Re: Weakness in the results of the three tests of GR shown in rhe lasr century,.

On Mon, 28 Oct 2024 16:34:48 +0000, rhertz wrote:

On Mon, 28 Oct 2024 13:19:34 +0000, ProkaryoticCaspaseHomolog wrote:
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On Mon, 28 Oct 2024 8:13:09 +0000, ProkaryoticCaspaseHomolog wrote:
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I would contend that Le Verrier Newcomb etc., confronted with a
discrepancy between theoretical and observed precessions, knew
better than to employ a naive Gauss ring computation.

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Note: In my "naive" Gauss ring simulation using circular, uniformly
weighted rings, the line representing accumulated precession over
time is completely straight. However, in a computation using
eccentric, weighted rings, the line is slightly curved. Over the
course of thousands of years, as Mercury's line of apsides works
its way around, the rate of precession estimated using a Gauss ring
approximation with eccentric, weighted rings will vary.

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What do you think about this approximation? It's a rather long article:
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Newtonian Precession of Mercury’s Perihelion
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https://www.mathpages.com/home/kmath280/kmath280.htm

"Kevin Brown" (MathPages https://tinyurl.com/2xuyj2j4) and
Prof Fitzpatrick (UT Austin https://tinyurl.com/yck7thzj) provide
slightly discrepant calculations for what a "naive" Gauss ring
simulation would predict assuming circular coplanar rings with uniform
mass distribution. Although my "naive" ring simulation agrees more
closely with Fitzpatrick's numbers than Brown's numbers, I am hesitant
to say that Fitzpatrick's numbers are better. Since my code has never
been peer-reviewed, there is always the possibly that it is my own
simulation that is at fault.
On the other hand, Price and Rush used a ring approximation to compute
531.9 arcsec/century, in amazingly close agreement with the best
current measured values. (Brown discounts this agreement as being the
spurious result of them committing two errors in their calculation
that happen to cancel each other.) https://tinyurl.com/4hzf3u6r
An important fact noted by Fitzpatrick, is that Gauss himself never
used a naive circular ring calculation, but included orbital
eccentricities, non-uniform angular velocities etc. in his calculation.
Since Gauss never used a naive circular ring calculation, it is fair
to assume that LeVerrier never did, either. This would explain why
LeVerrier's theoretical numbers are so remarkably close to the actual
values measured using current high precision technologies.
See Park et al. 2017
https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2