"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.

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