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

On Mon, 28 Oct 2024 3:56:57 +0000, rhertz wrote:

I understand the efforts that Paul and Prokaryotic have taken to develop
programs that show the orbit of planets under Newton's theory, within
the Sun's frame of reference. Both works are based on initial data of
Keplerian and/or State Vectors as provided by the (almost single) source
of information, which is the site of NASA JPL Horizon.
>
I have to tell that such site provides data with modifications BASED ON
GENERAL RELATIVITY. You can read it in the site "Disclaimer". So, it's
not a pure source of Newtonian information of positions and velocities,
but a site that provide HYBRID INFORMATION (Newton + GR), so it's not a
source to be trusted as one based on Newton-Kepler exclusively.
>
On the other hand, simplifications used since Le Verrier and as of today
are based on Gauss gravitational torus (Le Verrier, Newcomb, Clemence,
etc.), which give almost the same numbers (with some "enhancements"):
575"/cy observed versus 532"/cy derived from theoretical calculations.
And all of them (due to Gauss simplifications) give an unexplained
difference of about 43"/cy, which (allegedly) Einstein verified
theoretically.
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**************
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All the time that I wrote about the HOAX on Mercury mystery, I was based
on the impossibility (analytical and numerical) to SOLVE THE N-BODY
PROBLEM, in order to include EVEN the slightest influence of one planet,
moon, etc., over ANY OTHER PLANET.
>
And that is BECAUSE applying Newton to the 9 planets has to account the
influence of every planet over every each other, which become a problem
of ALMOST INFINITE RECURSION. Starting with the two heavier planets, for
instance, requires computing the MUTUAL EFFECT on both planets from
their barycenter, to LATER apply the gravitational effect of the Sun on
each one, WHICH FORCES A NEW CALCULATION on the influence of one planet
over the other, AND SO ON. Where is the limit of such problem of
recursion?
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Just take as an example the work of Lagrange on the 3-Body problem (Sun,
Earth, Moon). With all the efforts done by Lagrange, its solutions are
not final, because the Lagrangian points ARE  NOT STEADY and have
complicated motions. It's accepted that, in the average, these motions
can be included in orbital calculations for spatial observatories, but
still there is not a conclusive solution. Not to mention IF another
perturbation, like Jupiter, is included.
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So, my posture is that the adoption of the 562"/cy for Mercury's
perihelion advance IS AN APPROXIMATION, which gives the famous 43"/cy.
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BUT, if the N-Body problem is included (instead of Gauss Torus), the
result of the general influence WILL NOT BE of 532"/cy (or 5.32"/year),
but MUCH HIGHER THAN THAT, bringing down the famous 43"/cy (WHICH HAVE
BEEN WRITTEN IN STONE, FOR THE MENTAL HEALTH OF PHYSICISTS).
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Anyone questioning it is immediately labeled as a crank, crackpot, etc.
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But there are voices of reason that question such result, which is one
of the PILLARS of the validity of the general relativity.
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Here are some comments and papers that I searched for this post:

[deleted quotes]

Your main point seems to be that the Gauss Ring approximation is
inaccurate, calling into question the 43"/century discrepancy that was
resolved by GR

The "naive" Gauss ring approximation, which uses circular, coplanar
rings with uniform distribution of mass around the ring, is indeed
rather inaccurate.

My simulation using coplanar rings with equal masses uniformly
distributed around the circumference gave results very close to the
analytic computation of 554 arcsec/century given in
https://farside.ph.utexas.edu/teaching/celestial/Celestial/node44.html

However, my simulation using non-coplanar, elliptic rings with a
weighted distribution of masses gave results in close agreement with
the 532 arcsec/century figure given in
https://farside.ph.utexas.edu/teaching/celestial/Celestial/node45.html

See my attached figure.

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.