On Saturday, April 1, 2017 at 7:47:20 AM UTC+11, Craig Markwardt wrote:
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The question is what tolerance was required for the analysis. Anderson
et al's analysis was quite back of the envelope. A few Watts makes a
difference, so it was important to treat the analysis in more detail.

Solar Radiation Pressure and the Pioneer Anomaly

Stored here for convenience:
http://members.optusnet.com.au/mskeon/solr-rad.html

Fig.2 from this link
https://arxiv.org/pdf/1204.2507v1
apparently suggests that the Pioneer anomaly may only be the
result of mismodelling of the solar thermal contribution. But
such an error can't reside in the mismodelling of the solar
reflection/absorption characteristics of the HGA dish because
that was accurately determined prior to launch, and further
refined in the early stages of the mission. So where would it
be?

It's obvious that either Turyshev or Anderson made a fairly
significant error. But it's strange that Anderson is deemed
wrong when a significant number of others also demonstrated the
existence of the anomaly, including yourself (2002)? Why should
this new result override all others when the average result from
all contributors well and truly favors the anomaly's existence?
That's a funny way to do physics.

If Fig.2 from the above link was magnified by at least 20X the
true curve shapes for all the above elements would be more
obvious. Every one of them would follow a uniformly changing
curved path which can be traced right back to the sun. And the
same applies for every other source of acceleration to or from
the sun. The RTG's and on board thermal energy sources will
trace paths according to the rate at which their energies
diminish. The curves will never compare with the Pioneer
anomaly because there's nothing symmetrical about that curve
shape at all.

This image shows the relationship between the Pioneer anomaly and
solar radiation pressure, which can include any mix of residual
radiation from solar heating. Regardless of the mix, the general
curve shape never alters. The purpose of the raised curve is to
give a better comparison with the Pioneer anomaly (blue).

http://members.optusnet.com.au/mskeon/pnersolr.jpg

For John Anderson's analysis, each data point was obviously
generated using a common logic. There's no reason why anything
should change at any stage of the mission. The obvious point of
failure in Turyshev's analysis is between the sun and 20AU. How
can they possibly claim success while the very obvious change in
the "curve" direction between 5.2 and 6.9 AU, **which was
determined by Anderson's invariant logic,** is not addressed!!

The details in this image were generated from info given in
Fig.2 (above link).

http://members.optusnet.com.au/mskeon/watts.jpg

For reasons which should be obvious, the relationship between
solar heating and reflected solar radiation is taken from the
+50 watts line.

Reflected solar radiation contributes 60% of the driving force
away from the sun while solar heating emissions from the sun
facing surfaces contribute 40% of the total in that direction.
Which sets the total absorption rate at 400 watts on the graph
because thermal energy will freely conduct straight through the
HGA dish and into all contacting components of the clutter
attached to it. The reflection/absorption ratio is in fact 43%
reflection to 57% absorption.

If the dish alone was involved, absorbed solar radiation forces
driving to and from the sun would be equal. Reducing the HGA
reflection capability only slightly will affect the 8.74e-10
m/s^2 component of the Pioneer anomaly by almost 100% of the
change. Removing the anomaly would be a breeze.

An absorption rate of 57% of the total solar contribution doesn't
seem right to me either.

The Turyshev team have perhaps managed to squeeze out a positive
result within the error bars, but they certainly haven't managed
to remove the problem. They could only shift it down a little at
best.

The Pioneer anomaly is still a significant problem for current
theory. But an even bigger problem is that I can explain the
anomaly.

Two assumed realities can be compared as shown in this graph.
Gforce calculations for the true reality should trace a straight
line path along the zero line to the sun and the two theories
would compare as shown. The erroneous theory will not pass this
test. **Anomalies will emerge.**

http://members.optusnet.com.au/mskeon/pnerslr3.jpg

Theory 1 scribes the curve path shown while theory 2 follows a
straight line to the sun. Or theory 2 scribes the curved path
while theory 1 follows the straight line to the sun.

For the next graph, theory 1 is my theory and it plots the
straight line to the sun (zero gforce error) while current
theory (theory 2) plots the curved path (gforce errors). The zero
point for theory 2 is shifted downward. But it's actually shifted
upward from the zero point at the curve origin on the sun's
surface. At 1AU the curve passes by at 1.1e-6 m/s^2 below the
true zero point, which is only .00019 of the sun gforce at that
radius.

Current theory sets a new zero point at 6.34e-10 m/s^2 below the
true zero point. The data points for 5.2 and 6.9 AU are carried
upward with the curve.

http://members.optusnet.com.au/mskeon/pnerslr4.jpg

Increasing the mass of the sun will increase the orbital speed
for theory 2. But the increase is insignificant. And there's no
reason at all why it should be noticed.

e.g.
Sun mass = 1.99e30 kg (M)
Orbital speed v is proportional to sqr(G*M/r)
If the sun's mass = 1.99015522e+30 kg (Mx) in order to
maintain a common orbital speed, orbit radius (r2) boils
down to being proportional to Mx/(M/r).

The orbital speed at a 1.5e11 meter radius (r) around a
mass M, is 29747.045 m/sec. The same orbit speed is
generated for Mx at a radius of; Mx/(M/r) = 1.500117e+11
meters. Which is r2-r = 11700000 meters greater than r,
or .44 of a GPS satellite orbit radius.

Nobody would expect a radius increase, so why would anyone bother
looking for one so small?

The problem here is that the orbit cycle time is increased by 41
minutes. The obvious fix is to use the lesser orbit radius of
1.5e11 meters.

Any self consistent closed math loop can be designed with
absolute precision so that every element is perfectly
synchronized according to the chosen theory. But the loop will
be offset from reality if just one element is even slightly
inaccurate. One can't use the absolute precision of the loop as
some kind of proof of the credibility of each element.

i.e.
1.99e30 is far from being a precise figure for the mass of the
sun. The chances of 27 zeros aligning behind the 199 is almost
zero. It could just as well be 1990155220000000000000000000000
kg. It can all be varied to suit any theory. Nothing can be
proven here.

A theory will only fail when anomalies begin to appear in
nature.

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Max Keon