous effect?

Yes, by me. Changing from relativistic to classical Doppler shifts
essentially adds noise to the solution, which is of order a few Hz.
This is appropriate since the difference between the two kinds of
Doppler shifts occurs at second order in (v/c). It's also
understandable since the dominant Doppler shifts are the earth's
motion and rotation (factor of 2-3 times larger than the spacecraft
speed w.r.t. the sun). The anomaly itself is still present with both
methods, just noisier with classical Doppler shifts.

From the above quoted reference [arXiv:gr-qc/0104064 v5] it appears
that the Relativity corrections have been used both for improving
accuracy of the model and to use such an improved model for testing the
Relativity Theories. Quoting from pages 12 and 14 of this reference -

"Responding to the increasing demand of the navigational accuracy, the
gravitational field in the solar system is modeled to include a number
of relativistic effects that are predicted by the different metric
theories of gravity. Thus, within the accuracy of modern experimental
techniques, the parameterized post-Newtonian (PPN) approximation of
modern theories of gravity provides a useful starting point not only
for testing these predictions, but also for describing the motion of
selfgravitating bodies and test particles."

"Indeed, this dynamical model has been good enough to perform tests of
general relativity."

Or, from the above quoted reference [arxiv.org/gr-qc/0208046],

"The equations of motion I used [... included ... ] aN ... due to
Newtonian gravity"

and

"[Anderson et al 2002] considers additional terms for the
acceleration which allow for alternate theories of gravity (their
equation 3). I find that over the span of the data, these terms are
always smaller than 3x10^{-12} cm/s^2 and thus I neglect them for
the purposes of Doppler tracking analysis.

So, despite using Newtonian gravity, the anomaly was the same. Adding
the relativistic terms to the equation of motion did not change the
solution appreciably.

Thanks for the clarification.

Doesn't it appear to be fundamentally illogical to first use Relativity
to perfect the model and then to use that model to test Relativity. If
the Relativity does need to be tested then why use it till its
clearance through authentic testing?

Ignoring for the moment that your question is moot -- given the above
description -- the first "P" in the PPN theory of gravity is
"parameterized." The PPN theory is parameterized family of gravity
models, *not* just GR.

And is it also possible that some theoretical error in the Doppler
relations (4) and (5) could lead to the observed Anomalous effect?

Relations 4 and 5 are inexact representations of the Doppler shift.
The exact relativistic formulation improves the solution.

Craig

Kindly provide the ' exact relativistic formulation ' in place of
relations (4) and (5) or atleast provide a reference for the same.

Kindly consult the referred-to papers, for example, gr-qc/0208046 eq 2.

CM

Let me try to reproduce equation 2 from your paper gr-qc/0208046 since
I intend to have a detailed discussion on this issue.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ˆr12 · v2/c^2)/(1 - ˆr12 · v1/c^2)] ............. (2)
The unit vector ˆr12 points from the transmitting station to the
spacecraft,
i.e., ˆr12 = r12/r12.

A typo.

This equation appears to be wrong since it is not dimensionally
balanced. Perhaps it should have been as given below.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ˆr12 · v2/c)/(1 - ˆr12 · v1/c)] ............. (2')

Kindly confirm.

Confirmed.
CM

John C. Polasek writes:
On 27 Jun 2006 10:46:22 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
...
You must know that I am talking about all real, maser-verfiied clocks
that accelerate compared to the artificial clock in the model which
for several reasons must have a constant value. The result is the ramp
function on the chart.
...

For the nth time, there is no "artificial clock" in the model. The
station clock at the time of the tracking session is used in the
model. If you continue with your fiction, I can only assume that you
are not interested in substantiated debate.

CM
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier is
a mathematic constant being 1/WL.

If this is wrong, just say so and I can modify my model, but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the station
clock to drive the DDA, but that looks like a nullity also.

It is clear there is substantial misunderstanding somewhere.

Yes, you have a problem. Why don't you start to fix it by reading the
referred-to papers, or George or my previous posts, which you seem to
be conveniently ignoring?

CM

Craig Markwardt wrote:
John C. Polasek writes:
On 27 Jun 2006 10:46:22 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
...
You must know that I am talking about all real, maser-verfiied clocks
that accelerate compared to the artificial clock in the model which
for several reasons must have a constant value. The result is the ramp
function on the chart.
...

For the nth time, there is no "artificial clock" in the model. The
station clock at the time of the tracking session is used in the
model. If you continue with your fiction, I can only assume that you
are not interested in substantiated debate.

CM
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier is
a mathematic constant being 1/WL.

If this is wrong, just say so and I can modify my model, but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the station
clock to drive the DDA, but that looks like a nullity also.

It is clear there is substantial misunderstanding somewhere.

Yes, you have a problem. Why don't you start to fix it by reading the
referred-to papers, or George or my previous posts, which you seem to
be conveniently ignoring?

CM

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.

On 29 Jun 2006 02:05:58 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
On 27 Jun 2006 10:46:22 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
...
You must know that I am talking about all real, maser-verfiied clocks
that accelerate compared to the artificial clock in the model which
for several reasons must have a constant value. The result is the ramp
function on the chart.
...



CM
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier is
a mathematic constant being 1/WL.

If this is wrong, just say so and I can modify my model, but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the station
clock to drive the DDA, but that looks like a nullity also.

It is clear there is substantial misunderstanding somewhere.

Yes, you have a problem. Why don't you start to fix it by reading the
referred-to papers, or George or my previous posts, which you seem to
be conveniently ignoring?

I see where I muddied the waters by talking about -f0/c. I should have
said f0:
The model is totally artificial, a mathematical construct, and it
requires 3 prescribed numerical coefficients G, -f0/c and finally f0.
The important one is f0 which I say retains a constant prescribed
value, while the real clocks run away from it by Hubble acceleration.
(The part depending on -f0/c is as I have said, a negligible
contributor.)

The additive f0 in my flowgraph has to be a constant with the same
value today as it had 20 years ago, or show me how, and why, it has
been altered.

You say "the station clock at the time of the tracking session is used
in the model". Please tell veryspecifically how this can be done. (We
are looking for nothing more nor less than a new NUMERICAL value of f0
to go into the model). (As can be seen from the graph a new offset to
f0 would simply offset the graph).
To be facetious, (or realistic) what would cause the technician, who
has just turned on the station clock, to call up the computer room and
announce a new number for f0?

Checking the frequency with NIST would be simplest. You can update an
atomic clock over the telephone. Their site has a sample daily record
of a clock being checked, that shows infinitesimal *random* daily
changes about +-2e-13 which is nothing.
Remember that by hypothesis, NIST's masers have advanced by exactly
the same fraction as the statioin clock, so they all march together.
But f0 in the model is stuck in the past.

Tell me how the number f0 is custom adjusted to the station clock's
frequency, when there is no way of determining its frequency in the
first place.

My argument is simply that f0 is set in stone, and by hypothesis, all
atomic real clocks are secularly advancing, leading to the 1.5/8
discrepancy. It simply accounts for the anomaly.

CM

John Polasek
http://www.dualspace.net

Craig Markwardt wrote:
"GSS" writes:
Craig Markwardt wrote:
"GSS" writes:
......
So, despite using Newtonian gravity, the anomaly was the same. Adding
the relativistic terms to the equation of motion did not change the
solution appreciably.

Thanks for the clarification.
......

Let me try to reproduce equation 2 from your paper gr-qc/0208046 since
I intend to have a detailed discussion on this issue.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ^r12 · v2/c^2)/(1 - ^r12 · v1/c^2)] ............. (2)
The unit vector ^r12 points from the transmitting station to the
spacecraft,
i.e., ^r12 = r12/r12.

A typo.

This equation appears to be wrong since it is not dimensionally
balanced. Perhaps it should have been as given below.

d_12 = {sqrt[1 - |v1|^2/c^2]/sqrt[1 - |v2|^2/c^2]} .
[(1 - ^r12 · v2/c)/(1 - ^r12 · v1/c)] ............. (2')

Kindly confirm.

Confirmed.
CM

Again quoting from page 4 of your paper,

"The epoch of transmission from the Earth is t1, the epoch of
interaction of the signal with the Pioneer 10 spacecraft is t2, and the
epoch of reception back at the Earth is t3. All of these times are
referred to the Barycentric Dynamical Timescale (TDB), which is a
coordinate time at the solar system barycenter. TDB is also the
effective argument of the JPL planetary ephemerides. The 3-vectors r1,
r2, and r3 represent the positions of the corresponding antenna at the
corresponding epoch, and v1, v2, and v3 represent the velocities. *The
vector difference, r12, is defined as r1 - r2.* These vector
quantities are measured in the solar system barycenter frame."

Perhaps the vector difference, r12, should have been defined as r2 -
r1.

Further,
-----------------
"The final term in equation 1, DNu_path, represents additional Doppler
effects caused by small effective path length changes, aside from those
due to geometric antenna motions. Generally speaking, this term can be
written as,
DNu_path = -2 dl/dt.Nu_0/c,
where dl/dt is the time rate of change of effective photon trajectory
path length along the line of sight. The factor of 2 comes from the two
legs of the round trip path. In this paper I consider the effective
path length due to the "Shapiro" delay. The Shapiro delay reflects the
extra proper distance traveled by a photon, beyond the classical
geometric distance, in the Sun's gravitational potential, as predicted
by general relativity,"

" l_shap = 2.(GM/c^2).ln[(r1+r2+r12)/(r1+r2-r12)] ..... (3)"

"On an annual timescale, the impact parameter of the photon trajectory
increases and decreases, with a minimum distance of about 8×106 km.
Conversion to a Doppler shift is achieved by numerically
differentiating equation (3), which yields an annual signal with
amplitude ±150 mHz."
----------------------
During the period of your analysis (1987-1994), r2r1. Therefore,
apart from a cyclic term given by annual variation of r1 in equation
(3), we get a dominant, steadily varying term dependent on steadily
increasing r2 as,

l_shap = 2.(GM/c^2).ln[r2/r1] ..... (4)
This yields (approximately),
DNu_path/Nu_0 = -4(GM/c^2).(1/r2).(v2/c) .... (5)

This is the term which is expected to make a significant contribution
to the Doppler residuals apart from a cyclic term dependent on annual
variation of r1. Can you kindly give some quantitative figures for this
contribution to the Doppler residuals during the period of your
analysis?

GSS

"Aleksandr Timofeev" writes:

Craig Markwardt wrote:
John C. Polasek writes:
On 27 Jun 2006 10:46:22 -0500, Craig Markwardt
wrote:


John C. Polasek writes:
...
You must know that I am talking about all real, maser-verfiied clocks
that accelerate compared to the artificial clock in the model which
for several reasons must have a constant value. The result is the ramp
function on the chart.
...

For the nth time, there is no "artificial clock" in the model. The
station clock at the time of the tracking session is used in the
model. If you continue with your fiction, I can only assume that you
are not interested in substantiated debate.

CM
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier is
a mathematic constant being 1/WL.

If this is wrong, just say so and I can modify my model, but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the station
clock to drive the DDA, but that looks like a nullity also.

It is clear there is substantial misunderstanding somewhere.

Yes, you have a problem. Why don't you start to fix it by reading the
referred-to papers, or George or my previous posts, which you seem to
be conveniently ignoring?

CM

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.

The principle of equivalence has been tested quite narrow tolerances
in the solar system already (Williams et al 1996), so your supposition
will probably not be fruitful.

CM

References
Williams, Newhall & Dickey 1996, Phys Rev D, 53, 6730

"GSS" writes:

" l_shap = 2.(GM/c^2).ln[(r1+r2+r12)/(r1+r2-r12)] ..... (3)"

"On an annual timescale, the impact parameter of the photon trajectory
increases and decreases, with a minimum distance of about 8×106 km.
Conversion to a Doppler shift is achieved by numerically
differentiating equation (3), which yields an annual signal with
amplitude ±150 mHz."
----------------------
During the period of your analysis (1987-1994), r2r1. Therefore,
apart from a cyclic term given by annual variation of r1 in equation
(3), we get a dominant, steadily varying term dependent on steadily
increasing r2 as,

l_shap = 2.(GM/c^2).ln[r2/r1] ..... (4)
This yields (approximately),
DNu_path/Nu_0 = -4(GM/c^2).(1/r2).(v2/c) .... (5)

This is the term which is expected to make a significant contribution
to the Doppler residuals apart from a cyclic term dependent on annual
variation of r1. Can you kindly give some quantitative figures for this
contribution to the Doppler residuals during the period of your
analysis?

You are welcome to estimate it yourself, but they are negligible. The
"Shapiro effect" is very strongly detected; one can't simply ignore
some terms and accept other terms as you have done.

CM

"Joe Jakarta" writes:
Craig Markwardt wrote:

[...]

The principle of equivalence has been tested quite narrow tolerances
in the solar system already (Williams et al 1996), so your supposition
will probably not be fruitful.

I wonder how the anomalous Pioneer blue-drift compares for size with GR
one due to the Sun's gravity?

Do you mean the difference gravitational redshift between the earth
and the spacecraft? Since the spacecraft re-transmits the uplink
signal on the downlink channel, including the same frequency and
phase, any redshift of the signal on the uplink leg is cancelled by
an equal blueshift on the downlink leg.

CM

--
--------------------------------------------------------------------------
Craig B. Markwardt, Ph.D. EMAIL:
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
--------------------------------------------------------------------------

John C. Polasek writes:
I see where I muddied the waters by talking about -f0/c. I should have
said f0:
The model is totally artificial, a mathematical construct, and it
requires 3 prescribed numerical coefficients G, -f0/c and finally f0.
The important one is f0 which I say retains a constant prescribed
value, while the real clocks run away from it by Hubble acceleration.
(The part depending on -f0/c is as I have said, a negligible
contributor.)

The additive f0 in my flowgraph has to be a constant with the same
value today as it had 20 years ago, or show me how, and why, it has
been altered.

Your model description is not reflective of reality, therefore it is
irrelevant.

You say "the station clock at the time of the tracking session is used
in the model". Please tell veryspecifically how this can be done.

It's easy. The transmission frequency was *recorded* at that time,
thus it is available to be used in the model.

... (We
are looking for nothing more nor less than a new NUMERICAL value of f0
to go into the model).

There is no f0. Every tracking session contains its own record of the
frequency used *at that time*. Those frequencies are used in the
model. THERE IS NO "F0" FROM 1987 STORED IN THE MODEL. When will you
get this?

...(As can be seen from the graph a new offset to
f0 would simply offset the graph).
To be facetious, (or realistic) what would cause the technician, who
has just turned on the station clock, to call up the computer room and
announce a new number for f0?

Actually, the uplink frequency for a given session is crudely adjusted
so that when the signal arrives at the spacecraft, it will be within
the spacecraft receiver's bandpass. So the uplink frequency for each
tracking session is customized to the conditions.

....
My argument is simply that f0 is set in stone, and by hypothesis, all
atomic real clocks are secularly advancing, leading to the 1.5/8
discrepancy. It simply accounts for the anomaly.

Since your argument is erroneous, your conclusions are irrelevant.

CM