The creation of a myth: Mercury and Newton vs Gerber-Einstein.

[Richard Hertz]

Myth: a widely held but false belief or idea.

Today I was interested in knowing how did Einstein derived his "proof" about
the Mercury's perihelion phenomenon of the missed 45 arcsec/century, not
explained by Newton's Theory of Gravitation. Discovered by the French
Astronomer Urbain Le Verrier in 1859, after 16 years of research with data
recollected from 1697 to 1848 along all Europe, it puzzled astronomers and
physicists as well until 1898, when Gerber introduced the idea of delayed
gravitational potentials.

17 years later, Einstein did use his incomplete GR idea (modified 1914
Entworf) with covariance in the mathematical expression of
gravitational field due to Hilbert's solution sent to him 2 days before, and
presented it to the Prussian Academy of Sciences in Berlin, on 18 November
1915, one more time that year.

This presentation was published on 25 November 1915 in Koniglich Preußische Akademie der Wissenschaften and was buried into history.
Only many decades after, the publication was translated to English and
didn't gained any relevant interest.

On Nov 20 1915, Hilbert lectured to the Göttingen Academy about the
correct mathematical expression of the gravitational field equations, which
he had sent to Einstein only 4 days before. He, naively, didn't think that
Einstein was to move so fast (2 days) to present his forgotten paper to the
Prussian Academy (using 1914 calculations done with Michele Besso). And,
probably, it never crossed his mind that the fast-moving Einstein was going
to present HIS VERSION of Hilbert's solution only 9 days after he received
a copy of his work.

Einstein did his last presentation to the Prussian Academy on Nov 25, 1915
and got his paper published by Dec 2, 1915. A priority dispute arose between
Einstein and Hilbert, until the last withdraw his publication one month later.
After all, Hilbert was the top living mathematician in the world by then, not a
physicist, so for him it was not a big deal as it was for Einstein.

Now, about the birth of a myth on the explanation of Mercury's
perihelion and light deflection, born on the forgotten paper published
by 25 November 1915. The many flaws contained in the paper were
buried by Einstein in 1916 and later years, so the narrative was perfected
with the use of the Hilbert equations, which Einstein plagiarized.

Even the famous 43" that plagues the web, came from Einstein's paper
and not from historic observations from Le Verrier and others (45") and
this was admitted by Einstein himself on this forgotten paper.
It's worth to read it, to observe how humble and cautious was Einstein
with this paper, because he knew that it wasn't based on the correct
GFE that Hilbert sent to him, but he didn't had time to use. Instead, he
used 1914 Entwurf II data, already calculated by Besso and him. This
fast action of Einstein, after receiving Hilbert's letter days before,
generated an ironic written comment from Hilbert about his speed to
calculate (he knew Einstein had used data from the year before).

Einstein presentation and paper about Mercury and light deflection was
based on the incorrect Entwurf II 1914 theory, co-authored with Besso and
Grossman, and had several limitations:

1) It used a point-like mass (the Sun) in an universe void of matter and energy.
2) The time component was gone, and so his space-time.
3) It was based on gross 1st. and 2nd. order approximation, because
he wasn't able to find an exact analytical solution. Schwarzchild did,
because he was a mathematical prodigy as well as a cosmologist,
and he was following Einstein work. The problem is that he didn't
get the final Hilbert's solution and worked on the modified Entwurf II.
It only took a month for him to find an exact analytical solution, which
was modified in 1917 by Hilbert (the widely known metric), who
honored the deceased Schwarzchild naming his solution after him.
4) It contained several "hidden" steps in the approximation, which made
Schwarzchild to complain to him by Dec. 1915, prior his own
publication in Jan. 1916.

After the famous 1919 Eddington's expedition to photograph the eclipse,
Einstein jump to an status of worldwide celebrity, due to the press
coverage at US and several european countries, that celebrated the fall
of the great Newton with phrases like: "Newton dethroned", etc.

Well, that was highly exaggerated, as there were many counter-proofs
that proved that both theories provided almost the same result, when
properly used.

This link contains one of the MOST IMPRESSIVE PAPERS I've found:

Solution to the advance of the perihelion of Mercury
in Newtonian theory
Christian Corda
June 15, 2020

https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf

or this one, where co-gravity means Newton at close distances, which
yet doesn't openly question GR validity but support Newton:

Advance of Mercury Perihelion Explained by Cogravity

https://arxiv.org/ftp/gr-qc/papers/0005/0005040.pdf

And, finally, this PARTICULAR link:

Einstein’s Paper: “Explanation of the Perihelion Motion of Mercury
from General Relativity Theory”
Anatoli Andrei Vankov

https://www.researchgate.net/publication/228923053_Einstein%27s_PaperExplanation_of_the_Perihelion_Motion_of_Mercury_from_General_Relativity_Theory

This paper analyzes the English translation of the publication of Einstein's
publication about Mercury's perihelion and deflection of light, as well as
the letter Schwarzschild sent to him by early Dec. 1915. Both documents
are also in their original german. The link also contains analysis by the
author, who cast some doubts about the correctness of the mathematical
development of the approximations.

Maybe I'll post additional information later. I'm tired of this by now.

But, the first paper is an absolute proof of the exaggeration about claims
that Einstein's GR topped Newton's one. Not for nothing, it's the theory
used for space missions and explorations, Lagrangian sites included.

[Dono.]

On Tuesday, September 7, 2021 at 10:14:51 PM UTC-7, Richard Hertz frothed at the mouth:
> nothing of any value<

[Richard Hertz]

Excerpts from:

Solution to the advance of the perihelion of Mercury in Newtonian theory
Christian Corda
June 15, 2020

https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf

---------------------------------------------------------------------------------------------------------------------------------------------------

This discrepancy by 38" arcseconds per tropical century, which has been corrected to 43" by the
Canadian-American astronomer Simon Newcomb in 1882 seemed till now impossible to be accounted
through Newton's theory. Various ad hoc and unsuccessful solutions have been proposed, but such
solutions introduced more problems instead.
.............
Recent analyses due to the MESSENGER data plus the Cassini mission gave a value of about 42.98"
to the general relativistic contribution to the precession of perihelion for Mercury per tropical century
(Park et.al., 2017).
---------------------------------------------------------------------------------------------------------------------------------------------------

5 Conclusion remarks
It has been shown through THREE different approaches that, contrary to a longstanding
conviction longer than 150 years, the orbit of Mercury behaves as required by Newton's
equations with a very high precision if one correctly analyses the situation in the framework
of the two-body problem WITHOUT NEGLECTING THE the MASS of Mercury.

The results obtained are remarkable. The real value predicted by Newtonian theory concerning
the advance of the perihelion of Mercury is of 44.39" per tropical century that well approximates
the value of about 42.98" per tropical century of general relativity and the well known observational
value of 43" per tropical century.

Thus, the real difference between Einstein's and Newton's previsions concerning the advance of
the perihelion of Mercury is not of about 43" as astronomers and researchers were thinking for
more than 150 years.

Instead, such difference is only of 1.41" per tropical century. The physical interpretation of this
remarkable result is that it is Mercury's back reaction that generates the advance of the
perihelion of Mercury in Newtonian framework.

General relativity remains more precise than Newtonian theory regarding the precession of Mercury's
perihelion, but the difference is very little.

Another important point is that general relativity achieves a very precise value for the advance of the
perihelion of Mercury considering the planet as being a test mass immersed in the general relativistic
gravitational field of the Sun. NOTE: A TEST PARTICLE WITH ZERO MASS (1-BODY PROBLEM).

Instead, in order to gain power of predictability, Newtonian theory must consider Mercury's mass as being
not negligible. Thus, surely the results in this paper are not against the great power of predictability of Einstein's
theory.

They instead endorse the issue that Newtonian theory is more powerful than researchers and gastronomes
were thinking till now!
---------------------------------------------------------------------------------------------------------------------------------------------------

MY CONCLUSIONS:

By incorporating the mass of Mercury and working with Newton's theory on a 2-Body problem,
theoretical calculations give a value of 44.39" per tropical century.

Einstein's GR gives, for a 1-Body problem (Mercury as a point-test particle with zero mass) gives
42.98" per tropical century (as measured by space sondes like Cassini).

The difference of 1.41" between Newton GT and Einstein GR represent a newtonian value ONLY 3.28% higher
than modern measurements with space sondes.

And THIS SMALL DIFFERENCE doesn't account for the influence of the rest of the planets, nor Sun spin or oblation
and neither any theory concerning small fluctuations in the shape of the Sun (changes the center of mass) or any
influence of the solar wind (particles) or solar radiation pressure (quite high on Mercury, compared with Earth).

[Paul B. Andersen]

Den 08.09.2021 07:14, skrev Richard Hertz:
>
> This link contains one of the MOST IMPRESSIVE PAPERS I've found:
>
> Solution to the advance of the perihelion of Mercury
> in Newtonian theory
> Christian Corda
> June 15, 2020
>
> https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf

So let's see how impressive the paper is.

Chapter 2 Approximation of circular orbit



He starts with the equation for the period of a test particle
in orbit around a mass M.

T₀ = 2π√(r₀³/GM) See equation (5)

The period of a mass m in orbit around a mass M is:

T = 2π√(r₀³/G(m+M)) = 2π√(r₀³/GM)⋅(1/√(1+m/M))

T = T₀⋅(1/√(1+m/M)), see equation (17)

T₀ = T⋅√(1+m/M)

So Corda can conclude:

Hence, the angle that Mercury sweeps during the period T0 is:

φ = ωT₀ = 2π⋅√(1+m/M) ≈ 2π(1+m/2M) see equation (19)

Δϕ ≈ π⋅m/M see equation (19)

What does this mean?
It means that if a test particle and a planet
with mass m are orbiting in the same orbit,
then the planet will move faster and move
an extra angle Δϕ ≈ π⋅m/M while the test particle
makes one orbit.

What has this to do with the perihelion advance
of the planet?
Obviously nothing whatsoever, the idea is ludicrous.

But let us compare the angle Δϕ with the perihelion
advance predicted by GR, marked GR: below.

Mercury:
Δϕ = = 5.2154E-7 rad/orbit GR: 5.0185E-7 rad/orbit

Venus:
Δϕ = 7.6902E-6 rad/orbit GR: 0.25711E-6 rad/orbit

Earth:
Δϕ = 9.5518E-6 rad/orbit GR: 0.18594E-6 rad/orbit

Mars:
Δϕ = 1.0138E-6 rad/orbit GR: 0.12308E-6 rad/orbit

Jupiter:
Δϕ = 0.29996E-2 rad/orbit GR: 0.035810E-6 rad/orbit


We see that Mercury happens to be in the ballpark.
But all the other planets are more than a decade off.
Mercury is only accidentally in the ballpark.

Chapter 3 and 4 give the same results.

This paper is obviously nonsense.



--
Paul

https://paulba.no/

[Dono.]

On Wednesday, September 8, 2021 at 12:25:46 PM UTC-7, Paul B. Andersen wrote:
>
> This paper is obviously nonsense.

This is why his paper has been sitting in the crank repository vixra, no peer reviewed journal will pick it up.

[Richard Hertz]

What is missing in answers to the OP is "to read correctly" the topic of this thread:

It says, clearly, Gerber-Einstein. Both formulae are exactly the same, under different name of parameters.

And the Einstein's 2nd. order approximation was VALIDATED by Schwarzschild 1 month after Einstein
presented his "final" GR theory to the Prussian Academy of Science.

But Schwarzschild derivation was wrong, because was based on the correction of Entwurf II, not in the
final Hilbert's solution for gravitational field equation.

Hilbert and Droste, in 1917, corrected Schwarzschild derivation and republished it, naming as the
Schwarzschild metric, which is the one being know today.

Then, how come Gerber, Einstein and Schwarzschild arrived to the same solution for Mercury's perihelion
IF the applied theory was incorrect?

Why there is not a solution based on Hilbert-Droste metric for that phenomenon? Is that Mercury's behavior
has been settled to verify Einstein's presentation to the PAS and the publication was buried by historians to
cover-up Einstein's mistakes claiming his "finding/fudging"?

Einstein never went back to the problem of Mercury's behavior, nor he credited Schwarzschild or Hilbert. Why?

[Dono.]

On Wednesday, September 8, 2021 at 2:01:50 PM UTC-7, Richard Hertz wrote:

> It says, clearly, Gerber-Einstein. Both formulae are exactly the same, under different name of parameters.

There is no such thing as "Gerber-Einstein" odious kapo. Give sucking nazi cock a rest.

[Richard Hertz]

Historic document:

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Letter from K Schwarzschild to A Einstein dated 22 December 1915
(The letter is presented in English owing to Professor Roger A. Rydin)

Honored Mr. Einstein,

In order to be able to verify your gravitational theory, I have brought myself nearer to your work on the perihelion of
Mercury, and occupied myself with the problem solved with the First Approximation. Thereby, I found myself in A STATE
OF GREAT CONFUSION. I found for the first approximation of the coefficient g_uv OTHER than your solution the following two:

gᵨᵪ = −β.xᵨ.xᵪ /r⁵ + δᵨᵪ. (β/3r³) ; g₄₄ = 1

As follows, it had beside your α yet a second term, and the problem WAS PHYSICALLY UNDETERMINED.

From this I made at once by good luck a search for a full solution. A not too difficult calculation gave the following result:

It gave only a line element, which fulfills your conditions 1) to 4), as well as field and determinant equations,
and at the null point and only in the null point is singular.

If:

x₁ = r cos φ cos θ, x₂ = r sin φ cos θ, x₃ = r sin θ

R = (r³ + α³)^1/3

then the line element becomes:

ds² = (1 − γ/R) dt² − dR²/(1 − γ/R) − R².(dθ² + sin² θ.dφ²)

R, θ, φ are not “allowed” coordinates, with which one must build the field equations, because they
do not have the determinant = 1, however the line element expresses itself as the best.

The equation of the orbit remains exactly as you obtained in the first approximation (11), only one must
understand for x not 1/r, but 1/R, which is a difference of the order of 10^−12, so it has practically the same
absolute validity.

The difficulty with the two arbitrary constants α and β, which the First Approximation gave, resolves itself
thereby, that β must have a determined value of the order of α⁴ , so as α is given, so will the solution be
divergent by continuation of the approximation.

It is after all the clear meaning of your problem in the best order.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

This is the first time that Schwarzschild's metric appeared in a document, with α and γ as constants of integration.

Next time, the metric appeared in the published paper:

On the Gravitational Field of a Point-Mass, According to Einstein’s Theory
Karl Schwarzschild
Submitted on January 13, 1916

The paper was published on Feb. 1916, so he could read it before his death. It contains a final
form for his line element:

ds² = (1 − α/R) dt² − dR²/(1 − α/R) − R².(dθ² + sin² θ.dφ²)

R = (r³ + α³)^1/3

"This formula contains the sole constant of integration α, which is dependent on the numerical value
of the mass located at the origin of the coordinates."

Hilbert and Droste, in 1917, corrected Schwarzschild derivation and republished it, naming it after Schwarzschild.

Quoting Salvatore Antoci: DAVID HILBERT AND THE ORIGIN OF THE “SCHWARZSCHILD SOLUTION”
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
"It is reminded that Hilbert’s manifold suffers from two defects, that are absent in Schwarzschild’s manifold.
It does not admit a consistent drawing of the arrow of time, and it allows for an invariant, local, intrinsic
singularity in its interior."

ds² = (1 − 2m/r) dt² − dr²/(1 − 2m/r) − r².(dθ² + sin² θ.dφ²), with 0 < r < ∞

Salvatore Antoci warns: "the singularity that the metric components in the famous “Schwarzschild” expression
for the interval ds² exhibit, in “Schwarzschild” coordinates, at r = 2m. The reader is always ensured that this is a
spurious singularity, devoid of local physical meaning, due only to the bad choice of the coordinate system done
by Schwarzschild.

"Hilbert, with his revisitation [9] of the static, spherically symmetric problem, published in 1917, that definitely
imposed the ostracism on the original Schwarzschild solution. He did so by attaching the name of Schwarzschild
to the metric and the manifold defined by (1) and (2), that were instead the outcome of his own work, while
dismissing in a footnote as “not advisable” the inequivalent, pondered choice of the manifold done by Schwarzschild."
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

And, doing so (probably mocking at Einstein), Hilbert created the basis for the "Black Hole" theories that plagues
the modern cosmology.

Who would think that? Black Holes are derived from a "macabre joke" of Hilbert over Einstein?

Here is the Antoci paper (and is not the original source I found years ago. I find this today):

https://arxiv.org/pdf/physics/0310104.pdf

[Dono.]

On Wednesday, September 8, 2021 at 5:09:18 PM UTC-7, Richard Hertz wrote:
> Hilbert created the basis for the "Black Hole" theories that plagues
> the modern cosmology.
>

Dick,

1. Hilbert did not create the basis of the black hole theories, someone else did. Google to learn who.
2. Black holes have nothing to do with the singularity in the Schwarzschild solution
3. The singularity in the Schwarzschild solution has no physical meaning, it is easily avoided by a suitable change of coordinates.
4. You are a cretin. You were born this way, your only consolation is that you will die this way

[Richard Hertz]

There is a second historic document from Schwarzschild, which received even less attention
than his publication on January 1916, that complement the development of his metric for a
line element done in the previous paper.

In this 2nd. paper, Schwarzschild anticipates by almost 40 years the earlier development of
the theories of black holes with his critical radius and strange behaviors for light after
crossing his limit, which he developed in the paper.

At this paper, later modified (incorrectly) by Hilbert, Schwarzschild formulates the physical condition
of degeneration of the gravitational field, using G = 1 and c = 1, to simplify the analysis.

On the Gravitational Field of a Sphere of Incompressible Liquid, According to Einstein’s Theory
Karl Schwarzschild
Submitted on February 24, 1916

In this paper, Schwarzschild analyze the escape velocity from within the mass and derives the
limit at which such behavior can be observed from outside (the famous Schwarzschild radius).

Excerpt 1:
---------------------------------------------------------------------------------------------------------------------------------------------------
§1. As the next step of my study concerning Einstein’s theory of gravitation, I calculated the
gravitational field of a homogeneous sphere of a finite radius, consisting of incompressible fluid.

This clarification, “consisting of incompressible fluid”, is necessary to be added, due to the fact that
gravitation, in the framework of the relativistic theory, depends on not only the quantity of the matter,
but also on its energy.

For instance, a solid body having a specific state of internal stress would produce a gravitation other
than that of a liquid.

This calculation is a direct continuation of my presentation concerning the gravitational field of a
point-mass (see Sitzungsberichte, 1916, S. 189∗), to which I will refer here in short†.

---------------------------------------------------------------------------------------------------------------------------------------------------

Excerpt 2 (at the end of the paper):

---------------------------------------------------------------------------------------------------------------------------------------------------
For an external observer, as follows from (40), a sphere of the gravitational mass α/2k² cannot have
a radius measured from outside whose numerical value is less than

Pa = α

Concerning a sphere of incompressible liquid such a border should be 9/8 α.

(In the case of the Sun it should be 3 km, while for a mass of 1 gramme it should be 1.5×10−28 cm.)

---------------------------------------------------------------------------------------------------------------------------------------------------

Here, Schwarzschild states that his radius for an stellar spherical mass, non compressible, is:

M = α/2k² --------------------> α = 2k²M = Rs (in natural units)

I quote from Chris Impey's book on black holes:

"Schwarzschild realized the escape velocity could also reach the speed of light if a star like the Sun
collapsed to a high density. His solution had two striking features. The first was that gravity
collapses the object to a state of infinite mass density called a singularity. The second was the
prediction of a gravitational boundary that would forever trap what was inside. This is the event horizon.
A singularity and an event horizon are the two essential ingredients of a black hole."

In his modern form (in MKS and after Hilbert's correction), the Schwarzschild radius rs is:

rs = 2.G.M/c²

and 105 years after, it gives for the Sun an rs = 2.9541 Km (incredible precision from a true genius like Schwarzschild).
And he did all this while fighting on the russian front at WWI, from where he was discharged in March and died in May.

How can one compare this great mind, who wrote the first paper on cosmology in 1900 (age 27) and published two
two papers on binary star orbits when he was sixteen, in 1889. A true polymath.

With few exceptions, like Oppenheimer in 1939, the Schwarzschild singularities (and black holes) went into oblivion
well after WWII, when

In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, and slowly opened a door for
the theory of black holes to expand and gain interest, and in 12 years had gained a lot of traction (Hawkings, etc.).

The NYT, when John Wheeler died, published an article crediting him with the name "black hole", while at a conference
in New York in 1967, hit on the name “black hole” to dramatize this dire possibility for a star and for physics.

But science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early
1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people
entered but never left alive.

At any case, Schwarzschild is "to blame" (along with Hilbert) for the hysteria around black holes in the last 40
years, which is gaining momentum.

[Maciej Wozniak]

5.The clocks of GPS keep indicating t'=t, just like all
serious clocks always did.

[JanPB]

On Wednesday, September 8, 2021 at 5:09:18 PM UTC-7, Richard Hertz wrote:

> Historic document:
>
> ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> Letter from K Schwarzschild to A Einstein dated 22 December 1915
> (The letter is presented in English owing to Professor Roger A. Rydin)

Also in the original German if anyone is interested:
https://drive.google.com/file/d/0B2N1X7SgQnLRS2pQa0diM2lfbzA
(also easier to see the formulas than in the semi-ASCII here)

> Honored Mr. Einstein,
>
> In order to be able to verify your gravitational theory, I have brought myself nearer to your work on the perihelion of
> Mercury, and occupied myself with the problem solved with the First Approximation. Thereby, I found myself in A STATE
> OF GREAT CONFUSION. I found for the first approximation of the coefficient g_uv OTHER than your solution the following two:
>
> gᵨᵪ = −β.xᵨ.xᵪ /r⁵ + δᵨᵪ. (β/3r³) ; g₄₄ = 1
>
> As follows, it had beside your α yet a second term, and the problem WAS PHYSICALLY UNDETERMINED.
>
> From this I made at once by good luck a search for a full solution. A not too difficult calculation gave the following result:
>
> It gave only a line element, which fulfills your conditions 1) to 4), as well as field and determinant equations,
> and at the null point and only in the null point is singular.
>
> If:
>
> x₁ = r cos φ cos θ, x₂ = r sin φ cos θ, x₃ = r sin θ
>
> R = (r³ + α³)^1/3
>
> then the line element becomes:
>
> ds² = (1 − γ/R) dt² − dR²/(1 − γ/R) − R².(dθ² + sin² θ.dφ²)
>
> R, θ, φ are not “allowed” coordinates, with which one must build the field equations, because they
> do not have the determinant = 1, however the line element expresses itself as the best.
>
> The equation of the orbit remains exactly as you obtained in the first approximation (11), only one must
> understand for x not 1/r, but 1/R, which is a difference of the order of 10^−12, so it has practically the same
> absolute validity.
>
> The difficulty with the two arbitrary constants α and β, which the First Approximation gave, resolves itself
> thereby, that β must have a determined value of the order of α⁴ ,

Here Schwarzschild misspoke, he meant alpha^3.

> so as α is given, so will the solution be
> divergent by continuation of the approximation.

This entire English translation is bizarrely awkward. Who did it? My German is in a rather

inactive state but I think the sentence above says:

"The difficulty with the two arbitrary constants α and β, which the First Approximation gave, resolves itself

because β must have a determined value of the order of α⁴ [Schwarzschild's accidental mistake], with α as
given, otherwise the solution [obtained] by continuation of the approximation would be divergent."

> It is after all the clear meaning of your problem in the best order.

I think it says: "The uniqueness of your problem [meaning: of the solution] is also in good order."

He basically states that his derivation demonstrates the uniqueness of the solution (which
is something many cranks here deny BTW) since one is inexorably led to this formula from
the stated assumptions (spherical symmetry and a static metric). He states it again in his
paper.

> ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
>
> This is the first time that Schwarzschild's metric appeared in a document, with α and γ as constants of integration.
>
> Next time, the metric appeared in the published paper:
>
> On the Gravitational Field of a Point-Mass, According to Einstein’s Theory
> Karl Schwarzschild
> Submitted on January 13, 1916
>
> The paper was published on Feb. 1916, so he could read it before his death. It contains a final
> form for his line element:
>
> ds² = (1 − α/R) dt² − dR²/(1 − α/R) − R².(dθ² + sin² θ.dφ²)
>
> R = (r³ + α³)^1/3

This is the same formula as in his letter from December.

> "This formula contains the sole constant of integration α, which is dependent on the numerical value
> of the mass located at the origin of the coordinates."

It does depend on the mass but it's not located at the origin of the coordinates. This has not been
correctly understood until some time later, as "absolute calculus" (what we call "differential
geometry" today) was a very new thing at the time.

> Hilbert and Droste, in 1917, corrected Schwarzschild derivation and republished it, naming it after Schwarzschild.

There is nothing to correct in Schwarzschild's derivation except his incorrect assumption that
a singularity in tensor coefficients is necessarily due to a genuine physical singularity. This is
not true, a tensor coefficient singularity can come either: (1) from a genuine tensor or manifold
singularity, or (2) from the coordinates in which the tensor is written.

For example, the following metric in the xy-plane:

ds^2 = dx^2/x^4 + dy^2

...is singular at the entire y-axis (x = 0) and yet it describes the standard Euclidean metric in
the plane. The singular coefficient (1/x^4) appears here due to the poor coordinate choice
(using 1/x as the coordinate instead of the usual Cartesian x, and of course 1/x misbehaves at x = 0).

So ideally, when Schwarzschild saw the singular coefficients, he should have doublechecked
whether it was not just the coordinate choice that created the problem. To top it off, in his
case there was this seemingly low-hanging fruit available: the "obvious" (but FALSE!)
assumption that "r = 0" must represent the origin. This is what gave him beta = alpha^3
which is the correct result by the wrong reasoning. It happens sometimes.

Basically what happened was that he obtained the correct tensor whose singularity resided
at his coordinate x1 = -alpha^3/3 (i.e., r = -alpha), NOT at r = 0! The singularity at r = 0 turns
out to be a coordinate singularity and can be removed by a coordinate change analogous
to what I shown above with the Euclidean metric in the xy-plane (in that case one just
replaces x by 1/X and obtains: ds^2 = dX^2 + dy^2, which is now manifestly Euclidean).

It was just a particularly PERVERSE collusion of the circumstances that a coordinate
singularity of tensor coefficients appeared to be "obviously" due to the singularity
of the "origin r = 0". In the year 1915 it seems all but impossible to resist the wrong
assumption that "r = 0" must represent the origin, as in the standard spherical
coordinates (which they are NOT in the context of manifold theory! This was not
fully grasped back then. Physics has many instances of such wrong assumptions,
see e.g. the "renormalisation" that was needed to fix the wrong assumption of
charge constancy in vacuum, etc. etc.)

> Quoting Salvatore Antoci: DAVID HILBERT AND THE ORIGIN OF THE “SCHWARZSCHILD SOLUTION”

Antoci has a very bad track record here, I have never seen anything correct from him.

> ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> "It is reminded that Hilbert’s manifold suffers from two defects, that are absent in Schwarzschild’s manifold.
> It does not admit a consistent drawing of the arrow of time, and it allows for an invariant, local, intrinsic
> singularity in its interior."
>
> ds² = (1 − 2m/r) dt² − dr²/(1 − 2m/r) − r².(dθ² + sin² θ.dφ²), with 0 < r < ∞
>
> Salvatore Antoci warns:

He should get a job flipping burgers instead. I have zero respect for his "warnings".

[skipping Antoci's nonsense]

> And, doing so (probably mocking at Einstein), Hilbert created the basis for the "Black Hole" theories that plagues
> the modern cosmology.

No, this is wrong. Long story. I know there is an entire industry devoted to barking that
nonexistent tree. Good luck with that.

Truth, as always, is somewhat pedestrian, plain-Jane, with no big fireworks.

> Who would think that? Black Holes are derived from a "macabre joke" of Hilbert over Einstein?
>
> Here is the Antoci paper (and is not the original source I found years ago. I find this today):
>
> https://arxiv.org/pdf/physics/0310104.pdf

We've been through Antoci's "work" in excruciating detail around
here sometime in the 1990s. At the time he claimed special relativity was wrong because of
some problem he had found with rotations in SR, the usual Sagnac effect misunderstandings,
etc. Looks like he moved on to GR these days.

The guy is a crank.

--
Jan

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[Dono.]

On Wednesday, September 8, 2021 at 11:51:53 PM UTC-7, Richard Hertz wrote:

> At any case, Schwarzschild is "to blame" (along with Hilbert) for the hysteria around black holes in the last 40
> years, which is gaining momentum.

There is no "hysteria". Black holes have been observed, odious crank.

[Maciej Wozniak]

Sure, they were observed to emit light.

[JanPB]

More precisely, what has been observed is objects whose behaviour is consistent
with the predicted diameter, gravitational pull, the lack of surface, and the radiation properties
peculiar to matter falling toward a horizon (as opposed to matter falling toward a heavy dark star).

--
Jan

[Maciej Wozniak]

On Thursday, 9 September 2021 at 20:25:14 UTC+2, JanPB wrote:
> On Thursday, September 9, 2021 at 8:30:49 AM UTC-7, Dono. wrote:
> > On Wednesday, September 8, 2021 at 11:51:53 PM UTC-7, Richard Hertz wrote:
> >
> > > At any case, Schwarzschild is "to blame" (along with Hilbert) for the hysteria around black holes in the last 40
> > > years, which is gaining momentum.
> >
> > There is no "hysteria". Black holes have been observed, odious crank.
> More precisely, what has been observed is objects whose behaviour is consistent

Sure, it is consistent. As if they have a big mass...

[Christian Corda]

Dear Mr. Paul B. Andersen,

You claim that my paper is nonsense. I regret to inform you that your understanding of such a paper is completely null. You indeed wrote:

"What does this mean?
It means that if a test particle and a planet
with mass m are orbiting in the same orbit,
then the planet will move faster and move
an extra angle Δϕ ≈ π⋅m/M while the test particle
makes one orbit.

What has this to do with the perihelion advance
of the planet?
Obviously nothing whatsoever, the idea is ludicrous."

It is quite evident that you understand nothing of basic science. In fact, for more than 160 years astronomers considered planets as being test masses in both Newtonian gravity and general relativity. Although this approximation is very precise in both the theories, differently from general relativity, it is not sufficient to find the perihelion advance of the planet in Newtonian gravity. The extra angle Δϕ ≈ π⋅m/M is EXACTLY the perihelion advance of the planet. In fact, contrary to your claim, the planet seen as being a test mass orbites in a DIFFERENT orbit with respect to the planet seen as being a non-negligible mass. This is the key point. Thus, they are your crackpot claims which are ludicrous, not my idea. I also must inform you that a revised and improved version of my paper, which was indeed only a pioneristic approach, has been published in Physics of the Dark Universe, see http://dx.doi.org/10.1016/j.dark.2021.100834, which is a well known mainstream journal having a IF higher than 4. In such a paper I also clarify that, overall, the general theory of relativity remains more precise than Newtonian physics, but my approach shows that the Newtonian framework is more powerful than researchers and astronomers were thinking before this paper, at least for the case of Mercury. On the other hand, my Newtonian formula of the advance of planets' perihelion breaks down for the other planets, as you correctly stated. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, in my paper it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework that analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, I found a result consistent with the one of general relativity. Thus, the most important results of my published paper are: (1) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too large. (2) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects.
Thus, please be sure to understand the situation before slandering serious researchers like me with ridiculous crackpottery and elementary misunderstandings.

[Christian Corda]

Dear Mr. Dono,

You wrote:

"> This paper is obviously nonsense.
This is why his paper has been sitting in the crank repository vixra, no peer reviewed journal will pick it up."

I regret to inform you that a revised and improved version of my paper, which was indeed only a pioneristic approach, has been published in Physics of the Dark Universe, see http://dx.doi.org/10.1016/j.dark.2021.100834, which is a well known mainstream journal having a IF higher than 4. By the way, I am NOT a crank. I am instead a well known researcher in the fields of general relativity and gravitation, see my papers in arXiv: https://arxiv.org/search/?query=c.+corda&searchtype=author&source=header
Thus, after Mr. Paul B. Andersen, I invite also you to connect your mind with your hand before writing idiocies.

[Paul B. Andersen]

Den 16.09.2021 08:21, skrev Christian Corda:
> Dear Mr. Paul B. Andersen,
>
> You claim that my paper is nonsense. I regret to inform you that your understanding of such a paper is completely null. You indeed wrote:

>>

>> Solution to the advance of the perihelion of Mercury
>> in Newtonian theory
>> Christian Corda
>> June 15, 2020
>>
>> https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf
>>
>>
>> Chapter 2 Approximation of circular orbit
>>
>>
>> He starts with the equation for the period of a test particle
>> in orbit around a mass M.
>>
>> T₀ = 2π√(r₀³/GM) See equation (5)
>>
>> The period of a mass m in orbit around a mass M is:
>>
>> T = 2π√(r₀³/G(m+M)) = 2π√(r₀³/GM)⋅(1/√(1+m/M))
>>
>> T = T₀⋅(1/√(1+m/M)), see equation (17)
>>
>> T₀ = T⋅√(1+m/M)
>>
>> So Corda can conclude:
>>
>> Hence, the angle that Mercury sweeps during the period T0 is:
>>
>> φ = ωT₀ = 2π⋅√(1+m/M) ≈ 2π(1+m/2M) see equation (19)
>>
>> Δϕ ≈ π⋅m/M see equation (19)

>>
>> What does this mean?
>> It means that if a test particle and a planet
>> with mass m are orbiting in the same orbit,
>> then the planet will move faster and move
>> an extra angle Δϕ ≈ π⋅m/M while the test particle
>> makes one orbit.
>>
>> What has this to do with the perihelion advance
>> of the planet?
>> Obviously nothing whatsoever, the idea is ludicrous.
>>

>> But let us compare the angle Δϕ with the perihelion
>> advance predicted by GR, marked GR: below.
>>
>> Mercury:
>> Δϕ = = 5.2154E-7 rad/orbit GR: 5.0185E-7 rad/orbit
>>
>> Venus:
>> Δϕ = 7.6902E-6 rad/orbit GR: 0.25711E-6 rad/orbit
>>
>> Earth:
>> Δϕ = 9.5518E-6 rad/orbit GR: 0.18594E-6 rad/orbit
>>
>> Mars:
>> Δϕ = 1.0138E-6 rad/orbit GR: 0.12308E-6 rad/orbit
>>
>> Jupiter:
>> Δϕ = 0.29996E-2 rad/orbit GR: 0.035810E-6 rad/orbit
>>
>>
>> We see that Mercury happens to be in the ballpark.
>> But all the other planets are more than a decade off.
>> Mercury is only accidentally in the ballpark.
>>
>> Chapter 3 and 4 give the same results.

>>
>> This paper is obviously nonsense.
>>
>

> I found a result consistent with the one of general relativity. Thus, the most important results of my published paper are: (1) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too large. (2) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects.
> Thus, please be sure to understand the situation before slandering serious researchers like me with ridiculous crackpottery and elementary misunderstandings.
>

--
Paul

https://paulba.no/

[Richard Hertz]

Paul, is this the real Christian Corda, the researcher?

It seems so, because I felt that you and the non human specie didn't answer.

Did you both chickened out about replying to him?. Everything points to the fact that you both did.

Who had possibly thought that the author of such a deep paper would be a new guest at this forum?

Congratulations, Professor Corda!. Nice career!




https://scholar.google.it/citations?user=WfUTLj8AAAAJ&hl=it

Christian Corda - Top Italian Scientist in Physics
http://topitalianscientists.org/tis/35037/Christian_Corda_-_Top_Italian_Scientist_in_Physics

CURRICULUM VITAE
http://www.yellow-energy-plc.com/Yellow_Energy_22-09-12/Yellow_Directors/C%20Corda%20CV%20Web.pdf

[Maciej Wozniak]

On Thursday, 16 September 2021 at 08:46:50 UTC+2, Paul B. Andersen wrote:


> https://paulba.no/

In the meantime in the real world, however, the real
clocks of the real GPS keep indicating t'=t, just like all
serious clocks always did.

[Christian Corda]

On Thursday, 16 September 2021 at 08:46:50 UTC+2, Paul B. Andersen wrote:

Please, kindly clarify if you published some paper on general relativity and gravitation in serious, peer reviewed journals in your scientific career. In fact, in you website I see only some copy and past of well known results. There are no research papers there.

[Christian Corda]

Dear Mr. Paul B. Andersen,

Please, kindly clarify if you published some paper on general relativity and gravitation in serious, peer reviewed journals in your scientific career. In fact, in your website I see only some copy and past of well known results. There are no research papers there. If you did not publish some paper on general relativity and gravitation in serious, peer reviewed journals in your scientific career you do not have the scientific level needed in order to discuss with me.

[Christian Corda]

Thanks a lot for your kind congrats.

[Lou]

It’s amazing how Alberts idiots can’t figure out where he lied. Look at his
so called relativistic proof of The Mercury orbit. All he did was take Newton’s
Incorrect calculations, added the observed anomaly and got a real
mathematician to help him back calculate the data into a faked “derivation”
using field equations. Fortunately religious wackos pretending to be
physicists... are easy to con.

[Christian Corda]

Dear Mr. Lou,

Unfortunately for you, you are not an Albert's idiot. You are a complete idiot an ignorant and a crackpot instead.

[Dono.]

On Thursday, September 16, 2021 at 6:48:29 AM UTC-7, Christian Corda wrote:
> Dear Mr. Lou,
>
> Unfortunately for you, you are not an Albert's idiot. You are a complete idiot an ignorant and a crackpot instead.

Richard,

You just reached a new low by creating a fake persona and pretending to be Christian Corda. You did the same thing before, by resurrecting Koobee Wublee from the dead. You are the lowest scumbag and you are not fooling anybody.

[Dono.]

I know who you are.
The only reason you got published is that Physics of the Dark Universe is an all-Italian editorship
I did not call you a crank (you are a fringe physicist) , I called vixra a crank repository.
As for your paper, if you start "correcting" Newtonian mechanics with relativistic effects, it is no longer Newtonian, it is a hack that you hatched in order to match the experimental observations.

[Christian Corda]

Dear Mr. Dono,
I know who you are too. You are a little coward acting backward a nickname. Only via such a cowardly conduct can you accuse Physics of the Dark Universe of corruption because "it is an all-Italian editorship". You have not the balls to use your real name. Concerning the issue that I hatched a hack in order to match the experimental observations, your is only a squalid envy because I found a result that you cannot find even if your life will last 1000 years.... I am honoured to be called "a fringe physicist" by a poor envious man like you....

[Maciej Wozniak]

On Thursday, 16 September 2021 at 19:00:04 UTC+2, Dono. wrote:

In the meantime in the real world, however, the clocks of

[Dono.]

On Thursday, September 16, 2021 at 10:11:28 AM UTC-7, Christian Corda wrote:
> On Thursday, 16 September 2021 at 19:00:04 UTC+2, Dono. wrote:
> > On Wednesday, September 15, 2021 at 11:29:44 PM UTC-7, Christian Corda wrote:
> > > Dear Mr. Dono,
> > >
> > > You wrote:
> > >
> > > "> This paper is obviously nonsense.
> > > This is why his paper has been sitting in the crank repository vixra, no peer reviewed journal will pick it up."
> > >
> > > I regret to inform you that a revised and improved version of my paper, which was indeed only a pioneristic approach, has been published in Physics of the Dark Universe, see http://dx.doi.org/10.1016/j.dark.2021.100834, which is a well known mainstream journal having a IF higher than 4. By the way, I am NOT a crank. I am instead a well known researcher in the fields of general relativity and gravitation, see my papers in arXiv: https://arxiv.org/search/?query=c.+corda&searchtype=author&source=header
> > > Thus, after Mr. Paul B. Andersen, I invite also you to connect your mind with your hand before writing idiocies.
> > I know who you are.
> > The only reason you got published is that Physics of the Dark Universe is an all-Italian editorship
> > I did not call you a crank (you are a fringe physicist) , I called vixra a crank repository.
> > As for your paper, if you start "correcting" Newtonian mechanics with relativistic effects, it is no longer Newtonian, it is a hack that you hatched in order to match the experimental observations.
> Dear Mr. Dono,

> you accuse Physics of the Dark Universe of corruption because "it is an all-Italian editorship".

Truth hurts.

> Concerning the issue that I hatched a hack in order to match the experimental observations, your is only a squalid envy because I found a result that you cannot find even if your life will last 1000 years....

Err, your hack is not applied to Mercury precession but it has to be applied to the precession of all the other planets in order to match observation. Therefore....it is a hack.

[Christian Corda]

Mr. Dono, I am not interested in discussing with cowards acting backward a nickname. Use your real name if you have the balls. Alternatively, this discussion ends here and I wish you to fuck in hell.

[Dono.]

Looks like i struck a nerve: your hack is not applied to Mercury precession in order to match experimental results but it HAS to be applied to the precession of all the other planets in order to match observation. Therefore....it is a hack.

[Dirk Van de moortel]

Op 16-sep.-2021 om 19:28 schreef Christian Corda:

Whoever you are, you are trying to communicate with a typical
Trump voter. No meaningful communication is possible. Forget it.

Dirk Vdm

[Dono.]

Dick ,

You need to take your anti-TSD meds. You forgot about them again. You are also sucking dick not only to bidum but to a fringe physicist as well, you have just reached a new low.

[Richard Hertz]

On Thursday, September 16, 2021 at 2:51:59 PM UTC-3, Dirk Van de moortel wrote:
> Op 16-sep.-2021 om 19:28 schreef Christian Corda:

<snip>

> Whoever you are, you are trying to communicate with a typical
> Trump voter. No meaningful communication is possible. Forget it.
>
> Dirk Vdm

I like Christian Corda. Besides his intellectual capabilities, he can express himself
in English like a true Italian does.

Bravo, Christian! Keep doing your science and, may I (respectfully) to suggest to
you to read something about George Gamow's career and the opinion that von Neumann
had about him? It's very telling about the life and doing of such brilliant physicist, from
the Golden Age in physics.

[JanPB]

No, that's not what happened.

Why do adults feel they must fantasise about physics? Just change your hobby,
stop posting idiocies.

--
Jan

[Townes Olson]

On Tuesday, September 7, 2021 at 10:59:40 PM UTC-7, Richard Hertz wrote:
> Excerpts from:

> Solution to the advance of the perihelion of Mercury in Newtonian theory
> Christian Corda June 15, 2020

> It has been shown through THREE different approaches that, contrary to a longstanding
> conviction longer than 150 years, the orbit of Mercury behaves as required by Newton's
> equations with a very high precision if one correctly analyses the situation in the framework
> of the two-body problem WITHOUT NEGLECTING THE the MASS of Mercury.

The "reasoning" in that "paper" is utter nonsense. The Newtonian analysis of the two-body problem does *not* neglect the mass of either body... that's why it's called the two-body problem. The equations of Newtonian physics unambiguously lead to the conclusion that each of the massive spheres follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies. (Of course, the Sun isn't perfectly spherical, which does indeed produce some Newtonian precession, but that is insignificantly small because the Sun is only very slightly oblate.)

The fact that m/M is approximately equal to 6M/L (in geometric units, where L is the semi-latus rectum of Mercury's orbit) for Mercury is just an insignificant numerological coincidence, as can be seen by considering (for example) the asteroid Icarus. There is no rational basis for relating m/M to the orbital precession in Newtonian mechanics (nor in general relativity).

[Paul B. Andersen]

The issue is this paper:
https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf

As you quite correctly points out:
A planet with mass m in circular orbit around a star with mass M
will sweep an angle 2π+π⋅m/M while a body with mass 1 Kg in
the same orbit around the same star makes one orbit.

Please, kindly clarify why this fact implies that the perihelion
of a planet with mass m in elliptical orbit around a star with
mass M will advance an angle π⋅m/M per orbit, regardless of
what the eccentricity of the orbit is.

Please, kindly clarify if this prediction is in accordance
with the prediction of GR for the planets in our solar system.

--
Paul

https://paulba.no/

[Scot Dino]

Paul B. Andersen wrote:

> Please, kindly clarify why this fact implies that the perihelion of a
> planet with mass m in elliptical orbit around a star with mass M will
> advance an angle π⋅m/M per orbit, regardless of what the eccentricity of
> the orbit is.
>
> Please, kindly clarify if this prediction is in accordance with the
> prediction of GR for the planets in our solar system.

you don't know, huh?

[Dono.]

Corda is gone

He took it in the chin, started to swear at all people who pointed his crankeries and has withdrawn in his hole to lick his wounds. The only reason he managed to publish his crackpot stuff is that the journal he published in is a predatory one, for the 2350$ publishing charge they would publish anything.

[Christian Corda]

Dear Dirk Vdm,
Thanks for clarifying this point. In fact, I was thinking that I was trying to communicate with a perfect idiot. Thanks for confirming this. I will merely ignore him in the future.

[Christian Corda]

Dear Mr. Townes Olson,
You are a confused crackpot as well as Mr. Dono.
You wrote:
"The equations of Newtonian physics unambiguously lead to the conclusion that each of the massive spheres follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession." You do not know or do not understand that, in order to find the solution of the trajectory, one must reduce the two-body problem to the Kepler problem or to the simple harmonic oscillator. In that case, each problem admits TWO different solutions. The approximate one, which is usually used to analyse the planetary motion around the Sun, considers negligible the mass of the planet. In the latter, more precise one, you MUST consider that the reference frame in the center of the Sun is NOT inertial in Newtonian sense. Thus, the trajectory of a test mass is different with respect to the trajectory of a non-negligible mass in such a reference frame. I must also inform you that a revised and improved version of my paper, which was indeed only a pioneristic approach, has been published in Physics of the Dark Universe, see http://dx.doi.org/10.1016/j.dark.2021.100834, which is a well known mainstream journal having a IF higher than 4.

[Christian Corda]

Dear Paul B. Andersen,

You did not clarify how many papers you published on general relativity and gravitation in standard journals in order to discuss with me. In any case, the answers to your questions can be found in my published paper. Kindly notice that, contrary to the claims of Mr. Dono (what a perfect idiot...) Physics of the Dark Universe is NOT predatory. It indeed admits two different options of publication. The open one and the traditional non-open one. I chose the second, so it is completely false that I paid 2350$ publishing charge in order to get my paper published.

[Townes Olson]

On Thursday, September 16, 2021 at 11:38:44 PM UTC-7, Christian Corda wrote:
> > > Solution to the advance of the perihelion of Mercury in Newtonian theory
> > > Christian Corda June 15, 2020
> >

> > The "reasoning" in that "paper" is utter nonsense. The Newtonian analysis of the two-body problem does *not* neglect the mass of either body... that's why it's called the two-body problem. The equations of Newtonian physics unambiguously lead to the conclusion that each of the massive spheres follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.
>

> In order to find the solution of the trajectory, one must reduce the two-body problem

> to the Kepler problem or to the simple harmonic oscillator. In that case, each problem
> admits TWO different solutions.

No, the Newtonian equations yield a unique solution to the two-body problem of two spherical masses orbiting each other. The result is that each follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.

> The approximate one, which is usually used to analyse the planetary motion around
> the Sun, considers negligible the mass of the planet.

No, the two-body problem has a unique exact solution, as described above, and it does not neglect the mass of either body. This is a simple high school homework exercise.

> In the latter, more precise one, you MUST consider that the reference frame
> in the center of the Sun is NOT inertial in Newtonian sense.

Of course it is not. Both bodies orbit the center of mass. Each body follows an ellipse with a focus at the center of mass of the two bodies. The center of mass is not the center of either body. This is a simple high school homework exercise.

> Thus, the trajectory of a test mass is different with respect to the trajectory
> of a non-negligible mass in such a reference frame.

The simple exact solution of the two-body problem in Newtonian mechanics does not neglect the mass of either body. Your "paper" is juvenile nonsense.

[Christian Corda]

Dear Mr. Townes Olson,
OK, as you insist to claim that, verbatim "The result is that each follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession and is a simple homework exercise for high school students", I invite you to make such an exercise. Please, kindly find the trajectory of the Sun and the trajectory of Mercury in the center of mass of the system Sun-Mercury and kindly show that this implies that there is no-precession of Mercury in the non-inertial reference frame of the Sun. You claim that it is a simple homework exercise for high school students. Then, please, make it. Alternatively, one should think that your high school graduating is false.... I look forward to seeing your demonstration.

[Bryce Gold]

Christian Corda wrote:

>> Err, your hack is not applied to Mercury precession but it has to be
>> applied to the precession of all the other planets in order to match
>> observation. Therefore....it is a hack.
> Mr. Dono, I am not interested in discussing with cowards acting backward
> a nickname. Use your real name if you have the balls. Alternatively,
> this discussion ends here and I wish you to fuck in hell.

nonsense, you just made a fool of yourself, attacking the man, not the
issue. Kindergartenish, if you ask me. Keep focusing the issue, my friend.
The time of mainstream media monologue is over. You are on usenet right
now. Please behave accordingly. Contribute. Don't come to me with your
repetitive fake moon landing. We need empirical observation, facts and
indicators here.

[Christian Corda]

Dear Mr. Bryce Gold,
You misunderstand the points here. On one hand, if one asks me for some clarification to my paper in a kind way it will be my pleasure discussing with him/her and to clarify various issues. On the other hand, if one claims that my paper is "obvious nonsense", "crackpottery", "utter nonsense", etc, I want to know who is the guy who makes such strong offensive statements. General relativity and gravitation are NOT elementary issues, but very complicated ones. Thus, I can accept serious criticisms only from experts in such very complicated fields. Now, when I checked the publications by you, Mr. Paul B. Andersen and Mr. Townes Olson, I found that the total number of your publications is zero. Thus, your knowledge and understanding of general relativity and gravitation (admitting that you have them, but I am not sure) are completely negligible with respect to my proper ones, because I have published more than 100 paper in the fields of general relativity and gravitation in the most important and prestigious international journals. Thus, I cannot accept criticisms by all of you, because all of you have neither the competence, nor the eminence, nor the mathematical rigor to discuss technical details with me. For the same reason, I want to know the real name of Mr. Dono before further discussing with him. I cannot discuss very complicated issues with guys who NEVER seriously worked on such complicated issues.

[Christian Corda]

Thanks, I am honoured by your kind words. Concerning George Gamow, I agree with Hawking's judgement that he should have deserved the Nobel Prize in Physics.

[Paul B. Andersen]

Den 17.09.2021 08:48, skrev Christian Corda:
> Dear Paul B. Andersen,
>
> You did not clarify how many papers you published on general relativity and gravitation in standard journals in order to discuss with me.

And that's why you refuse to answer the questions below? :-D

>
> On Thursday, 16 September 2021 at 22:53:07 UTC+2, Paul B. Andersen wrote:
>> The issue is this paper:
>> https://web.ma.utexas.edu/mp_arc/c/20/20-47.pdf
>>
>> As you quite correctly points out:
>> A planet with mass m in circular orbit around a star with mass M
>> will sweep an angle 2π+π⋅m/M while a body with mass 1 Kg in
>> the same orbit around the same star makes one orbit.
>>
>> Please, kindly clarify why this fact implies that the perihelion
>> of a planet with mass m in elliptical orbit around a star with
>> mass M will advance an angle π⋅m/M per orbit, regardless of
>> what the eccentricity of the orbit is.

I bet you can't clarify this, of obvious reasons.

>>
>> Please, kindly clarify if this prediction is in accordance
>> with the prediction of GR for the planets in our solar system.

Since you of obvious reasons refuse the clarify this point,
I will do it for you:


Predictions [Δϕ/orbit]:
Planet Your GR
-----------------------------------
Mercury 5.2154E-7 5.0185E-7

Venus 7.6902E-6 0.25711E-6

Earth 9.5518E-6 0.18594E-6

Mars 1.0138E-6 0.12308E-6

Jupiter 0.29996E-2 0.035810E-6


--
Paul

https://paulba.no/

[Maciej Wozniak]

On Friday, 17 September 2021 at 15:14:34 UTC+2, Paul B. Andersen wrote:

> Predictions [Δϕ/orbit]:
> Planet Your GR

You're lying, Paul, as expected from relativistic
scum. Your alleged "GR" - the model used to
obtain these predictions - was applying euclidean
space and galilean time.

[Christian Corda]

You wrote:
> >> A planet with mass m in circular orbit around a star with mass M
> >> will sweep an angle 2π+π⋅m/M while a body with mass 1 Kg in
> >> the same orbit around the same star makes one orbit.
> >>
> >> Please, kindly clarify why this fact implies that the perihelion
> >> of a planet with mass m in elliptical orbit around a star with
> >> mass M will advance an angle π⋅m/M per orbit, regardless of
> >> what the eccentricity of the orbit is.
> I bet you can't clarify this, of obvious reasons.

Why do you write that a body with mass 1 Kg makes one orbit? Clearly, a body with mass 1 Kg will sweep an angle 2π+π⋅1Kg/M, which is different by one orbit (an angle 2π). Thus, I cannot clarify a wrong statement. Please, reformulate it. Thanks.

You wrote:

>> Please, kindly clarify if this prediction is in accordance
>> with the prediction of GR for the planets in our solar system.

Please, kindly read my paper published in Physics of the Dark Universe. It is stressed that my Newtonian formula of the advance of planets' perihelion breaks down for the other planets, as you correctly stated. The predicted Newtonian result is indeed too large for the planets that you cite. Therefore, in my paper it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework that analyzes gravity between Newton and Einstein, solve the problem.

[Dono.]

On Thursday, September 16, 2021 at 11:48:30 PM UTC-7, Christian Corda wrote:

> contrary to the claims of Mr. Dono (what a perfect idiot...) Physics of the Dark Universe is NOT predatory.

Sure it is, it charges 2350$ per paper publication charges. The fact that you are resorting to ad-hominem shows that you lost the argument.

[Dono.]

On Friday, September 17, 2021 at 6:45:51 AM UTC-7, Christian Corda wrote:

> Please, kindly read my paper published in Physics of the Dark Universe. It is stressed that my Newtonian formula of the advance of planets' perihelion breaks down for the other planets, as you correctly stated. The predicted Newtonian result is indeed too large for the planets that you cite. Therefore, in my paper it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework that analyzes gravity between Newton and Einstein, solve the problem.

So, your "solution" works only for Mercury.
For all other planets you are arbitrarily taking bits and pieces from GR , like "gravitational and rotational time dilation" which do not exist in the Newtonian frameworks. In other words, you made up a hack to prop up your claims.

[Townes Olson]

On Friday, September 17, 2021 at 2:00:19 AM UTC-7, Christian Corda wrote:
> > > > > Solution to the advance of the perihelion of Mercury in Newtonian theory
> > > > > Christian Corda June 15, 2020
> > > >
> > > > The "reasoning" in that "paper" is utter nonsense. The Newtonian analysis of the two-body problem does *not* neglect the mass of either body... that's why it's called the two-body problem. The equations of Newtonian physics unambiguously lead to the conclusion that each of the massive spheres follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.
>

> I invite you to make such an exercise.

The exact and unique solution of the two-body problem (for spherical masses) in Newtonian mechanics is presented in every introductory text book on dynamics. Working in terms of an inertial coordinate system whose origin is the center of mass of the system, the forces on the masses (with sign positive in the outward direction) are f12 = f21 = -G m1 m2 /(r1 + r2)^2, and we have r1/r2 = m2/m1, so the force on m1 can be written as f12 = -K1/r1^2 where K1 = G m1 m2 /[1 + (m1/m2)]^2, and similarly the force on m2 can be written as f21 = -K2/r2^2 where K2 = G m1 m2 /[1 + (m2/m1)]^2. Thus the force on each mass varies inversely as the square of the distance from the fixed origin, and hence each of the masses follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is already in Newton's Principia in 1687. Today it is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.

> in the non-inertial reference frame of the Sun.

Both bodies follow non-precessing elliptical orbits in terms of the celestial reference system, i.e., in reference to the directions of the distant stars and galaxies. This is the relevant frame for quantifying the precession (or, in this case, the absence of precession). Of course, this childish analysis is not the same as the actual grown-up analysis of the solar system, because there are multiple planets, all affecting the motion of the Sun in terms of the center of mass frame. The Sun's actual motion is quite chaotic, and sometimes the center of mass of the solar system is inside the Sun, and sometimes it is outside. Also, the planets interact with each other, e.g., Jupiter exerts a significant force on Earth, so the actual Newtonian analysis is not a two-body problem, it is an N-body problem. The point is that actual grown-up scientists can work out the results of this for the actual solar system, and determine very precisely the Newtonian prediction for the precessions of the planets, and then observations show the actual precessions, and the differences are all accurately accounted for in general relativity.

Your "paper" is just focused on the elementary two-body problem, which is a simple high school homework exercise, and you have botched it, so your "paper" is juvenile nonsense.

[Christian Corda]

Dear Mr. Townes Olson,

It is quite evident that you do not understand what you are speaking about, in a similar way to that idiot of Mr. Dono, who does not know the importance of a better understanding of gravity between Newtonian theory and general relativity. Thus, I am forced to correct your mistakes. When one refers to the advance of a planet's perihelion, one refers to the orbit of the planet AROUND the Sun. Thus, one refers neither to the orbit of the planet around the center of mass of the two body system, nor to the orbit of the Sun around such a center of mass. In general relativity one can use the Schwarzschild solution or an approximate solution of the Einstein field equation. In both the cases, the origin of the reference frame is fixed in the center of the Sun (despite in Schwarzschild coordinates the Schwarzschild radius become spacelike for values less than the gravitational radius but this is not a problem because one considers values much larger than the gravitational radius). Thus, one DOES NOT use the two body problem. Instead, as general relativity is more powerful than Newtonian gravity, one uses an approach where ALL the planets are considered test masses with respect to the mass of the Sun. In this framework, the two coordinate systems are equivalent to the inertial celestial reference system. Based on the power of general relativity, the problem of the advance of planets perihelion is solved in an excellent way in this approximation (I think that a possible solution via the two body problem in general relativity could be more precise). In Newtonian physics the situation is different. If one still considers the reference frame centered in the Sun as being equivalent to the inertial celestial reference system, then one must consider, AGAIN, the mass of the planets as being negligible (i.e. test masses) with respect to the mass of the Sun. In this approximation there is no advance of the planet's perihelion. Instead, if one considers non-negligible the value of the planet rotating around the Sun, then the reference frame fixed in the center of the Sun becomes non-inertial based on the planet's back reaction (third Newton Law). I am not considering the presence of the other bodies, I am referring to non-inertial behavior with respect to the two body problem. It is such a back reaction which generates the advance of planets perihelion, but this approximation works ONLY for Mercury, while it breaks down for the other planets because the effect is too strong with respect to the astrophysical observations.
So, your "comments" are nonsense of a frustrated old man who never published a single paper on general relativity and gravitation in his whole life... I strongly suggest that you relax and return to study. Gravitational theory is too complicated for your level of knowledge and understanding.

[Christian Corda]

I must correct a typo: "the Schwarzschild radius become spacelike " must be replaced with "the Schwarzschild radial coordinate become spacelike"

[Richard Hertz]

On Friday, September 17, 2021 at 12:24:38 PM UTC-3, Townes Olson wrote:

<snip>

> The exact and unique solution of the two-body problem (for spherical masses) in Newtonian mechanics is presented in every introductory text book on dynamics. Working in terms of an inertial coordinate system whose origin is the center of mass of the system, the forces on the masses (with sign positive in the outward direction) are f12 = f21 = -G m1 m2 /(r1 + r2)^2, and we have r1/r2 = m2/m1, so the force on m1 can be written as f12 = -K1/r1^2 where K1 = G m1 m2 /[1 + (m1/m2)]^2, and similarly the force on m2 can be written as f21 = -K2/r2^2 where K2 = G m1 m2 /[1 + (m2/m1)]^2. Thus the force on each mass varies inversely as the square of the distance from the fixed origin, and hence each of the masses follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is already in Newton's Principia in 1687. Today it is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.

I've read the posts at this thread and didn't want to post an opinion on the last discussion about Newton's law, but after
this post I want to express my opinion, using only an elementary guide for students (I think that's for High School):

https://openstax.org/books/university-physics-volume-1/pages/13-1-newtons-law-of-universal-gravitation

This interesting link, very simple and clear, also talks about Gravitational Potential Energy and Total Energy, Satellite Orbits and
Energy, Kepler's Laws, etc.

The historical Newton's Law for Gravity, as I know for more than 5 decades, still is (vectorial form):

F⁻₁₂ = G.m₁ . m₂ /r² . r⁻₁₂

where F⁻₁₂ is the force exerted on object 1 by object 2 and r⁻₁₂ is a unit vector that points from object 1 toward object 2.
(See Figure 13.2. F⁻₁₂ represents an attractive force. The opposite force F⁻₂₁ is the force on object 2 exerted by object 1)

Gravitational force act along a line joining the centers of mass of the two objects 1 and 2.

I don't see nor at this link nor at anyone else that I visited, an expression like yours: f12 = f21 = -G m1 m2 /(r1 + r2)^2.
I mean, no scalar addition of terms r1 and r2 (I assume they are represented by vectors).

Your comment: "Thus the force on each mass varies inversely as the square of the distance from the fixed origin, and hence

each of the masses follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession"

is not what I've read, when Kepler's Laws come into this picture. It's much complex than that. Kepler's first law states that
every planet moves along an ellipse, with the Sun located at a focus of the ellipse. (see Fig. 13.16)

> > in the non-inertial reference frame of the Sun.
> Both bodies follow non-precessing elliptical orbits in terms of the celestial reference system, i.e., in reference to the directions of the distant stars and galaxies. This is the relevant frame for quantifying the precession (or, in this case, the absence of precession).

This is NOT what Kepler Laws say. Nothing about distant stars and galaxies. Just two bodies and vectorial forms for
forces and distances. On this paper about planetary motions, you'll find an expression for perihelion on elliptic orbits:

https://www.math.ksu.edu/~dbski/writings/planetary.pdf

In polar coordinates, being u(r,θ) = P/r (dimensionless), solving the differential equation d²u/dθ² + u = 1 gives

P = r . (1 + e.cos θ) , with e: eccentricity of the ellipse and the perihelion on the positive x-axis (Equation 6), when θ = 0. In this
equation, represents the angle of the perihelion with reference to a polar coordinate (r, θ) for a planetary motion centered in a
focus (x=0, y=0) of the ellipse in cartesian coordinates.

<snip>

[Dono.]

On Friday, September 17, 2021 at 10:24:16 AM UTC-7, Christian Corda dug himself deeper:

> It is quite evident that you do not understand what you are speaking about, in a similar way to that idiot of Mr. Dono, who does not know the importance of a better understanding of gravity between Newtonian theory and general relativity.

The fact that you keep resorting to ad-hominem shows that you lost the argument and you are getting desperate to cover up the crankeries that you managed to publish. Not only that you spent 2350$ for the ego trip but you also embarrassed yourself in front of all the scientific community. And you continue to dig yourself deeper with every post. Way to go, Corda!

[Richard Hertz]

At any case, 2350$ is cheap compared with the 5500$ that publishers tried to make you pay for some shit, time ago, which
caused that you run like a fucking cheap bastard and started to post your idiocies and racial hate over here. You found a home,
reptilian lifeform, where it only cost you an ISP connection plus a borrowed computer or 3rd. hand smartphone. Probably, you
are stealing WiFi from your neighbors connections. It's what your pagan god would do if IT was alive, reptilian!

I'd bet that you live with 100$ a month and come here to vent your anger, resentment and frustration, scumbag!

[Dono.]

On Friday, September 17, 2021 at 11:12:37 AM UTC-7, Richard Hertz wrote:
> On Friday, September 17, 2021 at 3:04:49 PM UTC-3, Dono. wrote:
> > On Friday, September 17, 2021 at 10:24:16 AM UTC-7, Christian Corda dug himself deeper:
> > > It is quite evident that you do not understand what you are speaking about, in a similar way to that idiot of Mr. Dono, who does not know the importance of a better understanding of gravity between Newtonian theory and general relativity.
> > The fact that you keep resorting to ad-hominem shows that you lost the argument and you are getting desperate to cover up the crankeries that you managed to publish. Not only that you spent 2350$ for the ego trip but you also embarrassed yourself in front of all the scientific community. And you continue to dig yourself deeper with every post. Way to go, Corda!
> At any case, 2350$ is cheap compared with the 5500$ that publishers tried to make you pay

Never happened, you need to stop lying odious kapo.

[Townes Olson]

On Friday, September 17, 2021 at 10:24:16 AM UTC-7, Christian Corda wrote:
> > > > Solution to the advance of the perihelion of Mercury in Newtonian theory
> > > > Christian Corda June 15, 2020
> > >

> > > The "reasoning" in that "paper" is utter nonsense. The exact and unique solution of the two-body problem (for spherical masses) in Newtonian mechanics is presented in every introductory text book on dynamics. Working in terms of an inertial coordinate system whose origin is the center of mass of the system, the forces on the masses (with sign positive in the outward direction) are f12 = f21 = -G m1 m2 /(r1 + r2)^2, and we have r1/r2 = m2/m1, so the force on m1 can be written as f12 = -K1/r1^2 where K1 = G m1 m2 /[1 + (m1/m2)]^2, and similarly the force on m2 can be written as f21 = -K2/r2^2 where K2 = G m1 m2 /[1 + (m2/m1)]^2. Thus the force on each mass varies inversely as the square of the distance from the fixed origin, and hence each of the masses follows an elliptical orbit with a focus at the center of mass of the two bodies, and there is zero precession. This is already in Newton's Principia in 1687. Today it is a simple homework exercise for high school students, and it takes full account of the non-zero masses of both bodies.

> > Both bodies follow non-precessing elliptical orbits in terms of the celestial reference system, i.e., in reference to the directions of the distant stars and galaxies. This is the relevant frame for quantifying the precession (or, in this case, the absence of precession). Of course, this childish analysis is not the same as the actual grown-up analysis of the solar system, because there are multiple planets, all affecting the motion of the Sun in terms of the center of mass frame.
> >

> > Your "paper" is just focused on the elementary two-body problem, which is a simple high school homework exercise, and you have botched it, so your "paper" is juvenile nonsense.

> When one refers to the advance of a planet's perihelion, one refers to the orbit of
> the planet AROUND the Sun.

No, it is understood in astronomy, since the time of Newton, that the objects in the solar system, including the Sun itself, orbit the center of mass of the solar system. The Sun's actual motion is quite chaotic, and sometimes the center of mass of the solar system is inside the Sun, and sometimes it is outside. Also, the planets interact with each other, e.g., Jupiter exerts a significant force on Earth, so the actual Newtonian analysis of the solar system is not a two-body problem, it is an N-body problem. The point is that actual grown-up scientists can work out the results of this for the actual solar system, and determine very precisely the Newtonian prediction for the precessions of the planets, and then observations show the actual precessions, and the differences are all accurately accounted for in general relativity.

> Thus, one refers neither to the orbit of the planet around the center of mass
> of the two body system, nor to the orbit of the Sun around such a center of mass.

If one does that, one is mistaken. One should see above.

> In general relativity one can use the Schwarzschild solution or an approximate
> solution of the Einstein field equation. In both the cases, the origin of the reference

> frame is fixed in the center of the Sun...

The Schwarzschild solution applies only to the one-body problem, i.e., it assumes perfect spherical symmetry, and it gives the trajectories of infinitesimal test particles of negligible mass in the vicinity of a gravitating spherical mass. Unlike Newtonian physics, there is no closed-form analytic solution of the two-body problem in general relativity, but it can be solved numerically to any desired precision, and it yields the well-known non-Newtonian precession. Now, we get almost exactly the same precession simply by examining the orbit of a test particle using the Schwarzschild solution, in fact, it can be shown that the precession predicted by the one-body Schwarzschild solution differs from the precession predicted by the fully general numerical solution of the two-body problem only by about 0.0001 arcseconds/century, so it doesn't significantly affect the prediction of 43 arcseconds/century.

> Thus, one DOES NOT use the two body problem.

Again, your erroneous claim is that Newtonian physics predicts precession (for the two-body problem with spheres), and that claim is false, because Newtonian theory has a very simple and exact solution of the two-body problem, and it has exactly zero precession. Now, regarding general relativity, we must solve the two-body problem numerically, because there is no simple closed analytic solution, but that result happens to agree very closely with the result of the one-body trajectories given by the analytic Schwarzschild solution. See above.

[snip remainder of gibberish]

[JanPB]

On Thursday, September 16, 2021 at 10:51:59 AM UTC-7, Dirk Van de moortel wrote:
> Op 16-sep.-2021 om 19:28 schreef Christian Corda:

> > On Thursday, 16 September 2021 at 19:19:36 UTC+2, Dono. wrote:

> >> On Thursday, September 16, 2021 at 10:11:28 AM UTC-7, Christian

> >> Corda wrote:
> >>> On Thursday, 16 September 2021 at 19:00:04 UTC+2, Dono. wrote:

> >>>> On Wednesday, September 15, 2021 at 11:29:44 PM UTC-7,

> >>>> Christian Corda wrote:
> >>>>> Dear Mr. Dono,
> >>>>>
> >>>>> You wrote:
> >>>>>
> >>>>> "> This paper is obviously nonsense. This is why his paper
> >>>>> has been sitting in the crank repository vixra, no peer
> >>>>> reviewed journal will pick it up."
> >>>>>

> >>>>> I regret to inform you that a revised and improved version of

> >>>>> my paper, which was indeed only a pioneristic approach, has
> >>>>> been published in Physics of the Dark Universe, see
> >>>>> http://dx.doi.org/10.1016/j.dark.2021.100834, which is a well

> >>>>> known mainstream journal having a IF higher than 4. By the
> >>>>> way, I am NOT a crank. I am instead a well known researcher
> >>>>> in the fields of general relativity and gravitation, see my
> >>>>> papers in arXiv:
> >>>>> https://arxiv.org/search/?query=c.+corda&searchtype=author&source=header
> >>>>>
> >>>>>
> Thus, after Mr. Paul B. Andersen, I invite also you to connect your mind
> with your hand before writing idiocies.
>
> >>>> I know who you are. The only reason you got published is that
> >>>> Physics of the Dark Universe is an all-Italian editorship I did
> >>>> not call you a crank (you are a fringe physicist) , I called
> >>>> vixra a crank repository. As for your paper, if you start
> >>>> "correcting" Newtonian mechanics with relativistic effects, it
> >>>> is no longer Newtonian, it is a hack that you hatched in order
> >>>> to match the experimental observations.
> >>> Dear Mr. Dono, you accuse Physics of the Dark Universe of
> >>> corruption because "it is an all-Italian editorship".
>
> >> Truth hurts.
>
> >>> Concerning the issue that I hatched a hack in order to match the
> >>> experimental observations, your is only a squalid envy because I
> >>> found a result that you cannot find even if your life will last
> >>> 1000 years....
>

> >> Err, your hack is not applied to Mercury precession but it has to
> >> be applied to the precession of all the other planets in order to
> >> match observation. Therefore....it is a hack.
> > Mr. Dono, I am not interested in discussing with cowards acting
> > backward a nickname. Use your real name if you have the balls.
> > Alternatively, this discussion ends here and I wish you to fuck in
> > hell.
> >

> Whoever you are, you are trying to communicate with a typical
> Trump voter. No meaningful communication is possible. Forget it.
>
> Dirk Vdm

Actually, in my experience it's the other way around (in the US).

--
Jan

[Odd Bodkin]

Acquaintance with a real textbook would help. Or maybe you can just bonk
yourself on the head once you see it. If r is the distance between centers
of the bodies with mass m1 and m2, then r = r1 + r2, where r1 is the
distance from the first body to the center of mass, and r2 is the distance
from the second body to the center of mass. Since the center of mass is
collinear with the two bodies, no vector confusion arises.

>
> Your comment: "Thus the force on each mass varies inversely as the square
> of the distance from the fixed origin, and hence
> each of the masses follows an elliptical orbit with a focus at the center
> of mass of the two bodies, and there is zero precession"
>
> is not what I've read, when Kepler's Laws come into this picture. It's
> much complex than that. Kepler's first law states that
> every planet moves along an ellipse, with the Sun located at a focus of
> the ellipse. (see Fig. 13.16)

No, the center of mass is at the focus of the ellipse. If course, in
Kepler’s day, there was no measure of the masses so no way to distinguish
this.

>
>>> in the non-inertial reference frame of the Sun.
>> Both bodies follow non-precessing elliptical orbits in terms of the
>> celestial reference system, i.e., in reference to the directions of the
>> distant stars and galaxies. This is the relevant frame for quantifying
>> the precession (or, in this case, the absence of precession).
>
> This is NOT what Kepler Laws say. Nothing about distant stars and
> galaxies. Just two bodies and vectorial forms for
> forces and distances. On this paper about planetary motions, you'll find
> an expression for perihelion on elliptic orbits:
>
> https://www.math.ksu.edu/~dbski/writings/planetary.pdf
>
> In polar coordinates, being u(r,θ) = P/r (dimensionless), solving the
> differential equation d²u/dθ² + u = 1 gives
>
> P = r . (1 + e.cos θ) , with e: eccentricity of the ellipse and the
> perihelion on the positive x-axis (Equation 6), when θ = 0. In this
> equation, represents the angle of the perihelion with reference to a
> polar coordinate (r, θ) for a planetary motion centered in a
> focus (x=0, y=0) of the ellipse in cartesian coordinates.
>
> <snip>
>
>

--
Odd Bodkin -- maker of fine toys, tools, tables