On 09.06.2013 01:05, Koobee Wublee wrote:
On Jun 8, 2:46 pm, "Paul B. Andersen" wrote:
Koobee Wublee wrote:
"Paul B. Andersen" wrote:
According to:
Myles Standish, Jet Propulsion Laboratory (1998)
GR predicts 42.98 +/- 0.04 arc secs per century.
According to:
Clemence, G. M. (1947). "The Relativity Effect in
Planetary Motions".
Reviews of Modern Physics 19 (4): 361–364.
The tug from other planets is 531.63 +/- 0.69
and the observed is 574.10 +/- 0.65 arc secs per century
(both relative to 'stationary space')
So the 'anomaly' is 42.45 +/- 1.13 arc secs per century
GR's prediction is well inside the error bars.
Has Paul ever examine the precession of the equinox more
closely? shrug
http://en.wikipedia.org/wiki/Axial_precession
According to the above link, the exact period is 25,772
years (with no error bar given) which translates to 257.72
centuries.
360 * 60 * 60 / 257.72 = 5,028.7”
As Paul has pointed out, Le Verrier had observed 5,600.0”
(with no error bar given and with unknown digits of
significance but at least 2).
5,600.0” – 5,028.7” – (531.63” +/- 0.69”) = 39.7” +/- 0.7”
It is about 3” less than the fudged prediction of the
Schwarzschild metric. So, it looks like the data is
fudged as well as the prediction. shrug
Never mind the number (38”) that Le Verrier had computed. What is
important is the overall perihelion advance of Mercury which according
to Le Verrier is 5,600” per century because we know how to compute for
the anomaly from known effects of perihelion advance/retardation.
shrug
The 38” is considered as historical interest like what you said, but
the 5,600” is of great importance to modern science. The accuracy of
the latter number cannot be handwaved away since the accuracy of the
said anomaly is thoroughly dependent on the accuracy of this 5,600”.
shrug
And note that the more resent data I gave above were
relative to 'stationary space', that is relative to
a frame of reference that doesn't rotate with the equinoxes.
This is impossible. The earth’s rotational axis is wobbling, and over
time it will show up in every single terrestrial measurement of
astronomical interests. shrug
http://en.wikipedia.org/wiki/Axial_p...ion_(astronomy)
To get to (42.45” +/- 1.13”) of accuracy calculated by Paul Andersen,
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” +/- ?
Why are you so obsessed with Le Verrier's observations?
Clemence made his measurement during the years 1943-1947.
He observed a shift extrapolated to a century: 5599.74" +/- 0.41
It looks like Clemence was just repeating Le Verrier’s observation by
adding an error bar. Did Tom read through Clemence justification for
the claimed accuracy on Le Verrier’s observation? That is assuming we
still trust Tom’s professionalism. shrug
** Precession of the equinox = 5,028.7” +/- ?
Clemence evaluated the precession of the equinox per century
to be: 5025.645" +/- 0.5"
Clemence was using the number 25,787 years as the period of the
precession known at that time during Le Verrier’s time.
That seems to be correct.
However,
modern astronomy has improved the accuracy to 25,772. That will
affect the accuracy in the final anomaly value. shrug
Quite.
As far as I can understand, this paper from 2003 contains
the values now commonly used:
http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf
On the bottom of page 39, the following equation
is given for the precession of the equinox:
p_A = 5028".796195t + 1".1054348t + higher order terms
where t is Julian centuries since J2000.
The rate of the precession is the derivative:
p = 5028".796195 + 2".2108696t + higher order terms.
This will give the period 25,772 years at J2000.
However, Clemence's measurments were done some
0.55 century before J2000, which will give the value:
p = 5027".58.. per century
I am not sure of the precision, it is considered in the paper,
but it isn't easy to see what impact it will have on the final result.
If we use this value together with Clemence's measurements,
we get the anomaly 40".53 +/- ~1"
So GR's prediction is some 1".4 outside of the error bar.
But I am pretty sure the last word isn't said about the precession
of the equinoxes. And there is a comment in the paper above which I
find a bit puzzling:
"The classical "general precession" which mixes the motion of
the equator in the GCRS and the motion of the ecliptic in the
ICRS (and moreover may not be defined in the framework of
General Relativity without fundamental problems) should no
longer be regarded as a primary precession quantity. It is
considered here as a derived quantity,.."
I wonder if there isn't any newer measurements of the precession
of the perihelion of Mercury. I have looked for it, but can't
find any.
Anybody know?
** Tugs from other planets = 531.63” +/- 0.69”
Among them, the precession of the equinox has been the most accurately
measured besides the human history has only spanned a third of the
period of the precession.
The anomaly due to the processor of the
equinox should be constant over time. shrug
Le Verrier was a great astronomer, and there is no doubt about that.
He was able to observe Uranus’s orbital anomaly to deduce the presence
of Neptune from calculations dependent on the positions of both
planets at a given amount of time. That is why he was able to guide
the observatory to look for Neptune at the right place and the right
moment. shrug
If Le Verrier had modeled Neptune as a ring, then there would be no
anomaly in Uranus’s orbit due to that ring outside of Uranus’s orbit.
With that said, if you have modeled all planets into rings, there
would be no orbital anomaly to Mercury. Why? Koobee Wublee senses
another great debate with Paul if Paul wishes to challenge Koobee
Wublee on that one. :-)
Thus, tugs from other solar objects have to be time dependent with
dependencies on the locations (a function of time) of the planets
throughout the course of measurement which is 100 years. This means
the number you quoted (531.63” +/- 0.69”) would vary somewhat
drastically depending for example if all planets are lined up.
Intuitively, the net result should be zero if averaged out over time.
In the next century, odds are against you to measure anything close to
532” from the gravitational effect of other planets. shrug
That 43” is just a myth conjured up by self-styled physicists to sell
their garbage in SR and GR just because Paul Gerber was able to do it
first. shrug
So the shift observed by Clemence is 574.10" +/- 0.65" per century
relative to 'stationary space'.
This number suggests to Koobee Wublee that Clemence was just using Le
Verrier’s observation. So, nothing has changed per our discussion.
shrug
Assuming Le Verrier’s 5,600” and 532” are right on and due to modern
placement on the accuracy of the period to 25,772 years, the final
anomaly number is off by 10% or so which is still not bad, but it
certainly shatters the blind faith among the self-styled physicists,
no? shrug
The anomaly is less that 4% off the GR prediction, surely
not enough to falsify GR.
I would question Clemence's measurements. How precise were
they really? His measurements were done during only four years.
--
Paul
http://www.gethome.no/paulba/