What GR predicts for the perihelion advance of planets

[Paul B. Andersen]

The motions of the planets in the Solar system are simulated.
Each planet is simulated as a two body problem, planet - Sun.
The Newtonian gravitational acceleration is replaced by
the post-Newtonian approximation of the acceleration predicted by GR.

For each planet is the advance of the perihelion measured to
show what GR predicts the rate of perihelion advance would be
if the only existing bodies in the Universe were the planet
and the Sun.

https://paulba.no/pdf/GRPerihelionAdvance.pdf

https://paulba.no/PerihelionAdvance.html

--
Paul

https://paulba.no/

[Maciej Wozniak]

On Thursday, 14 October 2021 at 12:25:01 UTC+2, Paul B. Andersen wrote:
> The motions of the planets in the Solar system are simulated.

Sure; they are simulated in - a banned by your ideology euclidean
3 dimensional space with a non local, independent on observer
time. But you will impudently lie that the simulation is using
your GR shit.

[Kendale Gross]

great, now model the galaxy rotation without dark matter and dark energy.
Win that noble prize.

[Richard Hertz]

On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:

You can't use 2-Body calculations for each planet, to obtain a general result. So: what do you want to probe with your formulae?

The general equation for the N-Body problem is highly NON LINEAR, and imply to use about 8x7 formulae (Newton or GR) computed
along 100 years to obtain a true value of Mercury's perihelion shift. Not to mention the influence on other planets perihelion shift, with
the impact of the longest orbital period (Neptune).

Only by approximations, you add each 2-Body result to obtain 575.31 arcsec/Julian century for Mercury shift, as it was obtained in
this paper:

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft
Ryan S. Park, William M. Folkner, Alexander S. Konopliv, James G. Williams, David E. Smith, and Maria T. Zuber

The Astronomical Journal, 153:121 (7pp), © 2017 AAS
March https://doi.org/10.3847/1538-3881/aa5be2

--------------------------------- Excerpt from Page 6, Table 3 (simplified by me for this post) -------------------------------------------------------

Table 3
The Breakdown of Estimated Contributions and Uncertainties from the Planets, Asteroids, GE effect, LT effect, and
Solar Quadrupole Moment to the Precession Rate of Mercuryʼs Perihelion Computed in the coordinate Frame Defined
in Section 4 (i.e., along Mercuryʼs Mean Orbit Plane)

Mercury: 0.005 arcsec/century
Venus: 277.4176 arcsec/century
Earth/Moon: 90.8881 arcsec/century
Mars: 2.4814 arcsec/century
Jupiter: 153.9899 arcsec/century
Saturn: 7.3227 arcsec/century
Uranus: 0.1425 arcsec/century
Neptune: 0.0424 arcsec/century

Total for Newtonian gravity: 532.2896 arcsec/century

Gravitoelectric (Schwarzschild-like): 42.9799 arcsec/century

Total for GR gravity: 575.2695 arcsec/century

Total for other perturbations: 0.0405 arcsec/century

Total for Newtonian and non-Newtonian contributions: 575,31 arcsec/century

-------------------------------------------------------------------------- End of excerpt ------------------------------------------------------------------------------------------

In your case, the result of 2-Body results per orbit (rad/orbit) with your formula:


δφᵤ = 6π (GM)² /[G(M + mᵤ) aᵤ.(1 −eᵤ²) c²] = Σᵤ (6π.G.M²/c²)/[(M + mᵤ) aᵤ.(1 −eᵤ²)] , for u = 1, 2, 3, ....,8

dismiss the effects of the other bodies plus non-linear perturbations, which worsen as you go far away from the Sun and
closer to massive planets, which is a simplification in a HIGH DEGREE. In your Table 3: Perihelion advance of the planets

Mercury: 42.982717 "/century
Venus: 8.624984 "/century
Earth: 3.838873 "/century
Mars: 1.350975 "/century
Jupiter: 0.062276 "/century
Saturn: 0.013674 "/century
Uranus: 0.002382 "/century
Neptune 0.00077 "/century

It is evident that your result is ALMOST THE SAME as the Gravitoelectric effect (Schwarzschild-like): 42.9799 arcsec/century
that the quoted paper display in Table 3, but it doesn't imply that the effect on Mercury can be generalized as a 2-Body problem
for the rest of the planets.

If true, it could be solved with an ENIAC computer by 1945.

So, GR can be used to explain Mercury's perihelion advance but, unless an N-Body solution is used, it can't be generalized.

As far as I know, gravitational effects on the Solar System (with advanced solutions within agencies for Space Dynamics) are
calculated using discrete approximations in supercomputers. And this computation is beyond the "simplicity" of GR, when
complex perturbations have to be accounted.

And, at any case, Newton is more reliable than GR for PERMANENT CALCULATIONS of trajectories of Deep Space Sondes or
for Sondes sent to Mars, for instance.

Here is other paper, from a Russian physicist, who details the problems related above. He and his staff have more than 20 years
of experience on in research on the evolution of orbital and rotary movement of the Earth and planets. Watch the equations that
are used for numerical integration of the equations of interaction of N bodies under Newton’s law of gravity. The computer program
is recursive, with each run adapting parameters as time evolves. It's used for a finite number of loops, due to the time involved.


Gravitation, Field, and Rotation of Mercury Perihelion
Joseph J. Smulsky
Institute of the Earth Cryosphere of the Russian Academy of Sciences
Siberian Branch, Tyumen, RUSSIA

https://www.researchgate.net/publication/228428991_Gravitation_field_and_rotation_of_mercury_perihelion

QUOTE: "It is established that under the influence of Newtonian gravity, the perihelion turns in a motionless reference system by
529.9" per century, whereas the data of observation shows that it turns on 582.3" per century. In early work, the effect rotation
of the Sun on the movement of planets was not taken into account."

[Richard Hertz]

On Thursday, October 14, 2021 at 3:02:01 PM UTC-3, Richard Hertz wrote:

Typo corrected. Σᵤ should be there:

δφᵤ = 6π (GM)² /[G(M + mᵤ) aᵤ.(1 −eᵤ²) c²] = Σᵤ (6π.G.M²/c²)/[(M + mᵤ) aᵤ.(1 −eᵤ²)] , for u = 1, 2, 3, ....,8

It is, instead:

δφᵤ = 6π (GM)² /[G(M + mᵤ) aᵤ.(1 −eᵤ²) c²] = (6π.G.M²/c²)/[(M + mᵤ) aᵤ.(1 −eᵤ²)] , for u = 1, 2, 3, ....,8 (8 Planets)

[Kendale Gross]

you cant, you have to sum them up.

[Prokaryotic Capase Homolog]

On Thursday, October 14, 2021 at 1:02:01 PM UTC-5, Richard Hertz wrote:
> On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:
>
> You can't use 2-Body calculations for each planet, to obtain a general result. So: what do you want to probe with your formulae?

The simplest case, obviously. Anomalous precession does not require
additional planets to be manifest.

If you throw in all of the other planets, you get a lot of extra complexity
without really adding much in the way of extra insight:
https://drive.google.com/file/d/0B8XIf0XcrpOcSmdrY0VUVXh3dkE/view?usp=sharing&resourcekey=0-YaO_tG3fpDc5_KKg2zHmmQ

[Townes Olson]

On Thursday, October 14, 2021 at 3:25:01 AM UTC-7, Paul B. Andersen wrote:
> The motions of the planets in the Solar system are simulated.
> Each planet is simulated as a two body problem, planet - Sun.

A genuine two-body solution takes into account the motions of both bodies, relative to their center of mass. The formula you are using in your simulation isn't a two-body formula, it assumes the Sun is stationary and just describes geodesic trajectories around a single gravitating body. That's the one-body solution. (Also, note that if you actually performed a separate two-body solution for each planet, the Sun's motion would be different in each of those individual solutions, so they wouldn't be coherently accounting for the Sun's motion.) Naturally, you're comparing your simulation results with the one-body analytic solution (to the first order) of general relativity. For purposes of assessing the relativistic contribution to the precession to within observation precision, the analytic solution of the one-body problem suffices.

[Richard Hertz]

On Thursday, October 14, 2021 at 8:47:47 PM UTC-3, Townes Olson wrote:

<snip>

> A genuine two-body solution takes into account the motions of both bodies, relative to their center of mass. The formula you are using in your simulation isn't a two-body formula, it assumes the Sun is stationary and just describes geodesic trajectories around a single gravitating body. That's the one-body solution. (Also, note that if you actually performed a separate two-body solution for each planet, the Sun's motion would be different in each of those individual solutions, so they wouldn't be coherently accounting for the Sun's motion.) Naturally, you're comparing your simulation results with the one-body analytic solution (to the first order) of general relativity. For purposes of assessing the relativistic contribution to the precession to within observation precision, the analytic solution of the one-body problem suffices.

δφᵤ = (6π.G.M²/c²)/[(M + mᵤ) aᵤ.(1 −eᵤ²)] , for u = 1, 2, 3, ....,8}
δφᵥ = (6π.G.M²/c²)/[(M + mᵥ) aᵥ.(1 −eᵥ²)] , for v = 1, 2, 3, ....,8}

δφᵤ/δφᵥ = [(1 + mᵥ/M) aᵥ.(1 −eᵥ²)]/[(1 + mᵤ/M) aᵤ.(1 −eᵤ²)] ≈ [(1 + mᵥ/M) aᵥ ]/[(1 + mᵤ/M) aᵤ ] , for u,v > 1

Mercury: 1
Venus: 2
Earth: 3
Mars: 4
Jupiter: 5
Saturn: 6
Uranus: 7
Neptune 8

It can be seen that the influence of contiguous planets is, on average, high. So, maybe they can't be neglected so easily.

For example, the quotient between these two planets gives a ratio:

δφ₂/δφ₃ = 2.247 for Venus and Earth

δφ₃/δφ₄ = 2.842 for Earth and Mars

δφ₅/δφ₆ = 4.554 for Jupiter and Saturn


I might be wrong with this interpretation, which is roughly of very first order (and as average within 100 years period).

[Paul B. Andersen]

Den 15.10.2021 01:47, skrev Townes Olson:
> On Thursday, October 14, 2021 at 3:25:01 AM UTC-7, Paul B. Andersen wrote:
>> The motions of the planets in the Solar system are simulated.
>> Each planet is simulated as a two body problem, planet - Sun.
>>

>> https://paulba.no/pdf/GRPerihelionAdvance.pdf
>>
>> https://paulba.no/PerihelionAdvance.html

>
> A genuine two-body solution takes into account the motions of both bodies, relative to their center of mass. The formula you are using in your simulation isn't a two-body formula, it assumes the Sun is stationary and just describes geodesic trajectories around a single gravitating body. That's the one-body solution. (Also, note that if you actually performed a separate two-body solution for each planet, the Sun's motion would be different in each of those individual solutions, so they wouldn't be coherently accounting for the Sun's motion.) Naturally, you're comparing your simulation results with the one-body analytic solution (to the first order) of general relativity. For purposes of assessing the relativistic contribution to the precession to within observation precision, the analytic solution of the one-body problem suffices.
>

It is a two body _simulation_. It means that the motion
of each body is caused by the gravitational acceleration
from the other body.
So it is _obviously_ done in the centre of gravity frame.
Both bodies are moving in elliptic orbits around the barycentre
- of course.

https://paulba.no/pdf/GRPerihelionAdvance.pdf

If the acceleration of the planet according to equation (3) is a⃗,
then the acceleration of the Sun is -(m/M)⋅a⃗

Note however that the advance of perihelion is measured
relative to the Sun.

The point with the simulation is really to evaluate
the acceleration in equation (3). Since this
acceleration gives a perihelion advance so close to
the theoretical value, the conclusion is that
it is a very good approximation of the gravitational
acceleration predicted by GR.

I will use this in a simulation of the 9-body simulation
of the Solar system. (A much more complex task, obviously.)

A Newtonian simulation of the solar system can be seen here:

https://paulba.no/SolarSystem/SolarSystem.jar
https://paulba.no/SolarSystem/Results.pdf
https://paulba.no/SolarSystem/Screenshots.pdf
https://paulba.no/SolarSystem/SolarSystem.pdf

--
Paul

https://paulba.no/

[Maciej Wozniak]

On Friday, 15 October 2021 at 09:49:42 UTC+2, Paul B. Andersen wrote:

> It is a two body _simulation_. It means that the motion
> of each body is caused by the gravitational acceleration
> from the other body.

What a heresy is that, Paul, poor idiot? Your insane guru
has discovered and announced that gravitational
acceleration doesn't exist and free-falling objects
are inertial.

[Townes Olson]

On Friday, October 15, 2021 at 12:49:42 AM UTC-7, Paul B. Andersen wrote:
> It is a two body _simulation_. It means that the motion
> of each body is caused by the gravitational acceleration
> from the other body.

I guess one could call *anything* a two-body "simulation", including just treating it as a one-body problem. But, to be clear, the equation you're using is a one-body equation, in the sense that (as explained in your source) it is simply derived as an approximation to the paths of geodesics in Schwarzschild's solution around the Sun, which is purely a one-body solution. That's how it's used in your source, for comets and asteroids around the Sun. Now, although you didn't mention it in your write-up, you could alternately apply this equation (in terms of a naively defined but incoherent system of coordinates) first to an incremental motion of the planet in the Sun's field, and then to an incremental motion of the Sun in the planet's field (strictly two different coordinate systems), and you could call this a two-body simulation, but the whole reason there is no simple analytic two-body solution in general relativity is that it's non-linear, so solutions don't just "add up".

> So it is _obviously_ done in the centre of gravity frame.

You could add that to your write-up, and state that you are doing the alternate incremental procedure described above, and then provide some rationale (if you can think of one) for why this should be regarded as a valid "two-body simulation" with better accuracy than just using the Schwarzschild one-body solution (on which your equation is based).

> The point with the simulation is really to evaluate
> the acceleration in equation (3). Since this
> acceleration gives a perihelion advance so close to
> the theoretical value, the conclusion is that
> it is a very good approximation of the gravitational
> acceleration predicted by GR.

The fact that you reproduce the analytic *one-body precession* result to several significant digits doesn't lend support to the idea that this approach includes valid two-body effects. It's really just a plausibility argument confirming what we already knew, i.e., that the magnitude of the two-body effects for planets around the Sun is fairly negligible for purposes of evaluating the non-Newtonian precession.

[Richard Hertz]

On Friday, October 15, 2021 at 10:53:12 AM UTC-3, Townes Olson wrote:

<snip>

> The fact that you reproduce the analytic *one-body precession* result to several significant digits doesn't lend support to the idea that this approach includes valid two-body effects. It's really just a plausibility argument confirming what we already knew, i.e., that the magnitude of the two-body effects for planets around the Sun is fairly negligible for purposes of evaluating the non-Newtonian precession.

I think that the projection of the calculated precession for 1 orbit, as the original 1898 formula provides (rederived in 1915) to a 100 years
time lapse, with the multiplication of 1 orbit result by about 415 (orbits in 100 years) is also questionable since it has been proven recently
that such precession per orbit has random variations along time. So, a more serious study including other gravitational perturbations has
to be performed along a large enough number of Mercury's orbits, in order to obtain an approximation to the main value and its standard
dispersion. The final result can differ from the 43° written in stone since GR come out in Nov. 1915.

[Dono.]

On Friday, October 15, 2021 at 7:26:56 PM UTC-7, Richard Hertz wrote:
> The final result can differ from the 43° written in stone since GR come out in Nov. 1915.

Utter Imbecile

43°is MEASURED.

[Richard Hertz]

On Friday, October 15, 2021 at 11:30:01 PM UTC-3, Dono. wrote:

<snip>

>
> 43°is MEASURED.

As usual, you appear as an opinionated ignorant, even with a BsC in Mathematics and a PhD in EinsteinLand.

The most accurate measurements about Mercury perihelion were done by the MESSENGER (MErcury Surface, Space
ENvironment, GEochemistry, and Ranging) probe in orbit, between 2011 and 2015, about Mercury to estimate the
precession of Mercury’s perihelion, along with many other parameters related to the planet.

Results about Mercury perihelion SHIFT were projected for a century and are ABSOLUTE: 575.3100 ± 0.0015″/century.

MESSENGER wasn't used to PROVE GR. The result from 4 years measurements (16 orbits around the Sun) didn't provide
a differential value for non-newtonian calculations (Schwarzschild-like effects).

Given the ABSOLUTE VALUE of 575.3100 ± 0.0015″/century, in 2017 a team of scientists generated the following paper,
at which they TRY to breakdown the 575.31 value into its THEORETICALLY computed components. I posted the values
in a recent post but you, as a cretin, don't acknowledge that post.

Get the paper and read it:

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

Ryan S. Park, William M. Folkner, Alexander S. Konopliv, James G. Williams, David E. Smith, and Maria T. Zuber

(JPL, Caltech, NASA, MIT and Department of Earth, Atmospheric and Planetary Sciences). published 2017 February 21

I just post a summary of 3 subtotals (do your own work):

THEORETICAL COMPUTATION for Newtonian gravity (8 planets): 532.2896 ± 0.0008″/century
THEORETICAL COMPUTATION for Schwarzschild effect (Mercury): 42.9799 ± 0.0009″/century
THEORETICAL COMPUTATION for other perturbations (Newton): 0.0405 ± 0.0104″/century
----------------------------------------------------------------------------------------------------------------------------------------------------------
TOTAL PROJECTED value from MESSENGER mission 2011-2015: 575.3100 ± 0.0015″/century,

Do you UNDERSTAND? The most accuracy value measured on 4 years and projected to 100 years is the one above.

Only theoretical decomposition in EXACTLY 19 parameters was obtained by the teamwork. THEORETICAL!

And the contribution of GR (1 in 19) is based on the 1915 GR formula, presented by Einstein on Nov. 18, 1915 (his 43").

So, STOP being a jerk and assume it: nothing changed in 100 years. The 43" value is the one that Einstein presented that day.
In Einstein's words, on a translation ending his Nov. 18, 1915 paper about Mercury:

"This calculation leads to the planet Mercury to move its perihelion forward by 43 ′′ per century, while
the astronomers give 45 ′′±5′′, an exceptional difference between observation and Newtonian theory.
This has great significance as full agreement."

Now, try to DISPROVE both values (NASA 2017 and Einstein 1915), imbecile.

The famous and centenary 43" are A CALCULATION done by Einstein 105 years ago. And for JPL, NASA, MIT, Caltech, etc., nothing
has changed since then. And such a thing is extremely curious as it shows an effort to prove Einstein right one more time.

Who wrote the paper are suckers. All of them.

[Tom Roberts]

On 10/14/21 5:08 PM, Prokaryotic Capase Homolog wrote:
> If you throw in all of the other planets, you get a lot of extra
> complexity without really adding much in the way of extra insight:

Extra insight, perhaps not much. But if you want to actually TEST THE
THEORY, you must include all the planets, and even some large asteroids
-- many of them affect the precessions of perihelia more than the GR effect.

Tom Roberts

[Dono.]

On Friday, October 15, 2021 at 9:19:22 PM UTC-7, Richard Hertz wrote:
> On Friday, October 15, 2021 at 11:30:01 PM UTC-3, Dono. wrote:
>
> <snip>
>
> >
> > 43°is MEASURED.
>

> The famous and centenary 43" are A CALCULATION done by Einstein 105 years ago.

Stubborn imbecile,

43° was a measurement KNOWN since the times of LeVerrier (and even before him). Keep eating shit.

[Dono.]

https://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf

[Richard Hertz]

DONO: You are a disgrace as a lifeform and a pathetic and lame Einstein's pretorian guard.
He would spit in your face if he was alive.
You are a disgrace for everyone standing up to defend Einstein, due to your continuous tirade of lies.

Fucking retarded. I don't know how do you manage to live with yourself, but it might be your due punishment.

Now read this original, in custody by the University of Jerusalem, Princeton, Harvard and almost any site licensed to
post this document, presented by Einstein by Nov. 18, 1915, to the

Preussische Akademie der Wissenschaften,
Sitzungsberichte, 1915 (part 2), 831–839


Volume 6: The Berlin Years: Writings, 1914-1917 Page 242

https://einsteinpapers.press.princeton.edu/vol6-doc/270
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie.
Von A. Einstein.
..........................
"Die Rechnung liefert fur den Planeten Merkur ein Vorschreiten des Perihels um 43" in hundert Jahren, während die
Astronomen 45" ±5" als unerklärten Rest zwischen Beobachtungen und Newtonscher Theorie [17] angeben.
Dies bedeutet volle Übereinstimmung."
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Translation of this excerpt, the last part of such paper:
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Explanation of the perihelion movement of Mercury from the general theory of relativity.
By A. Einstein.
........................
"For the planet Mercury, the calculation yields an advance of the perihelion by 43" in a hundred years, while the
Astronomers state 45 "± 5" as the unexplained remainder between observations and Newton's theory [17].
This means full agreement. "
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

[Richard Hertz]

On Saturday, October 16, 2021 at 2:53:27 AM UTC-3, Dono. wrote:

<snip>

> > 43° was a measurement KNOWN since the times of LeVerrier (and even before him). Keep eating shit.
> https://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf

You and Pollock are two retarded of the same kind: a disgrace for humanity.

Even the formula (42) from Pollock is WRONG, imbecile both of you!

He wasn't even capable to copy the 1915 formula correctly. The formula (42) in Pollock's paper has 1/c missing
on the expression of precession.

Shame on you and shame on him.

IDIOTS!!!!


Formula from paper on Nov. 18, 1915

𝜖 = 24π³.a²/[c² . T². (1- e²)]

[Maciej Wozniak]

On Saturday, 16 October 2021 at 07:59:01 UTC+2, Richard Hertz wrote:
> On Saturday, October 16, 2021 at 2:33:26 AM UTC-3, Dono. wrote:
> > On Friday, October 15, 2021 at 9:19:22 PM UTC-7, Richard Hertz wrote:
> > > On Friday, October 15, 2021 at 11:30:01 PM UTC-3, Dono. wrote:
>
> <snip>
>
> > > > 43°is MEASURED.
> > >
> > > The famous and centenary 43" are A CALCULATION done by Einstein 105 years ago.
>
> > Stubborn imbecile,
> >
> > 43° was a measurement KNOWN since the times of LeVerrier (and even before him). Keep eating shit.
> DONO: You are a disgrace as a lifeform and a pathetic and lame Einstein's pretorian guard.
> He would spit in your face if he was alive.

He was actually quite similiar to Dono. There is an
interview, anyone opposing him was a fucken
antisemitist.

[Paul B. Andersen]

Den 14.10.2021 20:01, skrev Richard Hertz:
> On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:
>
> You can't use 2-Body calculations for each planet, to obtain a general result. So: what do you want to probe with your formulae?

https://paulba.no/pdf/GRPerihelionAdvance.pdf

If the only objects in the universe were a planet with
mass m and a star with mass M, and the planet and the star
were orbiting each other with semi-major axis a and
eccentricity e, then GR predicts that the perihelion
advance per orbit δϕ would be as shown in equation (8).

If we have a planet with mass m, and a star with mass M,
and the distance vector star->planet is r⃗ and the velocity of
the planet relative to the star is v⃗, then GR predicts that
the gravitational acceleration of the planet caused by
the star is a⃗ as shown in equation (3).

To test this equation, we can pretend that the only
objects in the universe are a planet with mass m
and a star with mass M, and make a two body simulation
where the acceleration of the planet is a⃗ , and the acceleration
of the star is -(m/M)⋅a⃗ . We can measure the perihelion
advance per orbit, and compare it with GR's prediction δϕ in eq.(8).

This is what I have done for all the planets, and the result
is that the accordance between the simulated values and eq.8
is very good for all the planets.

So what I have achieved is to show that equation (3)
is a very good approximation of the acceleration of
a planet caused by the Sun.

>
> The general equation for the N-Body problem is highly NON LINEAR, and imply to use about 8x7 formulae (Newton or GR) computed
> along 100 years to obtain a true value of Mercury's perihelion shift. Not to mention the influence on other planets perihelion shift, with
> the impact of the longest orbital period (Neptune).

Of course.
https://paulba.no/SolarSystem/SolarSystem.pdf
Equation (11) shows the Newtonian acceleration of object
number 'i' caused by all the other 8 objects in the solar system.

>
> Only by approximations, you add each 2-Body result to obtain 575.31 arcsec/Julian century for Mercury shift, as it was obtained in
> this paper:

I have done the Newtonian simulation.
The simulation:
https://paulba.no/SolarSystem/SolarSystem.jar
Some screenshots:
https://paulba.no/SolarSystem/Screenshots.pdf
The results:
https://paulba.no/SolarSystem/Results.pdf

If you look at the latter, you will see that according to
my simulation, the perihelion of advance of Mercury caused
by the Newtonian pull of the other planets is ≈ 532.3 "/century.
If you add 42.98 "/century, you get 475.28 "/century which
is very close to the value in the paper below, which includes
the relativistic effect.

>
> Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft
> Ryan S. Park, William M. Folkner, Alexander S. Konopliv, James G. Williams, David E. Smith, and Maria T. Zuber
>
> The Astronomical Journal, 153:121 (7pp), © 2017 AAS
> March https://doi.org/10.3847/1538-3881/aa5be2

Since adding the relativistic value to the Newtonian
value seems to give such a good value, I will make a new
simulation of the solar system where I use equation (3) in:
https://paulba.no/pdf/GRPerihelionAdvance.pdf
for the acceleration of the planet caused by the sun,
and equation (11) in:
https://paulba.no/SolarSystem/SolarSystem.pdf
for the acceleration caused by the other planets.


--
Paul

https://paulba.no/

[Maciej Wozniak]

On Saturday, 16 October 2021 at 09:35:59 UTC+2, Paul B. Andersen wrote:
> Den 14.10.2021 20:01, skrev Richard Hertz:
> > On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:
> >
> > You can't use 2-Body calculations for each planet, to obtain a general result. So: what do you want to probe with your formulae?
> https://paulba.no/pdf/GRPerihelionAdvance.pdf
>
> If the only objects in the universe were a planet with
> mass m and a star with mass M, and the planet and the star
> were orbiting each other with semi-major axis a and
> eccentricity e, then GR predicts that the perihelion
> advance per orbit δϕ would be as shown in equation (8).

Stop lying, trash. The model you've used for simulation
and prediction was euclidean with galilean time. Even
you are not stupid enough to try applying your idiocies
for real, you just pretend you do, for some ideological
reasons.

[Prokaryotic Capase Homolog]

That last is an interesting point. I hadn't realized...

[Paul B. Andersen]

I don't think the asteroids' contribution to the precession of
the perihelion of Mercury is very significant.

See Park & al: Precession of Mercury’s Perihelion from

Ranging to the MESSENGER Spacecraft

https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2/pdf

Table 3: estimated contribution from asteroids: 0.0012 "/century
The estimated total precession of Mercury's perihelion is:
575.3100±0.0015 "/century, so the contribution from the asteroids
is less than the uncertainty in the total precession.

The contribution may be a bit bigger for the planets closer
to the asteroid belt, but I think I will keep ignoring
the asteroids in my simulation of the Solar system.

It would however be a simple matter to include the biggest
asteroids Ceres, Vesta, Pallas and Hygiea (as long as I don't
measure their perihelion advance), so I will consider it.

--
Paul

https://paulba.no/

[Richard Hertz]

If you want to make an innovative contribution to the subject, instead of point-like masses (Schwarzschild 1st. 1916 paper),
try to use the Sun as a non-rotating sphere (Schwarzschild 2nd. 1916 paper), so you can deal with a more realistic scenario.
You can even dismiss the mass of Mercury and treat it as a test particle.

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

That would be new, instead of repeating Einstein-Schwarzschild work, that is 105 years old.

After all, if Schwarzschild could find such gravitational expression for the Sun one century ago, I don't see why you can't provide
an innovative way to see the problem in 2021.

I'm not even asking to use the rotation of the Sun, as Einstein-Besso did with his failed formula by 1913-1914.

Read the Einstein-Besso manuscript about the calculations. I wrote an OP in a thread with their name weeks ago.

[Dono.]

On Friday, October 15, 2021 at 11:13:02 PM UTC-7, Richard Hertz admitted:

> On Saturday, October 16, 2021 at 2:53:27 AM UTC-3, Dono. wrote:
>
> <snip>
> > > 43° was a measurement KNOWN since the times of LeVerrier (and even before him). Keep eating shit.
> > https://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf

> I, Richard Hertz, admit that I am retarded and a disgrace to humanity.

Yep

[carl eto]

Einstein is structurally unifying an electromagnetic field with a mass (m) using the inertial mass Eo/c2 (equ 52) since the formation of a light wave requires a medium (ether) composed of matter yet the ether does not physically exist (vacuum), In addition, the inertial mass is used to justify the electromagnetic ether but the inertial mass (m = Eo/c2) is massless since Eo represents the energy of an electromagnetic photon. Compton photon momentum (p = λ/h) is used to justify the inertial mass but experimentally, a 3 W laser beam or 1 W X-ray (dt = .1s) does not displace a gold foil which invalids Einstein concept the photon inertial mass.

[JanPB]

It makes no difference, just like in Newtonian theory certain relevant objects can be
considered FAPP pointlike.

> That would be new, instead of repeating Einstein-Schwarzschild work, that is 105 years old.

Not new, it has been done and found unimportant.

> After all, if Schwarzschild could find such gravitational expression for the Sun one century ago, I don't see why you can't provide
> an innovative way to see the problem in 2021.
>
> I'm not even asking to use the rotation of the Sun, as Einstein-Besso did with his failed formula by 1913-1914.
>
> Read the Einstein-Besso manuscript about the calculations. I wrote an OP in a thread with their name weeks ago.

Likewise, the frame dragging effect you are alluding to here is unimportant in this context.

Why do you forever assume that your insights had not been thought of and VERY
seriously considered before?

--
Jan

[veria buty]

"But as they gradually became convinced that none of the mechanical theories of ether provided a particularly impressive picture of electromagnetic phenomena, they got accustomed to considering the electric and magnetic fields as entities whose mechanical interpretation is superfluous. Thus, they have come to view theses fields in the vacuum as special states of the ether" (Einstein4, § 1).

[Richard Hertz]

On Saturday, October 16, 2021 at 2:39:06 PM UTC-3, JanPB wrote:

<snip>

> Why do you forever assume that your insights had not been thought of and VERY
> seriously considered before?

I repeat here a reply to Paparios that I posted recently, about physics, physicists and reality. Read it as a reply to your post.

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

On Saturday, October 16, 2021 at 11:00:25 AM UTC-3, Paparios wrote:

<snip>

> > > The real problem is you are not a physicist (I'm also not a physisist) so you have not a clue about how a physics model is built.
> > is fallacious, because it ties physics with a diploma and not with inquisitive minds in whichever field they decide to get involved.

<snip>

> Both institutes graduate students at the PhD level that will go to perform physics reasearch at the several physics laboratories and astronoica observatories, around the world.

> For sure, there are many people, like me, which loves physics and astronomy but that loving of science does not make me a physicists or astronomer.

Of course not, because they decided to pursue a CAREER as physicists and astronomers, as scientists with a DIPLOMA. That diploma
makes them PROFESSIONALS. There is a lot of people in the world (maybe ten of thousands) who love physics and astronomy as
much as professionals, but they don't have a DIPLOMA. They are called AMATEURS, and their contribution is RESPECTED within
scientific circles, being in astronomy where they reach the newspapers with some findings (either observational or experimental).

A very different specie are opinionated lovers of science (like you, me, Bodkin, Dono, JanPB, Moroney, etc..) who ONLY read, digest
and write here or at another site. They don't work actively in any field related to physics or astronomy, but their HOBBY is to learn
something and have an opinion (either supported by mathematics or just by a logical construction based on words).

So, you have PROFESSIONALS, AMATEURS and HOBBYISTS (the last being to lazy or cheap to do something during extended
periods of time). But NONE, NONE, of them OWN the truth (if there is a single one). Everyone can contribute to knowledge.

And any retarded here that negate such evident fact is just a jealous jerk, even when he/she is a professional, an amateur or a
hobbyist. And I call them RETARDED because of their intellectual RACISM, which causes them to put themselves above others
(without any merit) and are willing to defend their positions to death. It's like a fight between social classes (rich, poor and pretenders).

Physics is the field of free thoughts, not bounded to handbooks with formulae and examples of applied physics-math-chemistry and
engineering formulae and methodologies. This is what most technicians and engineers do in their entire lives, IF they work in the
experimental side of science and technology. MOST OF THEM are just technical bureaucrats, dealing with papers in a desk. If you
take any given big corporation (say Raytheon) and analyze the distribution of employees in fields of direct R&D, support to R&D,
documentation and presentation of R&D, and administrative support, you will find a ratio of 1:4:15:80.

You can have a fucking genius without a diploma working in the (1) zone, and a physicist with a BsC and two Masters working in the
(15) zone as a bureaucrat working with papers only. Not to mention many physicists working in the (4) zone, and even engineers and
physicists that got a job in the (80) zone. REALITY IS A BITCH.

On the other side, you are just a technician (not an engineer) but you couldn't afford to get a higher degree. Yet, you some an amazing
mind and you are curious. One day, you decide to study the efficiency of the use of energy in a SIMPLE AC MOTOR. You know basic
physics, math and EE and, being smart and after spending hundred of hours studying how it REALLY works, you find out that a lot of
energy is wasted without producing WORK. And you find that with a different re-wiring plus a capacitor in the right place, you raise
the efficiency of such motor from 85% to 95%. Are you an experimental physicist? Of course you are!

Only that, without a diploma, you are in the category of AMATEUR (Faraday and Tesla were, as an example).

Now, take such example of an amateur but physicist by heart, and apply it to the following fields:

- Sound
- Optics
- Electromagnetism
- Mechanics
- Heat and thermodynamics
- Astrophysics
- Quantum and nuclear physics
- Relativity
- Solid state physics and condensed matter

OF COURSE, the money involved to do something experimental is much higher in quantum and nuclear physics than in sound physics.
But INTELLIGENCE is something that money CAN'T BUY (not even lend). So, it's possible that a genius, being an amateur in 2021,
still can make contributions WITHOUT A DIPLOMA.

Because, at the root of it, physics is about HOW AND WHY nature works in any given way, either at an amateur lab or outdoors.

But, to make real contributions at any level (professional, amateur, hobbyist) requires commitment and hard and long work besides
the spark that intelligence provides (1% inspiration, 99% perspiration). You can do it on an improvised lab or on paper, and still apply.

What is VOID OF VALUE is to have the 1% inspiration and LET IT THERE, because you are not committed. Millions and millions of
events like this happens EVERY DAY, but we'll never know.

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

[veria buty]

The normalization of Schrodinger wave equation eliminates the atomic nucleus yet Schrodinger wave equation is used to derive the equations of the atomic orbitals. The box normalization eliminates the nucleus and depicts an electromagnetic wave that is oscillating within a hypothetic box. The electromagnetic wave resonating within a box does not require a nuclear charge and the nucleus is not part of Schrodinger wave equation. Also, Schrodinger resonating electromagnetic wave is replaced with an electron probability wave where the superpositioning (interference) of probability waves are used to form the equations of atomic orbitals but a position probability of an electron can only represent a positive value or zero and cannot depict a negative value that is required in representing destructive wave interference used to construct the atomic orbitals. Schrödinger complex conjugate is used to represent destructive wave interference of the electron probability waves (Schrödinger, p. 1066) but the result of the complex conjugate is the cancellation of positive vectors which is mathematically invalid and nullifies the derivation of the equations of the atomic orbitals.

[JanPB]

On Saturday, October 16, 2021 at 11:06:00 AM UTC-7, Richard Hertz wrote:
> On Saturday, October 16, 2021 at 2:39:06 PM UTC-3, JanPB wrote:
>
> <snip>
> > Why do you forever assume that your insights had not been thought of and VERY
> > seriously considered before?
> I repeat here a reply to Paparios that I posted recently, about physics, physicists and reality. Read it as a reply to your post.

I did and your post is irrelevant.

You repeatedly make naive and/or trivial points and present then as revelations
without ever stopping and asking yourself: wait, how is it possible nobody
had thought of it before? (Answer: they did, many times over.) Why do you
always behave like a child here?

--
Jan

[Prokaryotic Capase Homolog]

On Saturday, October 16, 2021 at 6:56:22 AM UTC-5, Paul B. Andersen wrote:

> The contribution may be a bit bigger for the planets closer
> to the asteroid belt, but I think I will keep ignoring
> the asteroids in my simulation of the Solar system.
>
> It would however be a simple matter to include the biggest
> asteroids Ceres, Vesta, Pallas and Hygiea (as long as I don't
> measure their perihelion advance), so I will consider it.

There is an exact solution for Gauss' ring approximation that
should be easy to apply and doesn't require computer programming.
https://www.mathpages.com/home/kmath280/kmath280.htm

If I have time, I'll set up my TI-89 calculator to get the Newtonian
contribution for these asteroids.

I've been extremely busy these last few weeks, however.... :-(

[Paul B. Andersen]

I suppose you are referring to equation (6) in the referred paper.
But this is the contribution to the perihelion advance of
Mercury only, and the contribution from all the asteroids
is only 0.0014 "/century. Ceres is a third of the mass in
the asteroid belt and its contribution would probably be in
the order of 0.0005 "/century. Negligible!

I was however wondering if Ceres possibly could affect
the perihelion advance of Mars who is closer to the asteroid belt.
But I am pretty sure it would be negligible, so I won't
bother to include Ceres in the simulation.

-----

Another matter is that equation (6) give the total Newtonian
advance from all bodies in the Solar system (Neptune and inside)
to be 549.7 "/century. I think this is way to much.

See the results from my simulation:
https://paulba.no/SolarSystem/Results.pdf
The perihelion advance is almost exactly equal to
the prediction of Park et al, 532.2 "/century.

And it is decreasing with time, as it should
according to Simon et al:
https://paulba.no/pdf/Simon.pdf

--
Paul

https://paulba.no/

[Richard Hertz]

Jan, one difference between us is that while you believe that I'm an idiot, I KNOW for certain that YOU are an idiot, and 10O% of
the time. You have no rest being an idiot, and not only here. It's on your DNA.

How can I know it? It only takes the effort to correlate most posts you wrote here, and your posts speak for you.

[JanPB]

On Sunday, October 17, 2021 at 1:43:25 PM UTC-7, Richard Hertz wrote:
> On Saturday, October 16, 2021 at 6:03:53 PM UTC-3, JanPB wrote:
> > On Saturday, October 16, 2021 at 11:06:00 AM UTC-7, Richard Hertz wrote:
> > > On Saturday, October 16, 2021 at 2:39:06 PM UTC-3, JanPB wrote:
>
> <snip>
>
> > > > Why do you forever assume that your insights had not been thought of and VERY seriously considered before?
> > > I repeat here a reply to Paparios that I posted recently, about physics, physicists and reality. Read it as a reply to your post.
>
> > I did and your post is irrelevant.
> >
> > You repeatedly make naive and/or trivial points and present then as revelations without ever stopping and asking yourself:
> > wait, how is it possible nobody had thought of it before? (Answer: they did, many times over.) Why do you
> > always behave like a child here?
> Jan, one difference between us is that while you believe that I'm an idiot, I KNOW for certain that YOU are an idiot, and 10O% of
> the time. You have no rest being an idiot, and not only here. It's on your DNA.

You are now repeating - yet again - the standard crank strategy here since 1995:
repeat my words.

> How can I know it? It only takes the effort to correlate most posts you wrote here, and your posts speak for you.

Stop posting nonsense. Simple.

--
Jan

[Prokaryotic Capase Homolog]

On Sunday, October 17, 2021 at 2:21:00 PM UTC-5, Paul B. Andersen wrote:

> I suppose you are referring to equation (6) in the referred paper.
> But this is the contribution to the perihelion advance of
> Mercury only, and the contribution from all the asteroids
> is only 0.0014 "/century. Ceres is a third of the mass in
> the asteroid belt and its contribution would probably be in
> the order of 0.0005 "/century. Negligible!
>
> I was however wondering if Ceres possibly could affect
> the perihelion advance of Mars who is closer to the asteroid belt.
> But I am pretty sure it would be negligible, so I won't
> bother to include Ceres in the simulation.

It certainly does seem negligible.

My original program had a factor-of-ten error in converting from
radians to arcseconds. I manually fixed the diagram here:
https://drive.google.com/file/d/0B8XIf0XcrpOcSmdrY0VUVXh3dkE/view?usp=sharing&resourcekey=0-YaO_tG3fpDc5_KKg2zHmmQ

> Another matter is that equation (6) give the total Newtonian
> advance from all bodies in the Solar system (Neptune and inside)
> to be 549.7 "/century. I think this is way to much.

The naive Gauss ring simulation presented in my illustration gave a
figure of 554.7 arcsec/century, which is fairly close to the Eq (6)
calculation. My figure was too high for several reasons:
1) My rings were coplanar with the ecliptic, when they should have
been tilted.
2) My rings were circular, when they should have been elliptical.
3) The rings were of uniform density. Instead, the rings should have
been less dense at perihelion then they were at aphelion.

When I repeated my Gauss calculation with non-coplanar, elliptical,
varying density rings, I got a number which was rather close to
Park's calculation. Likewise, when I repeated my N-body simulation
with non-coplanar orbits, my results were similar to Park's and to
yours.

Unfortunately, my results are sitting on a dead computer in my study.
I never had a chance to graph my raw output.

I am quite certain that LeVerrier did not do a naive Gauss calculation
with circular rings to achieve his figure of 526.7 arcsec/century. As
Kevin Brown noted, the naive uniform coplanar circular ring approximation
over-estimates the correct values.

> See the results from my simulation:
> https://paulba.no/SolarSystem/Results.pdf
> The perihelion advance is almost exactly equal to
> the prediction of Park et al, 532.2 "/century.

I see that you started with the complete set of ephemeris data. That I
didn't do; instead I started with the planets all lined up at t=0.

[Wayde Ring]

Prokaryotic Capase Homolog wrote:

>> I was however wondering if Ceres possibly could affect the perihelion
>> advance of Mars who is closer to the asteroid belt.
>> But I am pretty sure it would be negligible, so I won't bother to
>> include Ceres in the simulation.
>

> My original program had a factor-of-ten error in converting from radians
> to arcseconds. I manually fixed the diagram here:
> https://drive.google.com/file/d/0B8XIf0XcrpOcSmdrY0VUVXh3dkE/view?
usp=sharing&resourcekey=0-YaO_tG3fpDc5_KKg2zHmmQ

ohh my, the uneducated retard, bill gaytes, ate the biggest 4 star
general in history, Colin Powell, just by believing in fraudci
"science"!! What an idiot, and just think at the friends he had.

[Richard Hertz]

On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:
> The motions of the planets in the Solar system are simulated.
> Each planet is simulated as a two body problem, planet - Sun.
> The Newtonian gravitational acceleration is replaced by
> the post-Newtonian approximation of the acceleration predicted by GR.
>
> For each planet is the advance of the perihelion measured to
> show what GR predicts the rate of perihelion advance would be
> if the only existing bodies in the Universe were the planet
> and the Sun.
>
> https://paulba.no/pdf/GRPerihelionAdvance.pdf
>
> https://paulba.no/PerihelionAdvance.html
>
> --
> Paul
>
> https://paulba.no/

The formula (8) on the paper is equal to Einstein's Eq. 13 (paper Nov. 18, 1915)

(Equation 13) ε = + 3π α/[a (1 – e²)]

with an error lower than 1.6E-07

[Dono.]

On Saturday, November 20, 2021 at 11:23:18 PM UTC-8, Richard Hertz wrote:
> On Thursday, October 14, 2021 at 7:25:01 AM UTC-3, Paul B. Andersen wrote:
> > The motions of the planets in the Solar system are simulated.

> > https://paulba.no/
>
> The formula (8) on the paper is equal to Einstein's Eq. 13 (paper Nov. 18, 1915)
>
> (Equation 13) ε = + 3π α/[a (1 – e²)]
>
> with an error lower than 1.6E-07

So, you have been eating (a lot) of shit all along.

[Paul B. Andersen]

https://tinyurl.com/yzzbratp

>
> (Equation 13) ε = + 3π α/[a (1 – e²)]
>
> with an error lower than 1.6E-07
>

Or equation (14): ε = 24π³a²/T²c²(1−e²)

This is the equation you will find in many books and papers.

T² = 4π²a²/GM (1)
where T is the period of a test particle in orbit
around a mass M. a is the semi-major axis.

My equation (8): ε = 6π(GM)²/G(M+m)a(1−e²)c²

If we in this equation set (GM)²/G(M+m) ≈ GM when m/M << 1
and from (1): GM = 4π²a²/T²
we get the equation: ε ≈ 24π³a²/T²c²(1−e²)
which is the same as Einstein's equation (14)

The difference is that Einstein's equation (the equation commonly used)
is the perihelion advance of a test particle in orbit around a mass M,
while my equation (8) is the perihelion advance of a mass m in orbit
around a mass M.

The relative difference is (as you said):
((GM)²/G(M+m) - GM)/GM = -1.66E-7
which obviously is negligible, probably less than the precision
of G, M and m.

That's why Einstein's equation (14) safely can be used.


BTW, thanks for a sensible post.
You haven't produced many of those lately.

--
Paul

https://paulba.no/

[Maciej Wozniak]

In the meantime in the real world, however, forbidden by
your moronic religion GPS clocks keep measuring t'=t,
just like all serious clocks always did.

[Richard Hertz]

You're welcome, Paul.

[Ross A. Finlayson]

"Ceres is a third of the mass in

the asteroid belt "...

I'll be damned I didn't get that impression in terms of the
contents of the solar orbit between Earth and Mars and
between Mars and Jupiter.

" Orbital resonances occurred where the orbital period of an object in the belt formed an integer fraction of the orbital period of Jupiter, perturbing the object into a different orbit; the region lying between the orbits of Mars and Jupiter contains many such orbital resonances"

"The article on resonant interactions describes resonance in the general modern setting. A primary result from the study of dynamical systems is the discovery and description of a highly simplified model of mode-locking; this is an oscillator that receives periodic kicks via a weak coupling to some driving motor. The analog here would be that a more massive body provides a periodic gravitational kick to a smaller body, as it passes by. The mode-locking regions are named Arnold tongues. "


https://en.wikipedia.org/wiki/Arnold_tongue


Then it seems the Allais effect, in the Arnold tongues,
here is that the tongue is the setting what effects mass
equivalencies what otherwise would be distant,in passing.
(The two tongues, the Arnold tongue.)

I.e., it's two of the three principal components, what reflect
the either of the two terms gravitational and crossing,
what that otherwise the space is non-component.

While it is component....

Train and draft for example: here is for simple notes in terms.

Attaining orbit or otherwise for effecting landing in passing,
here is attaining orbit from outside besides the usual to orbit,
the "from" orbit.

It surprised me that orbits were elliptical then even highly elliptical.

The syzygy's usually identified the Sun, planet, planet crossing.

Then Sun, planet, Earth, and Sun, Earth, Moon make eclipses,
also what result in the optical that the chance of a total eclipse
is small.

Otherwise that the planets are usually or "for the entire
forseeable future", reasonably spaced and stable in their
orbits, it's a usually expected thing besides this "50 AU's ,
not 80 or 100, out to Jupiter."

I notice that you have written this and read it.

https://paulba.no/pdf/GRPerihelionAdvance.pdf

[Ross A. Finlayson]

I wonder how mass is computed except in terms of the solar orbits
and the stellar mass.

There's basically wobble it seems for usual occlusions to
estimate body's masses in terms of their estimates of
position and direction or images.