On 27 Jun 2006 09:58:04 -0700, "GSS"
wrote:


John C. Polasek wrote:
On 26 Jun 2006 09:44:15 -0700, "GSS"
wrote:


Craig Markwardt wrote:
"GSS" writes:

May I request the learned readers to kindly explain (if possible) how
exactly did we come to the conclusion from the available Doppler data
that the Anomaly exists? More precisely, how do we compute the
Anomalous acceleration from the available Doppler data?


In short, there is a model of the forces on the spacecraft and the
physical effects on the radio waves in the solar system. After
solving for the trajectory of the spacecraft by adjusting the initial
conditions, there still remains a residual which cannot be accounted
for by known physics. Hence, the "anomaly."

Why not read more here?
http://arxiv.org/gr-qc/0104064 Anderson et al.
http://arxiv.org/gr-qc/0208046 Markwardt

Craig

Let me include a few relations from the above quoted reference for
subsequent discussion.

Let D represent delta, v_mod represent the outward velocity of the
spacecraft at the given instant t as used in the comprehensive
trajectory model and v_obs represent the corresponding velocity as
derived from the observed Doppler frequency Nu_obs.

Nu_mod = Nu_0 [1-(2.v_mod/c)] ..... (1)
DNu_mod = Nu_0 - Nu_mod ..... (2)
DNu_obs = Nu_0 - Nu_obs ..... (3)
From (1)
DNu_mod/Nu_0 = 2 v_mod/c ..... (4)
And
2 v_obs/c = DNu_obs/Nu_0 ..... (5)

It has been observed from the Pioneer-10 Doppler data that over a long
period of time the Doppler Residuals given by [DNu_obs-DNu_mod] or by
[v_obs-v_mod] showed a continuous decreasing trend. This has been found
to be an Anomalous effect. This anomalous effect has been modeled by an
anomalous acceleration term a_p directed towards sun/earth.

DNu_obs/Nu_0 - DNu_mod/Nu_0 = 2.a_p.t/c .... (6)

Tremendous efforts have been put in for finding some acceptable
satisfactory explanation for this anomaly and too many weird proposals
have been put forward for resolving it but without success. In the
process all aspects of the comprehensive trajectory model have been
thoroughly analyzed.

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??

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

GSS

I tried to show you in my flowgraph paper on my website, that Doppler
isn't even in it. The round trip times are too small.

Even for a 20 hr. round trip the Doppler change in beat is a
fractional change df/f0 = 2e-13 or 4.8e-4Hz, and after 8 years (the
other end of the chart) you have the same values 2e-13 and 4.8e-4Hz.
There would be nothing to plot.

The chart shown would be the same if you used the station clock,
without the Doppler returned signal. The only thing that can
reasonably cause that is a continuously increasing station clock rate
or a mystery acceleration which we can rule out.

John Polasek
http://www.dualspace.net

I appreciate your efforts for putting up a new proposal under the
'banner' of 'New Physics'. Exploring all possibilities is the normal
scientific approach.

However, I am sorry, I cannot agree to your proposal.
Trouble is that I cannot agree to your fundamental assumption of an
expanding space. Hence your argument of 'continuously increasing
station clock rate' is not convincing even if you believe that it can
explain the anomaly.

GSS
How far can we get if you equate expanding clock rate with expanding
space? Dual Space is a large theory replacing relativity and the BB
and it explains why clock rates are changing.

Look at my Gravity paper (#2) on my website and see Eq. 1, the Navier
Stokes equation that explains gravity as being the consequence of the
removal of that which was created out of the pair-space substance.

Eq. 1c has the development cdc/dr = MG/r^2, where it turns out dc/dr
is the Hubble constant, which equals Ap for proper M and r, the mass
of the universe and its radius.

The chapter is about showing how the results of GR are achieved in
cartesian space after separating space and time. The GPS example is a
nice test case.

It is quite plain that relativity and space-time have nothing useful
to say in regard to the Pioneer 10 nor even the Michelson Morley null
which is explained in Fig. 7.

John Polasek
http://www.dualspace.net