On Saturday, October 16, 2021 at 8:56:22 AM UTC-3, Paul B. Andersen wrote:
> Den 16.10.2021 07:03, skrev 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
> 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/

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.

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

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.

On Saturday, October 16, 2021 at 8:45:58 AM UTC-7, Richard Hertz wrote:
> On Saturday, October 16, 2021 at 8:56:22 AM UTC-3, Paul B. Andersen wrote:
> > Den 16.10.2021 07:03, skrev 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
> > 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/
> 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

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

"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).

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.

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

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.

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

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.... :-(

Den 17.10.2021 07:55, skrev 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.... :-(
>

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/

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.

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

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

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.

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 states, the naive ring approximation over-estimates the
correct values.
> See the results from my simulation:
> https://paulba.no/SolarSystem/Results.pdf

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.

> 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

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

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.

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" rel="nofollow" target="_blank">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

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.

Den 21.11.2021 08:23, skrev 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" rel="nofollow" target="_blank">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)

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/

On Sunday, 21 November 2021 at 20:12:42 UTC+1, Paul B. Andersen wrote:
> Den 21.11.2021 08:23, skrev 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" rel="nofollow" target="_blank">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)
> 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.

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.

On Sunday, November 21, 2021 at 4:12:42 PM UTC-3, Paul B. Andersen wrote:
> Den 21.11.2021 08:23, skrev 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" rel="nofollow" target="_blank">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)
> 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/

You're welcome, Paul.

On Sunday, November 21, 2021 at 11:43:13 AM UTC-8, Richard Hertz wrote:
> On Sunday, November 21, 2021 at 4:12:42 PM UTC-3, Paul B. Andersen wrote:
> > Den 21.11.2021 08:23, skrev 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" rel="nofollow" target="_blank">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)
> > 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/
> You're welcome, Paul.

"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

On Sunday, November 28, 2021 at 4:38:29 PM UTC-8, Ross A. Finlayson wrote:
> On Sunday, November 21, 2021 at 11:43:13 AM UTC-8, Richard Hertz wrote:
> > On Sunday, November 21, 2021 at 4:12:42 PM UTC-3, Paul B. Andersen wrote:
> > > Den 21.11.2021 08:23, skrev 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" rel="nofollow" target="_blank">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)
> > > 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/
> > You're welcome, Paul.
> "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

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.