The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: TheMatrix on October 21, 2019, 09:35:14 PM

FE Wiki rather vagely describes the stars as 'luminous elements'. Anyone on the FE side care to elaborate on what that means a bit? What causes them to be luminous, how far away are they and why are some brighter than others?

space is invisible minddust and stars are wishes
I could not say it better my self 8)

If I was after a purely poetic reply then that would be perfect.
Lets now try for a reply that actually tells me sonething useful.

If I was after a purely poetic reply then that would be perfect.
Lets now try for a reply that actually tells me sonething useful.
There are a lot of FE models. The twinkling things in the night sky could be described very differently based on the different FE models:
1. They could be described as luminous elements
2. They could be described as giant balls of gas generating heat and light
3. They could be described as pieces of heaven in a more biblical FE model

Well out of those three I would imagine that FE theorists would favour 1 and 3 since they are based on nothing more than fantasy or faith.
The twinking effect of course has got nothing to do with the stars themselves but is due to the turbulent atmosphere. The twinkling effect is greatest for stars low down near the horizon as they light from those is passing through a thicker later of atmosphere based on the location of the observer.
I understand that the astrophysical account of the nature of the stars will be largely incompatible with the FE view of the stars and so most of that will be dismissed. However you cannot argue with direct observations and there has been more than enough research carried out into the nature of starlight to understand that the stars are indeed balls of gas which are self energising.

How come , using direct observation , the planets don't twinkle ? Doesn't their weak reflected light travel through the turbulent atmosphere ?

Because planets have measurable disks. Stars are point sources of light owing to their great distance compared to their size. Therefore all the light from a star is coming from the same spot on the sky which as you will appreciate is a lot more prone to turbulent distortion than a planet is where the light is spread over a small but nonpoint source. Any source of light on the sky which is not a point source is known as an extended object.
The pockets or bubbles of air which are continually moving around in the air (along very short mean free paths) are smaller than the sizes of planetary disks and so the light from the is not affected by them in the same way.

Waffle .
Here's an attempt at a proper explanation .
https://earthsky.org/space/whydontplanetstwinkleasstarsdo

So what is different about what your link says and what I said? Take two lines from your link for example and compare with what I said. I think you will find its the same. I use slightly different words but that doesn't alter the meaning.
Stars twinkle because … they’re so far away from Earth that, even through large telescopes, they appear only as pinpoints.
Planets shine more steadily because … they’re closer to Earth and so appear not as pinpoints, but as tiny disks in our sky.
Anyway, what has that got to do with my original question... what are the stars according to FE theorists?

You presented your explanation as established fact . Read the article I linked properly  that explanation uses the word "might " in it's explanation that light traveling from different edges of a planet may due to a "zigzag" effect cancel refraction . That is theory because science cannot find a satisfactory explanation .
The stars are near but out side ,or part of the dome , the planets sun and moon are luminaries and are inside the dome  that's the simple explanation why they don't twinkle . That's one FE view .

Waffle .
Here's an attempt at a proper explanation .
https://earthsky.org/space/whydontplanetstwinkleasstarsdo
Your link literally agreed with the post you are arguing against.

That is theory because science cannot find a satisfactory explanation .
First, you obviously do not know what "theory" means in science.
Second, about satisfactory explanations:
A) You'd need a definition in order to identify one
B) Please offer a definition that can make even the slightest sense of the FE wiki.

You presented your explanation as established fact . Read the article I linked properly  that explanation uses the word "might " in it's explanation that light traveling from different edges of a planet may due to a "zigzag" effect cancel refraction . That is theory because science cannot find a satisfactory explanation.
I think you read the article wrong. Here.
You might think of it as the light traveling a zigzag path to our eyes, instead of the straight path the light would travel if Earth didn’t have an atmosphere.
She's not expressing doubt, this is a well understood phenomenon. She's simplifying it so it might be easier to understand to those unfamiliar with the concepts. She uses 'Might' three times in the article. That was the first time. Here's the second:
You might see planets twinkling if you spot them low in the sky. That’s because, in the direction of any horizon, you’re looking through more atmosphere than when you look overhead.
Interestingly points out a flaw in the claim that planets don't twinkle. The third:
Experienced observers often can, but, at first, if you can recognize a planet in some other way, you might notice the steadiness of its light by contrasting it to a nearby star.
Neat article. Thanks for posting it. :)
Addendum: missed one, and it looks like this is the one you were talking about.
But – while the light from one edge of a planet’s disk might be forced to “zig” one way – light from the opposite edge of the disk might be “zagging” in an opposite way. The zigs and zags of light from a planetary disk cancel each other out, and that’s why planets appear to shine steadily.
Although the use of the word 'might' still isn't used to cast doubt on the concept itself. The article even points out that planets can still twinkle if viewed closer to the horizon, meaning that sometimes the refraction is severe enough that they won't cancel each other out.

You presented your explanation as established fact . Read the article I linked properly  that explanation uses the word "might " in it's explanation that light traveling from different edges of a planet may due to a "zigzag" effect cancel refraction . That is theory because science cannot find a satisfactory explanation.
I think you read the article wrong. Here.
You might think of it as the light traveling a zigzag path to our eyes, instead of the straight path the light would travel if Earth didn’t have an atmosphere.
She's not expressing doubt, this is a well understood phenomenon. She's simplifying it so it might be easier to understand to those unfamiliar with the concepts. She uses 'Might' three times in the article. That was the first time. Here's the second:
You might see planets twinkling if you spot them low in the sky. That’s because, in the direction of any horizon, you’re looking through more atmosphere than when you look overhead.
Interestingly points out a flaw in the claim that planets don't twinkle. The third:
Experienced observers often can, but, at first, if you can recognize a planet in some other way, you might notice the steadiness of its light by contrasting it to a nearby star.
Neat article. Thanks for posting it. :)
Addendum: missed one, and it looks like this is the one you were talking about.
But – while the light from one edge of a planet’s disk might be forced to “zig” one way – light from the opposite edge of the disk might be “zagging” in an opposite way. The zigs and zags of light from a planetary disk cancel each other out, and that’s why planets appear to shine steadily.
Although the use of the word 'might' still isn't used to cast doubt on the concept itself. The article even points out that planets can still twinkle if viewed closer to the horizon, meaning that sometimes the refraction is severe enough that they won't cancel each other out.
Here is another nice article  a bit more scientific and less confusing .
http://curious.astro.cornell.edu/aboutus/58oursolarsystem/planetsanddwarfplanets/planetwatching/251whydoplanetsnottwinkleintermediate
The assistant professor of physics and physical science (at the time of writing ) states a bit more specifically that " No , planets never twinkle to the naked eye for exactly this reason ." in his explanation for this fact .
Of course any luminary would twinkle when distant and very low near the horizon ,especially on the plane or seen through say the exhaust of a rocket or jet .
I would like to point out that according to science planetary light is sunlight reflected from a distant sun and obeying the laws optics , reflection of light rays from a spherical object is a big problem for these explanatory theories , spherical bodies scatter light . Unless the planets are luminaries and close by , as in FE theory .

I would like to point out that according to science planetary light is sunlight reflected from a distant sun and obeying the laws optics , reflection of light rays from a spherical object is a big problem for these explanatory theories , spherical bodies scatter light.
I’m unclear why you think this is a problem.
The problem with the planets being close is we have radar measurements and can use parallax to demonstrate they are not.
And the problem with them being luminaries is we observe phases and moons casting shadows on them.

I would like to point out that according to science planetary light is sunlight reflected from a distant sun and obeying the laws optics , reflection of light rays from a spherical object is a big problem for these explanatory theories , spherical bodies scatter light .
Well, when you observe a beach ball in daylight at the beach you are observing sunlight from a distant sun being reflected off a spherical object. So why does this become a problem if the sphere is bigger, like the moon or Jupiter?

He’s mentioned a hot spot before which I have dealt with but just in case he does again, that is a feature of a smooth, reflective surface, not a rough terrain like a moon or planet.

So , we now see there is no heliocentric model explanation for the fact that the planets do not twinkle , only an unsatisfactory theory  which includes the word "might" and requires light rays , from the outer edges of the planets , to be focused .

So , we now see there is no heliocentric model explanation for the fact that the planets do not twinkle
Well, there actually is. The size subtended by planets to viewers on earth is large compared to the tiny distortions caused by the slight turbulence between areas of different density in the atmosphere. Therefore those distortions make no visible difference to how we observe them (at least to the naked eye and even small telecscopes). It is as simple as that. Stars are true point sources of light that are smeared and appear to wobble and change size (and hence brightness) by those same tiny distortions. They twinkle.

So , we now see there is no heliocentric model explanation for the fact that the planets do not twinkle
You have to be trolling at this point.
You literally posted a link above with the explanation (strangely, you did so replying to disagree with a post giving you that exact explanation). By the very nature of twinkling it implies the effects of a chaotic atmosphere, the word “might” reflects that. The light might do one thing or another, it depends on the atmospheric effects which change over time, hence the twinkling.
And I see you are doing the tired FE thing of trying to poke holes in the heliocentric model (as usual, because of your failure to understand it) while ignoring the huge chasms and contradictions in your own “model”.

Twinkling does not imply a chaotic atmosphere at all , or the planets would twinkle since their weak reflective light has to travel through the atmosphere according to the model.
You , and science are unable to explain this phenomena  which is why the word "might" is used in the explanation. I show you a link where it is clearly stated that planets do not twinkle .
I do not need to poke holes in the heliocentric theory . The holes are everywhere . You are unable to accept them for what they are , which is why you end up mincing words , or changing the direction of the thread .

Twinkling does not imply a chaotic atmosphere at all , or the planets would twinkle since their weak reflective light has to travel through the atmosphere according to the model.
Your poor comprehension skills do not constitute a disproof of anything. To imply the atmosphere is not subject to chaotic behavior is to deny weather. Maybe it's possible you live in an area that has never had strong buffeting wind or a thunder storm, or even clouds in the sky but you must have heard of them.
You can find hundreds of online explanations as to why stars twinkle and planets do not. Some better than others, but all essentially saying the same thing. Most do not include the word 'might'. Like this one you provided: http://curious.astro.cornell.edu/aboutus/58oursolarsystem/planetsanddwarfplanets/planetwatching/251whydoplanetsnottwinkleintermediate (http://curious.astro.cornell.edu/aboutus/58oursolarsystem/planetsanddwarfplanets/planetwatching/251whydoplanetsnottwinkleintermediate)
Your finding one that was badly worded and interpreting that as meaning it and all the others are wrong is astonishing.

Are you unable to think clearly ? I do not imply anything about the atmosphere . The stars always twinkle whether there are "chaotic" (as you put it ) conditions or not . The planets do not ever . The link I gave was written by a scientist . What is your problem with that ? Doesn't fit your agenda?
The fact that you have found hundreds of online explanations says it all . There is no explanation . Heliocentrism in a nut shell .
Explained with simplicity in FE theory .

The fact you think that the atmosphere is only chaotic sometimes just shows your complete lack of understanding.
Can you please provide the FE explanation, including the explanation of observed phases of planets and their moons casting shadows on them.

The link I gave was written by a scientist . What is your problem with that ? Doesn't fit your agenda?
Right, and the one that you provided that I reposted was also written by a scientist and it does not use the word "might".
The fact that you have found hundreds of online explanations says it all .
All the ones I found give the SAME explanation.
Heliocentrism in a nut shell .
You do know what the term "nut shell" means, don't you?
Explained with simplicity in FE theory .
Please, go right ahead.
Also, what's with the 'space comma', 'space period' and 'space question mark'? Is there a problem with your keyboard?

The fact you think that the atmosphere is only chaotic sometimes just shows your complete lack of understanding.
Can you please provide the FE explanation, including the explanation of observed phases of planets and their moons casting shadows on them.
Have a look at the Tycho Brahe geocentric model , a supposed advancement of the Ptolemaic model . You will find that all observations of planetary phase and motion were explained within these models in which the earth is stationary .
The heliocentric model brought no new observation or experiment which required the sun to be at the system's centre and earth in motion . Science still has not verified the assumptions of motion or curvature .
Stars are small , not distant and they scintillate . Planets are nearer and are luminaries within the reaches of the atmosphere which is why they do not scintillate ever .
Science cannot explain how Saturn reflects sunlight which after travelling 9.5 AU is then scattered and a minute amount can travel a further 8.5 AU back to earth , through the van Allen belts and our light scattering atmosphere and produce stable image which we can see with the naked eye . Same for all planets.
Your nonsense about what you say I think or have stated about the atmosphere is irrelevant and a diversionary tactic .

Have a look at the Tycho Brahe geocentric model , a supposed advancement of the Ptolemaic model . You will find that all observations of planetary phase and motion were explained within these models in which the earth is stationary.
And his explanation of phases was, surely, the same as the heliocentric model's  that the planets are not "luminaries", they are objects being lit by a light source, the sun. Luminaries do not have shadows or phases as we see on the moon or the inner planets.
The heliocentric model brought no new observation or experiment which required the sun to be at the system's centre and earth in motion. Science still has not verified the assumptions of motion or curvature.
Then why is that the prevailing scientific view? Obviously the hundreds of people who have been to space can attest to the shape of the earth, amateurs with balloons can demonstrate curvature. The evidence for motion is things like the the Coreolis effect and the good people at Globebusters managed to measure the 15 degree per hour drift caused by the earth's rotation.
Stars are small , not distant and they scintillate . Planets are nearer and are luminaries within the reaches of the atmosphere which is why they do not scintillate ever.
Evidence?
Science cannot explain how Saturn reflects sunlight which after travelling 9.5 AU is then scattered and a minute amount can travel a further 8.5 AU back to earth , through the van Allen belts and our light scattering atmosphere and produce stable image which we can see with the naked eye .
Is this really something science something cannot explain or just something you cannot understand?
Can we agree that the sun is quite bright? You literally can't look at it safely. And that's at 1 AU. So yeah, obviously it will be dimmer at 9.5 AU but still very much visible and Saturn has an albedo of about 0.5, it reflects about half of the light back. And Saturn is very big. So the fact Saturn is visible with the naked eye is not a mystery.
Same for all planets.
Well no, not all planets because the outer planets are further away and smaller and have a lower albedo (although still quite high) and can't be seen with the naked eye. But yes, with the right equipment they can be seen for the exact same reason Saturn can.
Your nonsense about what you say I think or have stated about the atmosphere is irrelevant and a diversionary tactic .
It's completely relevant. It shows your lack of understanding. Basing beliefs on ignorance leads you to the wrong conclusions.
If you think the atmosphere is only chaotic at times then you don't understand what the term means in this context.

The fact you think that the atmosphere is only chaotic sometimes just shows your complete lack of understanding.
Can you please provide the FE explanation, including the explanation of observed phases of planets and their moons casting shadows on them.
Implying the atmoplane is in constant chaos?
Am I reading your statement correctly?

Implying the atmoplane is in constant chaos?
The atmosphere is in constant chaos. It is the poster child for chaos theory. In physics a chaotic system is one where predictability at a fine scale is difficult or impossible such that the behavior of the system seems random and is easily perturbed. For instance, you can never predict the instantaneous direction of velocity of the wind, no matter how energetic, nor the shape of a cloud, or the exact temperature or humidity of the air at a particular spacetime coordinate. Even bulk predictions are almost impossible. Witness the inaccuracy of longer term weather forecasts despite that the worlds largest and most powerful computers are employed to the task. Short term forecasts are based on the direction and speed of travel of existing weather (it's sunny in St. Louis today, so it will likely be sunny in Raleigh tomorrow), but even those predictions can be far off the mark.

Have a look at the Tycho Brahe geocentric model , a supposed advancement of the Ptolemaic model . You will find that all observations of planetary phase and motion were explained within these models in which the earth is stationary.
And his explanation of phases was, surely, the same as the heliocentric model's  that the planets are not "luminaries", they are objects being lit by a light source, the sun. Luminaries do not have shadows or phases as we see on the moon or the inner planets.
The heliocentric model brought no new observation or experiment which required the sun to be at the system's centre and earth in motion. Science still has not verified the assumptions of motion or curvature.
Then why is that the prevailing scientific view? Obviously the hundreds of people who have been to space can attest to the shape of the earth, amateurs with balloons can demonstrate curvature. The evidence for motion is things like the the Coreolis effect and the good people at Globebusters managed to measure the 15 degree per hour drift caused by the earth's rotation.
Stars are small , not distant and they scintillate . Planets are nearer and are luminaries within the reaches of the atmosphere which is why they do not scintillate ever.
Evidence?
Science cannot explain how Saturn reflects sunlight which after travelling 9.5 AU is then scattered and a minute amount can travel a further 8.5 AU back to earth , through the van Allen belts and our light scattering atmosphere and produce stable image which we can see with the naked eye .
Is this really something science something cannot explain or just something you cannot understand?
Can we agree that the sun is quite bright? You literally can't look at it safely. And that's at 1 AU. So yeah, obviously it will be dimmer at 9.5 AU but still very much visible and Saturn has an albedo of about 0.5, it reflects about half of the light back. And Saturn is very big. So the fact Saturn is visible with the naked eye is not a mystery.
Same for all planets.
Well no, not all planets because the outer planets are further away and smaller and have a lower albedo (although still quite high) and can't be seen with the naked eye. But yes, with the right equipment they can be seen for the exact same reason Saturn can.
Your nonsense about what you say I think or have stated about the atmosphere is irrelevant and a diversionary tactic .
It's completely relevant. It shows your lack of understanding. Basing beliefs on ignorance leads you to the wrong conclusions.
If you think the atmosphere is only chaotic at times then you don't understand what the term means in this context.
Mercury and Venus orbit the Sun which gives them their phases  they are moons of the Sun which orbits the earth , geocentric model , or circles the earth plane in FE . Have you not looked at the geocentric model . They are the only two planets which don't have moons , another problem for the heliocentric model .
Present the scientific peer reviewed papers of globebusters proving rotation or curvature and stop waffling about chaos and the atmosphere .We all know about the weather and chaos . Still don't make the planets twinkle .
If you want real chaos then investigate the effect of chaos theory and the nbody problem associated with the orbits in the solar system model .

Sorry, how is Venus and Mercury not having moons a problem for any model?

Explained with simplicity in FE theory .
This explanation is still pending. Use FE theory to explain by derivation from theory why stars scintillate and planets do not. Just saying stars do and planets do not is not explaining anything, it is merely making an empty statement.
For RE theory, including the chaotic nature of the atmosphere is an essential part of the derivation. It is the mechanism in RE theory that makes the stars scintillate and their tiny (point source) size is what allows small chaotic motions in the atmosphere produce this effect. As I said before, planets still do experience the effects of the chaotic nature of the atmosphere, but they are large enough that these effects appear to cancel out when viewed by the human eye, or even a toy telescope. Viewed through the Mount Palomar scope with a high resolution, high speed sensor and you will record the planets shimmering.

luminious elements? perhaps neon. Some flat earth models allow for gravity, so perhaps neon grouped due to gravity. for models without gravity, perhaps supernatural forces cause them to cluster?

Mercury and Venus orbit the Sun which gives them their phases  they are moons of the Sun which orbits the earth , geocentric model , or circles the earth plane in FE.
Can you provide some evidence for that claim? I've asked you a few times for evidence of your wild assertions, you have yet to provide any.
Present the scientific peer reviewed papers of globebusters proving rotation or curvature
Well, Globebusters are FE and therefore don't publish papers or get them peer reviewed. I have provided evidence for rotation and curvature, you have provided no evidence for any of your claims.
We all know about the weather and chaos . Still don't make the planets twinkle.
The reason for this has been explained to you. You then basically posted "nuhuh" and then provided a link which explained it in exactly the way you just said was wrong.
And yes, the chaotic atmosphere is part of the explanation. A chaotic system means something in mathematics.
If you want real chaos then investigate the effect of chaos theory and the nbody problem associated with the orbits in the solar system model.
Yes. This is another example of a chaotic system. As is a double pendulum. Just because the future of a system cannot be perfectly predicted with our current models, doesn't mean the models are not useful. It's a bit of a leap from "you can't model the 'n' body problem perfectly" to "the earth is flat.

Implying the atmoplane is in constant chaos?
The atmosphere is in constant chaos. It is the poster child for chaos theory. In physics a chaotic system is one where predictability at a fine scale is difficult or impossible such that the behavior of the system seems random and is easily perturbed. For instance, you can never predict the instantaneous direction of velocity of the wind, no matter how energetic, nor the shape of a cloud, or the exact temperature or humidity of the air at a particular spacetime coordinate. Even bulk predictions are almost impossible. Witness the inaccuracy of longer term weather forecasts despite that the worlds largest and most powerful computers are employed to the task. Short term forecasts are based on the direction and speed of travel of existing weather (it's sunny in St. Louis today, so it will likely be sunny in Raleigh tomorrow), but even those predictions can be far off the mark.
I agree that portions of the atmoplane are in chaos at any given point.
This explains, in part, how the light of the sun is hidden from the surface of the flat earth.

This explains, in part, how the light of the sun is hidden from the surface of the flat earth.
Can you offer that explanation? State the theoretical mechanism and discuss how you derive from that how it hides the sun?

If you want real chaos then investigate the effect of chaos theory and the nbody problem associated with the orbits in the solar system model .
Are you really arguing that a 10body problem of the solar system is more chaotic than the 10^44  body system that is the atmosphere? Really?
Case in point  I can easily predict the orbits of all of the planets by numerically solving the nbody equation with a computer, and very accurately predict their positions for at least the next 100 years. Meanwhile the weather report can't even predict with 99% accuracy whether it's going to rain tomorrow.
You are not just a clown  you are the entire circus.

If you want real chaos then investigate the effect of chaos theory and the nbody problem associated with the orbits in the solar system model .
Are you really arguing that a 10body problem of the solar system is more chaotic than the 10^44  body system that is the atmosphere? Really?
Case in point  I can easily predict the orbits of all of the planets by numerically solving the nbody equation with a computer, and very accurately predict their positions for at least the next 100 years. Meanwhile the weather report can't even predict with 99% accuracy whether it's going to rain tomorrow.
You are not just a clown  you are the entire circus.
Refrain from personal attacks in the upper fora. Warned.

This explains, in part, how the light of the sun is hidden from the surface of the flat earth.
Can you offer that explanation? State the theoretical mechanism and discuss how you derive from that how it hides the sun?
I am unsure what further explanation you seek.
The atmoplane is certainly never in a state of 100 percent chaos, although there is 100 percent chaos in portions of the atmoplane at any given time.
Certain places experience direct blackouts at high noon, certainly occluding sunlight thousands of miles away.

I am unsure what further explanation you seek.
The atmoplane is certainly never in a state of 100 percent chaos, although there is 100 percent chaos in portions of the atmoplane at any given time.
Certain places experience direct blackouts at high noon, certainly occluding sunlight thousands of miles away.
For instance, what in FE theory accounts for these direct blackouts? What is doing the occluding and how is it doing it?

If you want real chaos then investigate the effect of chaos theory and the nbody problem associated with the orbits in the solar system model .
Are you really arguing that a 10body problem of the solar system is more chaotic than the 10^44  body system that is the atmosphere? Really?
Case in point  I can easily predict the orbits of all of the planets by numerically solving the nbody equation with a computer, and very accurately predict their positions for at least the next 100 years. Meanwhile the weather report can't even predict with 99% accuracy whether it's going to rain tomorrow.
You are not just a clown  you are the entire circus.
You should be aware that the "solar system " contains hundreds of bodies not just ten . This solar system is supposed to be part of a universe consisting of countless bodies  all in motion interacting through that magical force of attraction between masses . Chaotic indeed .
Planetary orbits are predictable through observation , always have been .
Meteorologist Edward Lorenz stumbled upon chaos theory while trying to predict weather patterns with his computer  read up on it .Thing about computers  put crap in , get crap out .

You should be aware that the "solar system " contains hundreds of bodies not just ten . This solar system is supposed to be part of a universe consisting of countless bodies  all in motion interacting through that magical force of attraction between masses . Chaotic indeed .
Planetary orbits are predictable through observation , always have been .
Meteorologist Edward Lorenz stumbled upon chaos theory while trying to predict weather patterns with his computer  read up on it .Thing about computers  put crap in , get crap out .
Hundreds? The Solar System contains at least hundreds of thousands, more depending on how you define it.
Let's say there are 1 trillion bodies (1e12) in our solar system. There are around 100 billion stars (1e11) in our galaxy. That means if you put all of the galaxies in the observable universe together (1e12), you get a 1e34body system, which is 10,000,000 times less than there are particles in our atmosphere.
Both are chaotic, nbody systems with very high n, but you seem to be suggesting that the solar system is highly chaotic and that the atmosphere isn't chaotic. Sorry if I misunderstood.
Planetary orbits are predictable through numerical simulations.
Please tell me where asteroid 2003 Harding (6559 PL) will be in 50 years through "observation". Tell me where its perihelion is, tell me its orbital eccentricity. You can't, but numerical simulations can.

Yes hundreds , glad we agree on that  your figure of 100,000s is more specific in that that figure is a thousand hundreds . Wasn't it you that specified the solar system as a 10 body problem ?
I don't suggest anything about the atmosphere and it is chaos theory and the nbody problem which suggests the solar system is unstable .
Numerical simulations are not solutions to problems . They are simulations that is all . A computer may model an orbit but that won't be reality . In order to calculate an nbody orbit then all nvariable initial conditions must be known exactly  which we can never know , and this is why the problem is unsolvable .
Not even asteroid 2003 etc orbit is calculable , although you may simulate the orbit numerically . If we can't see ass2003 with the naked eye then how can we ,by observation , tell you where it will be in 50yrs ?

Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.
People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.

I am unsure what further explanation you seek.
The atmoplane is certainly never in a state of 100 percent chaos, although there is 100 percent chaos in portions of the atmoplane at any given time.
Certain places experience direct blackouts at high noon, certainly occluding sunlight thousands of miles away.
For instance, what in FE theory accounts for these direct blackouts? What is doing the occluding and how is it doing it?
Same thing as RE theory, I guess.
Direct blackouts can occur when severe thunderstorms strike an area.

Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.
People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.
Software is a set of instructions directing your computer to give the required answer . Simulations are not the same thing as reality . Heliocentric system is chaotic by that models prediction , as is the gravitational universe . Reality is different though . We cannot predict planetary orbit in the heliocentric model .

Not being able to solve it isn't the same as it being impossible. If you use software to run a 3d simulation and throw a few hundred smaller balls vaguely in the direction of a ball with more mass you'll probably find at least some of them will start orbiting, right? This is basically the same thing. In all the chaos of the universe things have settled into an orbit by chance. in fact the more bodies there are in the universe the more chance of this happening.
People are assuming the few bodies in our solar system are the only bodies that were somehow made and thrown into a perfect orbit but it was more like a shotgun effect. throw enough objects at a sun and some will start to orbit just the same as if you throw a hundred of small marbles at a small hole in the wall, some may manage to get into the hole but most may not. That doesn't mean that the ones that managed to go into the hole were an impossibilty.
Software is a set of instructions directing your computer to give the required answer . Simulations are not the same thing as reality . Heliocentric system is chaotic by that models prediction , as is the gravitational universe . Reality is different though . We cannot predict planetary orbit in the heliocentric model .
Yes, thats why I used the marble example as well. if I'm holding a handful of marbles and I throw them at a wall with a hole in, some may go in. Can you precalculate which marbles will go exactly where and how many would go into the hole? If not, does that make it impossible for the that some may go in? The answer is obviously you cannot calculate this, and it's obviously still possible. Just as we can't fully calculate perfectly our solar system, yet that doesn't make it impossible.
"we can't solve the nbody problem so there's no way gravity and orbiting is possible" is a terrible argument I see a lot around here. Mind you mostly from TomB. What we can do in the marbles case is invent a machine (a gun) that is mechanically nearly perfectly made wit hthe exact calculations to shoot marbles into the hole perfectly. This isnt much different from how we can calculate exactly the kind of forces needed to put a rocket into orbit.

The availiable solutions for the Three Body Problem are very limited, need to be highly symmetrical and require at least two of the three bodies to be of the same mass.
https://web.archive.org/web/20191010222453/https://arxiv.org/pdf/1709.04775.pdf
The 1223 new periodic orbits of planar threebody problem with unequal mass and zero angular momentum  At the bottom of p.1 see “ Therefore, without loss of generality, we consider m1 = m2 = 1 and m3 is varied. ”
https://web.archive.org/web/20191010222522/https://www.newscientist.com/article/2148074infamousthreebodyproblemhasoverathousandnewsolutions/
Infamous threebody problem has over a thousand new solutions  “ Perhaps the most important application of the threebody problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit. But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane. ”
https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993
Over a thousand new periodic orbits of a planar threebody system with unequal masses  “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. ”
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations:  “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”
Where are the solutions with bodies of different masses?
These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.

Yes hundreds , glad we agree on that  your figure of 100,000s is more specific in that that figure is a thousand hundreds . Wasn't it you that specified the solar system as a 10 body problem ?
I don't suggest anything about the atmosphere and it is chaos theory and the nbody problem which suggests the solar system is unstable .
Numerical simulations are not solutions to problems . They are simulations that is all . A computer may model an orbit but that won't be reality . In order to calculate an nbody orbit then all nvariable initial conditions must be known exactly  which we can never know , and this is why the problem is unsolvable .
Not even asteroid 2003 etc orbit is calculable , although you may simulate the orbit numerically . If we can't see ass2003 with the naked eye then how can we ,by observation , tell you where it will be in 50yrs ?
I didn't quite understand your answer  do you understand that the atmosphere is also an analytically unsolvable nbody problem or not?
A numerical simulation can predict where an asteroid will be in 50 years with a known error. As it turns out, the solar system is 'calm' enough such that you can predict the position of any body within the solar system to very high accuracy for the next at least 100 years, probably a lot more.
Just to try and open your eyes, here's something to think about: can you tell me of any physical system that is analytically (i.e. exactly) solvable? You'll find that there are almost 0 problems in Physics that are analytically solvable. It's just a reality of the complex world we live in.

These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.
I've talked with you about this before. This post really demonstrates that you don't understand what's being talked about. Nobody is arguing that there are analytical solutions to the nbody problem, as you are implying.
I think you need to do some research on the basics of numerical integration and how it is different from an analytic solution before you comment again.
And as for a demonstration, just look up NASA's Horizons catalogue and you'll see that it has very accurate orbital information about hundreds of thousands of bodies in the solar system, all by using numerical integration.
Are you now going to argue that these numerical calculations that demonstrably very accurately match real life are somehow invalid?

Those are numerical simulations that I quoted.
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations:  “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”
Again, where can we find numerical simulations with different masses other than your statement that they exist?
Your reference to the NASA models are questionable, as they are using perturbation methods. (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbation_Search)

These systems are rediculous and are nothing like what is proposed by astronomy. Most configurations will fly apart or collapse. Not all combinations of systems stay together. If you guys are going to argue that the Three Body Problem can simulate the systems of astronomy then you will need to show and demonstrate, rather than providing speculation.
I've talked with you about this before. This post really demonstrates that you don't understand what's being talked about. Nobody is arguing that there are analytical solutions to the nbody problem, as you are implying.
I have to agree here. Many people do not seem to be able to, or do not wish to, distinguish between analytic solutions arrived at though numerical methods and numerical solutions. They are completely different.
Numerical solutions to 'Nbody' problems are quite accurate and stable, however they take a lot of computing power to run such simulations and have to be run for each defined problem and offer no analytic solution.
Analytic solutions have the advantage of being in teh form of an equation or function are able to be written down and used in further calculations. The drawback is the overall failure to produce general analytic solutions to 'N' body problems (as well as others) using numerical methods.

The three body problem is studied in the field of nonlinear ordinary differential equations with initial conditions: bifurcation theory, an exceedingly difficult branch of advanced mathematics.
https://books.google.ro/books?id=YhXnBwAAQBAJ&printsec=frontcover&dq=wiggins+introduction+to&hl=en&sa=X&ved=0ahUKEwj2yPuosdblAhVC3qQKHUXdByMQ6AEIMDAB#v=onepage&q=wiggins%20introduction%20to&f=false
Here are the known facts concerning the three body problem in the context of bifurcation theory:
https://forum.tfes.org/index.php?topic=10175.msg160183#msg160183
https://forum.tfes.org/index.php?topic=14559.msg191038#msg191038
The most intriguing is the discovery made by Professor Robert W. Bass.
Dr. Robert W. Bass
Ph.D. (Mathematics) Johns Hopkins University, 1955 [Wintner, Hartman]
A. Wintner, world's leading authority on celestial mechanics
PostDoctoral Fellow Princeton University, 195556 [under S. Lefschetz]
Rhodes Scholar
Professor, Physics & Astronomy, Brigham Young University
"In a resonant, orbitally unstable or "wild" motion, the eccentricities of one or more of the terrestrial planets can increase in a century or two until a near collision occurs. Subsequently the Principle of Least Interaction Action predicts that the planets will rapidly "relax" into a configuration very near to a (presumably orbitally stable) resonant, Bode'sLaw type of configuration. Near such a configuration, small, nongravitational effects such as tidal friction can in a few centuries accumulate effectively to a discontinuous "jump" from the actual phasespace path to a nearby, truly orbitally stable, path. Subsequently, observations and theory would agree that the solar system is in a quasiperiodic motion stable in the sense of Laplace and orbitally stable. Also, numerical integrations backward in time would show that no near collision had ever occurred. Yet in actual fact this deduction would be false."
"I arrived independently at the preceding scenario before learning that dynamical astronomer, E. W. Brown, president of the American Astronomical Society, had already outlined the same possibility in 1931."
Dr. Robert Bass, Stability of the Solar System:
https://web.archive.org/web/20120916174745/http://www.innoventek.com:80/Bass1974PenseeAllegedProofsOfStabilityOfSolarSystemR.pdf
Dr. E.W. Brown
Fellowship, Royal Society
President of the American Mathematical Society
Professor of Mathematics, Yale University
President of the American Astronomical Society
What this means is that the interval of assured reliability for Newton's equations of gravitational motion is at most three hundred years.
If any proofs can be provided that the solar system underwent cataclysmic planetary collisions in recent historical times, this fact would render any kind of heliocentric orbital calculations as completely useless.
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1936055#msg1936055 (part I)
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938384#msg1938384 (part II)
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938393#msg1938393 (part III)
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938396#msg1938396 (part IV)

Those are numerical simulations that I quoted.
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations:  “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”
Again, where can we find numerical simulations with different masses other than your statement that they exist?
Your reference to the NASA models are questionable, as they are using perturbation methods. (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbation_Search)
You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a userspecified time span less than 200 years."
"and are then numerically integrated ondemand by Horizons to other times of interest"
Need I go on?

Those are numerical simulations that I quoted.
Your opening line was "The availiable solutions for the Three Body Problem are very limited..." and then you go on to say "Where are the solutions with bodies of different masses?"
There are limited analytic solutions to the threebody problem. There are no general analytic solutions to the threebody problem with arbitrary masses.
I'm talking about numerical solutions, not analytic solutions. Whether there is an analytic solution to the threebody problem is entirely irrelevant  what matters is the thing we're actually discussing, which is the accuracy of the numerical solution.
P.S. do you have any coding experience? You can just open python or matlab etc. yourself and use premade and easy to use numerical integration algorithms, chuck in initial conditions for e.x. the solar system and see what happens.

I don't understand. Who was talking about analytical solutions? Those are numerical solutions that I linked you to:
https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993
Over a thousand new periodic orbits of a planar threebody system with unequal masses  “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. ”
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations:  “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a "clean numerical simulation"
Now, where can we find examples of numerical three body problem solutions with bodies of different masses?
Sandokhan, do you know where we can find them?
You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a userspecified time span less than 200 years."
"and are then numerically integrated ondemand by Horizons to other times of interest"
Need I go on?
From your link:
Comet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable stepsize integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.
Summing of perturbing forces?
This sounds like what Dr. Gopi Krishna Vijaya is explaining in his Replacing the Foundations of Astronomy paper:
https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdf
Epicycles Once More
Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.
In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise:
(https://i.imgur.com/5wxPNvF.png)
In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic  Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were rederived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical.
~
The Dead End
In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of nonlinear dynamics.
In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inversesquare law”, “gravitational attraction”, “gravitational mass” and “curved spacetime” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase

Now, where can we find examples of numerical three body problem solutions with bodies of different masses?
I gave you one about a year ago (or so).
Sandokhan, do you know where we can find them?
LOL!

One of the best accounts of the numerical methods applied to solar system stability questions:
http://immanuelvelikovsky.com/NewtonEinstein&Veli.pdf (chapter 3, Solar System Instability, pg 84  112, especially pg 97, 103111)

Really? I've read that book. It is solely based on the ramblings of Velikovsky, the poster child for pseudoscience. There is no mathematical models in it, either numercalyy simulated or analytical arrived at though numerical methods.
Page 97 in particular deals with the stability of a solar system in a universe full of massive rogue bodies that would surely perturb the orbits of all the planets. Well, the fact is that, whether the universe is full of massive rogue bodies or not, none have been witnessed in our time to have perturbed anything.
But enough of that. Briefly at the top of the page is a quote that mentions the instability in an analytic solution arrived at through numerical methods. This is something we don't have to go to rubbish like the Velikovskian to know about. Every 1st year mechanics (an I mean the branch of physics here, not fixing cars) student learns about the failure of numerical methods to provide a solution to the 'Nbody' problem. I actually think Tom was asking for a reference for a numerical solution, not an analytic solution arrived at through numerical methods. Again, there is a huge difference.

The book is written by Charles Ginenthal, one of the top scholars in the world.
Basically, what Velikovsky proposed is that electrical and magnetic forces must be included in celestial mechanics.
And he was right.
Here is the exact formula for the BIEFELDBROWN EFFECT:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2177793#msg2177793
(https://i.ibb.co/5YW8CPH/bie1.jpg)
(https://i.ibb.co/M8576CJ/bie2.jpg)
This is the WeylMajumdarPapapetrouIvanov solution.
https://arxiv.org/pdf/grqc/0507082.pdf
Weyl electrovacuum solutions and gauge invariance
Dr. B.V. Ivanov
https://arxiv.org/pdf/grqc/0502047.pdf
On the gravitational field induced by static electromagnetic sources
Dr. B.V Ivanov
Here is how the solution was derived in 1917 by Hermann Weyl, a physicists several ranks higher than Einstein:
http://www.jppetit.org/papers/cosmo/1917Weylen.pdf
If you do not like Velikovsky, then you are going to be enthralled by Kepler, who FAKED/FUDGED the entire set of data for the Nova Astronomia:
https://forum.tfes.org/index.php?topic=10175.msg160186#msg160186
https://forum.tfes.org/index.php?topic=10175.msg160200#msg160200
Here is an analysis of Jacques Laskar's numerical approach using only mainstream sources:
https://forum.tfes.org/index.php?topic=10175.msg160189#msg160189
Chapter 3 from Newton, Einstein & Velikovsky includes the references on numerical methods, a sure sign you did not read it at all.
https://arxiv.org/pdf/0708.2875.pdf
http://www.cs.toronto.edu/~wayne/research/papers/nphys728published.pdf
http://immanuelvelikovsky.com/NewtonEinstein&Veli.pdf (chapter 3, Solar System Instability, pg 84  112, especially pg 97, 103111)  these pages include a formidable analysis of the assumptions made by physicists who employ various kinds of numerical algorithsm to study celestial mechanics)

I have things to do right now. It's winter where I live and I have the mundane tasks of chopping and stacking firewood. Allow me to get back to on this. But as for Ginenthal being one of the top scholars in the world, that has to be a joke right? As far as I can tell, all he's ever really done is write in defense of Velikovsky's physics quackery. Velikovsky being a psychiatrist and all.

Back from my chores.
The book is written by Charles Ginenthal, one of the top scholars in the world.
Dealt with that above.
Basically, what Velikovsky proposed is that electrical and magnetic forces must be included in celestial mechanics.
I'm not going to read any more Velikovsky to try to determine if what your saying here is correct or not, but just as I would not take a hairdresser's advice on brain surgery, I would not take a psychiatrists advice on physics. Especially one that published so much unfounded rambling and is the foremost example of pseudoscience.
And he was right.
Possibly, but under what conditions? Certainly not those generally (or ever) found in universe.
Here is the exact formula for the BIEFELDBROWN EFFECT:
LOL! This is something Brown as a high school student and let it take his imagination away. Despite numerous attempts by others this effect has never been demonstrated. More quackery and pseudoscience.
This is the WeylMajumdarPapapetrouIvanov solution.
Weyl, Majumdar, Papapetrou independently did some interesting academic calisthenics for sure.
However, these solutions were an attempt to use Einstein's and Maxwell's work to predict, or find a solution for the classical distribution of a system of point charges. In Newtonian physics, this is simply done, however, even after the work of the above gentlemen a useful EinsteinMaxwell solution has not been found. Their solution(s) require a system of superhighly charged masses on the order of black holes, and the solutions only work in a simplified static case (time independent). Not something we've ever seen ... so ,yeah, just some interesting intellectual workouts.
Now, once you bring Ivanov into it you do the other an injustice. Ivanov did some real physics in his life, but his work on this was soundly rejected, especially when he proposed a static solution could provide a means of propulsion!
Hermann Weyl, a physicists several ranks higher than Einstein
Weyl was a real physicist alright, but not exactly a household name. Again, his work on this does not have teh application you are looking for and infact has no real application at all (so far).
If you do not like Velikovsky, then you are going to be enthralled by Kepler, who FAKED/FUDGED the entire set of data for the Nova Astronomia:
One writer's opinion piece. Meh...
Here is an analysis of Jacques Laskar's numerical approach using only mainstream sources:
And what Laskar said was that while you could predict the motions of the planets for 10,000,000 years, you could probably not predict them for 100,000,000 years. I can't see how bringing this up helps your point. It's not like he's saying "This thing can't exist as it's going to blow apart at any second!" I think you're desperately grasping at straws.
Chapter 3 from Newton, Einstein & Velikovsky includes the references on numerical methods, a sure sign you did not read it at all.
There is no math in that chapter. There is a lot of unsubstantiated rhetoric, but no math. Quite a typical approach in pseudoscience.
Also, right on the first page of that W. Hayes paper you linked to he states: "The Solar System is known to be ‘practically stable’, in the sense that none of the known planets is likely to suffer mutual collisions, or be ejected from the Solar System, over the next several billion years." Citing the work of Laskar. Again, I don't see how this helps your case. You are talking such tiny, tiny chaotic effects that the researchers don't even know what is casing them but they suspect observational data is not accurate enough to feed the models. Did you even read that paper?
Here is the introductory paragraph: "The existence of chaos among the jovian planets is a contested issue. There exists both apparently unassailable evidence that the outer Solar System is chaotic, and that it is not. The discrepancy is particularly disturbing given that computed chaos is sometimes due to numerical artefacts. Here, we discount the possibility of numerical artefacts and demonstrate that the discrepancy seen between various investigators is real. It is caused by observational uncertainty in the orbital positions of the jovian planets, which is currently a few parts in 10 million. Within that observational uncertainty, there exist clearly chaotic trajectories with complex structure and Lyapunov times—the timescale for the onset of chaos—ranging from 2 million years to 230 million years, as well as trajectories that show no evidence of chaos over 1Gyr timescales. Determining the true Lyapunov time of the outer Solar System will require a more accurate observational determination of the orbits of the jovian planets. A full understanding of the nature and consequences of the chaos may require further theoretical development."

I don't understand. Who was talking about analytical solutions? Those are numerical solutions that I linked you to:
https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993
Over a thousand new periodic orbits of a planar threebody system with unequal masses  “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass. ”
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations:  “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a "clean numerical simulation"
Now, where can we find examples of numerical three body problem solutions with bodies of different masses?
Sandokhan, do you know where we can find them?
You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a userspecified time span less than 200 years."
"and are then numerically integrated ondemand by Horizons to other times of interest"
Need I go on?
From your link:
Comet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable stepsize integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.
Summing of perturbing forces?
This sounds like what Dr. Gopi Krishna Vijaya is explaining in his Replacing the Foundations of Astronomy paper:
https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdf
Epicycles Once More
Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.
In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise:
(https://i.imgur.com/5wxPNvF.png)
In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic  Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were rederived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical.
~
The Dead End
In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of nonlinear dynamics.
In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inversesquare law”, “gravitational attraction”, “gravitational mass” and “curved spacetime” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase
Just because the reference that I gave you has the word "peturb" in doesn't mean it's not a numerical integration. That same paragraph also explicitly states they use numerical integration.
What exactly is your point here? I've given you the numerical solution to the nbody problem that you asked for, and you just dismissed it out of hand for seemingly no reason. If you don't want a discussion, don't bother replying.
Just reread all of BillO's posts  he seems to know exactly what he's talking about.

It appears to be based on perturbation theory.
https://en.wikipedia.org/wiki/JPL_Horizons_OnLine_Ephemeris_System
The real orbit (or the best approximation to such) considers perturbations [link takes us to the page on perturbation theory] by all planets, a few of the larger asteroids, a few other usually small physical forces, and requires numerical integration.
Numerical integration can be used with perturbations. Are you aware that Ptolmy's epicycles are numerical computations?
https://books.google.com/books?id=JVhTtVA2zr8C&pg=PA29&source=gbs_toc_r&cad=4#v=onepage&q&f=false
(https://i.imgur.com/tLawyDV.png)
So the favorite word, "numerical", really means nothing regarding a dynamic nbody simulation or the acceptability of a mathematical procedure.

It appears to be based on perturbation theory.
Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this? Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out? You had to be laughing when you wrote that, right?

It appears to be based on perturbation theory.
Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this? Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out? You had to be laughing when you wrote that, right?
To be fair, he did start a previous post with “I don’t understand”. A rare moment of selfawareness. Tom has repeatedly shown he doesn’t understand this. And even if there were no solutions, analytical or numerical, to model a system, why is that significant?
As others have pointed out, the behaviour of a double pendulum is chaotic, there is no way of predicting its future state over long timespans.
Tom’s logic here would claim that this fact shows that the theory that double pendulums exist must not exist.
It’s a common FE tactic. “I don’t understand this model ergo the model is wrong”, or “This model is imperfect which demonstrates that the system it’s modelling can’t exist”.
Not only is that poor logic, it’s particularly disingenuous when you consider the gaping holes and inconsistencies in FE models.

Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this? Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out? You had to be laughing when you wrote that, right?
Okay, you clearly don't understand what "contributing to a discussion" means. We'll see you in a few weeks.

Despite numerous attempts by others this effect has never been demonstrated.
But it has.
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2177463#msg2177463
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2178412#msg2178412
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2179065#msg2179065
Their solution(s) require a system of superhighly charged masses on the order of black holes, and the solutions only work in a simplified static case (time independent). Not something we've ever seen ... so ,yeah, just some interesting intellectual workouts.
No black holes required at all.
All you need is a simple capacitor.
Ivanov did some real physics in his life, but his work on this was soundly rejected, especially when he proposed a static solution could provide a means of propulsion!
The WeylIvanov solution cannot be rejected, it is a fact of science.
It represents the exact formula for the BiefeldBrown effect: then you can use supercapacitors as a form of propulsion, the formula spells this out very clearly.
(https://i.ibb.co/M1SJzmC/iv2.jpg)
(https://i.ibb.co/9TBrSBD/iv3.jpg)
Weyl was a real physicist alright, but not exactly a household name.
Weyl was the best theoretical physicists in the world, 19171955.
“And now I want to ask you something more: They tell me that you and Einstein are the only two real sureenough highbrows and the only ones who can really understand each other. I won’t ask you if this is straight stuff for I know you are too modest to admit it. But I want to know this  Do you ever run across a fellow that even you can’t understand?”
“Yes,” says he.
“This will make a great reading for the boys down at the office,” says I. “Do you mind releasing to me who he is?”
“Weyl,” says he.
(an interview that Paul Dirac gave in America back in April, 1929)
One writer's opinion piece.
Dr. Donahue's paper was peerreviewed and it includes the actual tables which do prove his point.
There is no math in that chapter.
But there is, the author references each and every conclusion with the very best works available today, which do include the calculations.
(https://image.ibb.co/e2EYGJ/gil00_zpslwerxjhx.jpg)
(https://image.ibb.co/d4EawJ/gil01_zpsbzfkgbpu.jpg)
(https://image.ibb.co/mtf4qd/gil02_zpsodpyookj.jpg)
(https://image.ibb.co/gDuxAd/gil03_zpsibabxpcg.jpg)
(https://image.ibb.co/b8Giiy/gil04_zps4wcpajjf.jpg)
(https://image.ibb.co/nPa9Oy/gil05_zpsmmpvvhcu.jpg)
(https://image.ibb.co/dx9VVd/gil06_zpsljjqeiia.jpg)
(https://image.ibb.co/bys63y/gil07_zpsalpm8lqo.jpg)
Now, let me address the numerical calculations for the nbody problem.
All Hamiltonian systems which are not integrable are chaotic.
Since the solar system is not integrable, and experiences unpredictable small perturbations, it cannot lie permanently on a KAM torus, and is thus chaotic.
KAM theory is valid for "sufficiently" small perturbations.
In reality, the perturbations in the solar system are far too large to apply KAM theory.
So, the mathematicians have to rely on computing Lyapunov exponents, in order to try to predict any region of instability/chaos.
Jack Wisdom (MIT): It is not possible to exclude the possibility that the orbit of the Earth will suddenly exhibit similar wild excursions in eccentricity.
Even measuring initial conditions of the system to an arbitrarily high, but finite accuracy, we will not be able to describe the system dynamics "at any time in the past or future". To predict the future of a chaotic system for arbitrarily long times, one would need to know the initial conditions with infinite accuracy, and this is by no means possible.
Lyapunov exponents and symplectic integration.
Let d(t) be the distance between two solutions, with d(0) being their initial separation. Then d(t) increases approximately as d(0)e^{λt} in a chaotic system, where λ is the Lyapunov exponent. The inverse of the Lyapunov exponent, 1/λ, is called the Lyapunov time, and measures how long it takes two nearby solutions to diverge by a factor of e.
Sussman and Wisdom's 1992 integration of the entire solar system displayed a disturbing dependence on the timestep of the integration (measurement of the Lyapunov time).
Thus, different researchers who draw their initial conditions from the same ephemeris at different times can find vastly different Lyapunov timescales.
Wayne Hayes, UC Irvine
To show the importance and the dependence on the sensitivity of the initial conditions of the set of differential equations, an error as small as 15 meters in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time.
“The word ‘chaotic’ summarizes many fundamental concepts characterizing
a dynamical system such as complex predictability and stability. But above
all, it acts as a warming of the difficulties which are likely to arise when trying to
obtain a reliable picture of its past and future evolution. As an example, a
commonly accepted definition states that a system is ‘unstable’ if the trajectories of
two points that initially are arbitrarily close . . . diverge quickly in time. This has
strong implications, as small uncertainties in initial conditions . . . might [also] be
consistent with completely different future trajectories: The conclusion is that we
can exactly reproduce the motion of a chaotic system only if WE KNOW, WITH
ABSOLUTE PRECISION, THE INITIAL CONDITIONS – A STATEMENT
THAT, IN PRACTICE, CAN NEVER BE TRUE."
Alessandra Celletti, Ettore Perozzi, Celestial Mechanics: The Waltz of the Planets
Let us take a closer look the chaotic dynamics of planetary formation; thus, a clear indication that the initial conditions cannot be predicted with accuracy (as we have seen, a mere 15 meters difference in the data will have catastrophic consequences upon the calculations).
OFFICIAL SCIENCE INFORMATION
Four stages of planetary formation
Initial stage: condensation and growth of grains in the hot nebular disk
Early stage: growth of grains to kilometersized planetesimals
Middle stage: agglomeration of planetesimals
Late stage: protoplanets
For the crucial stages, the initial and early stages, prediction becomes practically impossible.
As if this wasn't enough, we have absolute proof that in the age of modern man planet Earth underwent sudden pole shifts (heliocentrical version), thus making null and void any integration of the solar system/Lyapunov exponents calculations which do not take into account such variations of the system's parameters:
http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1635693#msg1635693
http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1546053#msg1546053
Let me show you what sensitive dependence on initial conditions means, using one of the most famous examples: the Lorenz attractor butterfly effect.
In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.
Here is the set of Lorenz equations:
(https://upload.wikimedia.org/math/b/0/e/b0ea9119f6aaa31302164c4212cce72d.png)
Now, the set of differential equations which describe the planetary orbits is much more complicated than this.
(https://image.ibb.co/kyYFVd/qu1_zpsilsnpvcb.jpg)
NOTHING can be said about the RE heliocentrical system beyond a time scale of 300 YEARS.
Dr. Robert W. Bass
Ph.D. (Mathematics) Johns Hopkins University, 1955 [Wintner, Hartman]
A. Wintner, world's leading authority on celestial mechanics
PostDoctoral Fellow Princeton University, 195556 [under S. Lefschetz]
Rhodes Scholar
Professor, Physics & Astronomy, Brigham Young University
"In a resonant, orbitally unstable or "wild" motion, the eccentricities of one or more of the terrestrial planets can increase in a century or two until a near collision occurs. Subsequently the Principle of Least Interaction Action predicts that the planets will rapidly "relax" into a configuration very near to a (presumably orbitally stable) resonant, Bode'sLaw type of configuration. Near such a configuration, small, nongravitational effects such as tidal friction can in a few centuries accumulate effectively to a discontinuous "jump" from the actual phasespace path to a nearby, truly orbitally stable, path. Subsequently, observations and theory would agree that the solar system is in a quasiperiodic motion stable in the sense of Laplace and orbitally stable. Also, numerical integrations backward in time would show that no near collision had ever occurred. Yet in actual fact this deduction would be false."
"I arrived independently at the preceding scenario before learning that dynamical astronomer, E. W. Brown, president of the American Astronomical Society, had already outlined the same possibility in 1931."
Dr. Robert Bass, Stability of the Solar System:
https://web.archive.org/web/20120916174745/http://www.innoventek.com:80/Bass1974PenseeAllegedProofsOfStabilityOfSolarSystemR.pdf
Dr. E.W. Brown
Fellowship, Royal Society
President of the American Mathematical Society
Professor of Mathematics, Yale University
President of the American Astronomical Society
What this means is that the interval of assured reliability for Newton's equations of gravitational motion is at most three hundred years.
Dr. W.M. Smart
Regius Professor of Astronomy at Glasgow University
President of the Royal Astronomical Society from 1949 to 1951
(https://image.ibb.co/dtvyuS/bass4.jpg)
(https://image.ibb.co/eRjPZS/bass5.jpg)
(https://image.ibb.co/ePj2M7/bass6.jpg)
(https://image.ibb.co/bPBMES/bass7.jpg)
Within this 300 year time interval, we again have the huge problem of the sensitive dependence on initial conditions.

[...]
Well after some toandfroing it seems like we actually agree on this one!

Within this 300 year time interval, we again have the huge problem of the sensitive dependence on initial conditions.
I think you've taken a very roundabout route to reach the same conclusion that I did in my first few posts in this thread: the universe is chaotic.

So the favorite word, "numerical", really means nothing regarding a dynamic nbody simulation or the acceptability of a mathematical procedure.
Okay, let me see if I can address this in a more constructive and contributory fashion.
There seems to be a lot of confusion about sorting out three separate and very different terminologies in mathematics. They are Numerical Methods, Numerical Simulations (direct/iterative methods) and Arithmetic Methods. These are not the same thing and cannot be used interchangeably regardless of how similar their names might imply they are. Let’s look at them one by one in the context solar system mechanics.
1) Numerical Methods. This term is used for an area of mathematical analysis wherein systems of ordinary or partial differential equations are solved using a process of successive approximation by making small changes the values of the variables in the differential equations until the result converges closely enough to the actual solution to be useful. For the ‘Nbody’ problem that is the solar system mechanics, the solution given by this process would be a set of equations of motion for each body in the solar system. Then a simulation of the solar system can be run using these equations of motion. As pointed out often by Tom, this method for solving the ‘Nbody’ problem has met with very limited success. If you are interested in more detail about these methods and you feel your math skills are good, look into Euler’s method.
2) Numerical Simulation. Or, if you prefer direct or iterative methods. These methods do not look for a solution in the form of an equation of motion. Rather, they directly apply the principles governing the motion of the objects and iteratively calculate the evolution of the system over time. In the case of the ‘Nbody’ problem of our solar system no analytic solution is found. Instead we start by giving each body a position and velocity representing a point in time. An initial state for the simulation. Then for each body in the system Newton’s universal law is applied between it and every other body one at a time to calculate the net force on each body due to the others. Newton’s 2nd law of motion is used to calculate the change in velocity of each object over some appropriate short interval of time, then that is used to calculate the new positions and velocities of the objects after the interval. This gives us the next state of the system. This process is repeated as required. This method is stable and arbitrarily accurate and becomes more accurate and stable as the time interval is reduced. This method has met with great success in providing simulations for our solar system. I provided an example of this method a year or so ago that runs on an Apple II computer. Even that very simple example running on a feeble computer with lousy precision can accurately ‘run’ the solar system for months and accurately predict the positions of the planets.
3) Arithmetic methods. These are any computational methods that use the four basic arithmetic operators (+, , *, /). Both of the preceding methods use arithmetic methods in their calculations. However the term is most often used to describe operations where only arithmetic is used, like in calculating averages, means, medians, and such. At the time of writing of the Almagest, all they had in their mathematical tool set was arithmetic, and while it was the best they could do at the time, they did not have the insights of Newton to assist with their calculations. What they did should not be confused with what we can do today now that we have knowledge of the principles that govern the motions of celestial bodies and tools like computers to do bulk calculations at arbitrary precision.

[...]
You mention Euler Method as being a 'Numerical Method' instead of a 'Numerical Simulation'  but the Euler Method is certainly iterative, and falls under the umbrella of RungeKutta methods (everyone's favourite, I'm sure) for numerical simulation/methods/integration. I'm not sure the line between 1) and 2) is quite as cutanddry as you claim.

Just a side note: why do flat earthers always dump on gravity based solely on the fact that it's not analytically solvable, and yet ignore all the other physics that's not analytically solvable? You'd think if this was really a problem, that flat earthers would be taking an equalsized dump on, say, electromagnetism, but I don't think that's ever happened. Just seems like cherrypicking to me.

[...]
You mention Euler Method as being a 'Numerical Method' instead of a 'Numerical Simulation'  but the Euler Method is certainly iterative, and falls under the umbrella of RungeKutta methods (everyone's favourite, I'm sure) for numerical simulation/methods/integration. I'm not sure the line between 1) and 2) is quite as cutanddry as you claim.
Perhaps you and I could discuss this in more detail, but I think we'd end up leaving a lot of folks behind. I guess you could use method 1 to run a simulation but the real power in the RungeKutta and other similar methods is in determining the approximate values of the unknown parameters and constants that are inevitable after doing the integrations to solve higher order differential equations which, in our case anyway, are formulated to give the equations of motion of the bodies. The simple fact is that these methods, even using minute iterations and adaptive techniques, have not produced very stable solutions to the 'Nbody' problem.
Method 2 makes no attempt to formulate differential equations or to solve them. In our case, it merely applies Newton's laws to the bodies. This approach provide much more stable results and responds well to reducing the iteration size. In fact, you can increase accuracy of the simulation arbitrarily by reducing the iteration size arbitrarily  as long as you have the mathematical precision to pull it off.
The two methods are discussed here with method 2 under the heading "Modern method" and method 1 under the heading "Integration": https://en.wikipedia.org/wiki/Numerical_model_of_the_Solar_System (https://en.wikipedia.org/wiki/Numerical_model_of_the_Solar_System)