On Jun 11, 3:28 pm, "Paul B. Andersen" wrote:
Koobee Wublee wrote:
"Paul B. Andersen" wrote:

So the 'anomaly' is 42.45 +/- 1.13 arc secs per century

GR's prediction is well inside the error bars.

To get to (42.45” +/- 1.13”) of accuracy calculated by Paul,
the precision of the following three quantities must be
called out to the second digit after the decimal. shrug

** Le Verrier’s observation = 5,600.00” +/- ?

** Precession of the equinox = 5,028.7” +/- ?

** Tugs from other planets = 531.63” +/- 0.69”

Clemence did no measurement. His result was a recycle of
Le Verrier’s observation about 8 decades prior. Le Verrier
was not set out to measure the accuracy down to the last second,
but his motivation was to find a sum of anomaly for him to
justify whether if there is another planet further inside the
orbit of Mercury. He did not find it. Thus, most of astronomers,
and perhaps Le Verrier himself, at that time just attributed the
lack of the extra planet to Le Verrier’s own observation accuracy.
shrug

Clemence realized without pinning down Le Verrier’s observation
with better accuracy, the confirmation of GR cannot be
definitively claimed. The question to ask is what Clemence’s
justification is to claim such extreme accuracy on Le Verrier’s
observation 8 decades prior. shrug

According to this paper:
http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf

The _accumulated_ precession, that is the angle of the
equinoxes with the angle at J2000 as the reference is:

pA = 5028".796195 t + 1".1054348 t^2 + 0".00007964 t^3
+ .. (up to t^5)

Where t is in Julian centuries since J2000.

This is only valid after 2000 and after for a few centuries. shrug

Not at all. The J[2]000 is but a - not entirely arbitrary -
chosen reference point.
[... accuracy good for] 50 years or so.
The equation is valid several centuries in both direction.

According to the paper, it says clearly that:

“The parameter t, used in the above expressions as well as in those
below, is the elapsed time in Julian centuries sinceJ2000...”

There is no indication that the study would cover the past. So, where
did you get the information that the equation is valid for several
centuries in both directions, and how many centuries? shrug

The motivation for the paper is that the authors felt the established
precession value then was not adequate to carry forward. The polar
ice caps experienced their greatest retreat in the past two decades.
Thus, there is no way that the precession would be linear in several
centuries. Besides, Le Verrier called out for 5025” per century then
with somewhat relatively primitive instrumentations. Koobee Wublee
thinks Paul just happens to find an arithmetic sweet spot and tries to
take the advantage of arguing for his beloved GR hypothesis. Of
course, Paul’s argument has no basis. Even the authors of the paper
specifically specified that the information is good from 2000 and on.
shrug

What supports Koobee Wublee’s interpretation of the author’s
intention? Well, the goal of the paper written in 2003 is to replace
the accepted model of 2000 where the formula says:

** PA = 5028”797 t – 1”111 t^2 – 0.000 t^3

If Paul bothers to work out the retroactive precession value, it is
embarrassingly out of the ball park. Thus, it can only mean that the
value is to be carried forward and not backwards. shrug

Clemence has also failed to justify why Le Verrier’s numbers are such
accurate, and Paul so far has failed to argument for Clemence. So, is
Paul disputing that any orbital anomaly is position dependent?
shrug

Thus, the justification to why Le Verrier’s measurement of 5,600” is
actually 5,599”74 +/- 0”5 remains not justified. According to
Clemence’s paper, he said:

“The contributions of the planets are directly proportional to their
several masses, which are NOT ALL KNOWN WITH THE DESIRED ACCURACY.
The quantities denoted by m^-1 are the reciprocals of the adopted
masses, the sun’s mass being taken as unity, and the attached probable
errors give rise to the probable errors associated with the
theoretical contributions to the motions. In the case of Mercury each
planetary contribution (except that of the Mercury itself) is the sum
of three parts: the motion of the perihelion in the plane of the
orbit, the contribution arising from the motion of the node, and the
contribution from the motion of the ecliptic...”

Clemence did not understand that the effect on Mercury’s orbit due to
other planets would depend on where the planets were during the course
of that 100 years. Clemence did not have any justification to place
Le Verrier’s numbers within such accuracy. It is almost impossible to
calculate, but it is easier (but still no trivial task) to simulate.
shrug

Also, all these effects on Mercury’s orbit including GR one if indeed
exists are not linearly additive. Any parameter will affect the final
outcome depending on what other parameters are. You will realize this
if you actually study the differential equations involved. Paul
Gerber simplified the system as linear, and Koobee Wublee thinks he
was wrong. The only way to address this is to do:

** The actual measurement which has more than 100 years of data

** Simulation on the entire system

The difference should be the value reflected by the precession of the
equinox. shrug

Of course, Paul can beat the precession of the equinox to death, but
as long as he has not addressed the others, there is still no
closure. shrug