On Jun 12, 2:39 am, "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)

“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

http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf

The results are quite consistent at the microarcsecond
level over several centuries.
. . .
The following series with 0.1 uas level of precision matches
the canonical 4-rotation series to sub-microarcsecond accuracy
over 4 centuries


If you look at figs 4-7 it is pretty clear that these four
centuries are from 1800 - 2200.

So, someone just drew a straight line from Le Verrier’s number with
today’s number. It does not say anything about the accuracy of Le
Verrier’s calculation. shrug

Bottom line:
The rate of precession of the equinoxes at 1850 is
according to this paper 5025.48 arcsecs per century.

What is important is not the rate of the precession but rather the
phase difference between 1750 and 1850. In the meantime, 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

The true bottom line is that there has been no such observation on the
anomaly to Mercury’s orbit since 150 years ago. The reason is most
likely that the measurement just does not agree with the Schwarzschild
metric. shrug