On 10.06.2013 05:30, Koobee Wublee wrote:
> On Jun 9, 1:45 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>
>>
>>>
http://en.wikipedia.org/wiki/Axial_precession_(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� +/- ?
>>
>>> ** Precession of the equinox = 5,028.7� +/- ?
>>
>>> Clemence was using the number 25,787 years as the period of the
>>> precession known at that time during Le Verrier�s time. However,
>>> modern astronomy has improved the accuracy to 25,772. That will
>>> affect the accuracy in the final anomaly value. <shrug>
>>
>> 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"
>
> With 38�, 39�, or 40� per 100 years, Le Verrier had weak justification
> to search for another planet. The anomaly is not as obvious as
> Uranus�s case. <shrug>
>
>> So GR's prediction is some 1".4 outside of the error bar.
>>
>> I would question Clemence's measurements. How precise were
>> they really? His measurements were done during only four years.
I was very wrong about the four years. See below.
> Clemence did no measurement. His result was a recycle of Le Verrier�s
> observation about 8 decades prior.
Not quite true.
Here is Clemence's paper:
http://www.gethome.no/paulba/pdf/Clemence.pdf
He says that he has used about 10,000 meridian observations
of Mercury from 1762 to 1937, and 17 transit observations
from 1799 to 1940. So Le Verrier's observations are included,
but he also used just about all available observations at the time,
which includes almost a century worth of observations after Le Verrier.
This is interesting, because the question is what the rate of
the precession of the equinoxes were at the time the measurements
were done. If we use 1850 as the middle year, the equation from:
http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf
p = 5028".796195 + 2".2108696t + ..
yields: p = 5025".48 per century at J1850, which is pretty
close to the number used by Clemence for the same year!
So to sum it up:
Observed precession of the perihelion of Mercury: 5599.74+/-0.5
Modern estimate of precession of equinoxes at J1850: 5025.48
Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5
The tug from other planets is 531.63 +/- 0.69
Anomaly = 42.63 +/- ~1.2
Conclusion:
GR's prediction for the 'anomaly': 42.98 +/- 0.04
is well inside the error bar.
> 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>
>
>> 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,.."
>
> During glacial periods with more ice tapped in the polar regions, the
> precession of the equinox might be slightly more pronounced as it is
> today, but for the large part, the precession of the equinox should be
> very a constant given a span of several hundred years. With global
> warming in the past few decades where ice from the polar regions are
> melting at an unprecedented level, the precession value might be a
> little bit higher during Le Verrier�s time. However, Koobee Wublee
> does not have the authority to claim 25787 years as did by Le
> Verrier. <shrug>
>
>>> ** 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>
>>
>>> 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>
>>
>> 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.
>
> With better computer simulation, the tugs from other planets should be
> a piece of cake to pin down, and measuring the overall Mercury�s
> perihelion since Le Verrier�s time should also be a piece of cake.
> The numbers would, of course, be drastically different from Le
> Verrier�s. Koobee Wublee thinks it had been done many timed before,
> but each time the net result showed great disappoint to the self-
> styled physicists. Le Verrier�s 140-year-old observation
> embarrassingly seems to be the best and only support to GR regarding
> Mercury�s orbital anomaly. Sad for self-styled physicists but very
> close to be true. Koobee Wublee would certainly like to know what the
> real value of this anomaly is. It does not look like it is anywhere
> close to +43� per 100 years from the lack of reports by the self-
> styled physicists. Koobee Wublee suspects it is more like null.
> <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>
>>
>> The anomaly is less that 4% off the GR prediction, surely
>> not enough to falsify GR.
>
> Clemence tried to justify the validity of GR by placing such precision
> on Le Verrier�s observation but instead shot himself in the foot where
> he fumbled with the precession of the equinox. The accuracy remains
> to be outside of GR�s prediction, and GR�s such prediction is very
> much �quantized� which leaves no room to negotiate with that extra 10%
> difference. Besides the Schwarzschild metric predicts only +20� to
> +30� (1 significant digit) per 100 years. The self-styled physicists
> are not interested to do anything for science but to prolong their
> elite status quo. Another example of fiasco is the GPS. Remember?
> <shrug>
>
> With that said, it is Adventure Time with Finn and Jake. Is Paul
> ready for more adventures in differential equations where Koobee
> Wublee has buried Paul every single time on simpler mathematics? :-)
> Is Paul beginning to wake up? <shrug>
>
--
Paul
http://www.gethome.no/paulba/