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From: hertz778@gmail.com (rhertz)
Newsgroups: sci.physics.relativity
Subject: Re: Weakness in the results of the three tests of GR shown in rhe lasr
 century,.
Date: Mon, 28 Oct 2024 03:56:57 +0000
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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.

**************

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?

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.

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.

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).

Anyone questioning it is immediately labeled as a crank, crackpot, etc.

But there are voices of reason that question such result, which is one
of the PILLARS of the validity of the general relativity.

Here are some comments and papers that I searched for this post:

----------------------------
The N-body problem is considered unsolved, as of today. There are
solutions to special cases of the problem, such as when there are only
two bodies.
----------------------------
The many multiple (n-body) interactions have historically made any exact
solution intractable.
----------------------------
Why is an N-body system so unpredictable?
It remains an article of faith that such a statistical validity holds
for the Newtonian N-body problem (Heggie 1991). Chaos, however, leads to
unpredictability due to temporal discretization, round-off, and
uncertainty in the initial realization (Miller 1964).
-----------------------------
Why is the N-body problem unsolvable?
The bad news is that there are certain aspects of the n-body problem
which make it unlikely we could ever put a solution on a t-shirt:
collisions that are singularities, resonances when frequencies of
multiple bodies lead to instabilities, and the lack of enough constants
of motion to lead to simple answers.
------------------------------
The n-body problem, which involves predicting the individual motions of
a group of celestial bodies interacting with each other gravitationally,
is a complex issue in physics and mathematics. While the two-body
problem can be solved analytically, the n-body problem (for three or
more bodies) is generally not solvable in a straightforward analytical
way due to its chaotic nature.

Current Understanding and Approaches:

    Numerical Methods: For practical purposes, scientists and
astronomers typically use numerical simulations to approximate solutions
to the n-body problem. These methods can provide highly accurate
predictions over limited time frames.
    Special Cases: Certain special cases of the n-body problem can be
solved analytically. For example, the restricted three-body problem,
where one body has negligible mass, has known solutions.
    Chaos Theory: The n-body problem is sensitive to initial conditions,
meaning small changes can lead to vastly different outcomes. This
chaotic behavior complicates long-term predictions.
    Advancements in Computing: As computational power increases, more
complex simulations can be run, allowing for better approximations of
the n-body problem in various contexts (e.g., astrophysics, molecular
dynamics).
-----------------------------------
The N-body problem

https://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=4780668&fileOId=4780676

Abstract
The N-body problem has been studied for many centuries and is still of
interest in contemporary science. A lot of effort has gone into solving
this problem but it’s unlikely that a general solution will be found
with the mathematical tools we have today. We review some of the
progress that has been made over the centuries in solving it. We take a
look at the first integrals, existence of solutions and where
singularities can occur. We solve the two body problem and take
a look at the special case of central configurations. We find all the
possible three-body central configurations, which are known as Euler’s
and Lagrange’s solutions. When analytic solutions are missing it is
natural to use numerical methods.
-----------------------------------