[edby]

If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.

It's not 'just patterns'.

That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.

Why on earth would it 'totally nullify the underlying theory'??

Give me a reason.

[RonJ]

Probably you continue to be confused (maybe intentionally) about what is happening.  Patterns tend to emerge from the data but those patterns are the result NOT the cause of any prediction. The cause of the predictions are the application of the basic laws of motion of bodies containing mass NOT the application of patterns that were noticed in the past.  It's like saying that there is a pattern for how you put a nut on a bolt.  'Righty Tighty / Lefty Loosie' is definitely a pattern that applies to a mechanical device but doesn't have much to do with how it actually operates.  The Fourier series is the application of the Sine Wave pattern (like a nut / bolt) that is useful for describing a lot of things that can happen in a cycle, like an orbital cycle.  It's just a tool that can be used to describe the overall motion of a body.  You can use a wrench to fix your car, but that doesn't have much to do with the laws of motion that are in force when you go around a curve.  It looks like there is a pattern in your ideas and replies and I'm thinking I may be able to base a prediction on your response.     

[Tom Bishop]

If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.

It's not 'just patterns'.

That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.

Why on earth would it 'totally nullify the underlying theory'??

Give me a reason.

Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.

[edby]

If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.

It's not 'just patterns'.

That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.

Why on earth would it 'totally nullify the underlying theory'??

Give me a reason.

Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.

What are these 'gravitational effects' they are talking about, whose theoretical existence is apparently nullified, according to you.

[Bobby Shafto]

Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.

The starting point for "perturbations" are the idealized motions themselves. They don't "nullify" them.

Neptune was discovered by the perturbation of the orbit of Uranus by an unseen object.   Uranus had an expected motion. It was the observed deviations from that expected motion that led to the prediction of another unseen body that ultimately turned out to be Neptune.

Perturbations are not an end unto themselves. They don't "nullify" laws of motion. They are modifiers.

[edby]

Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.

The starting point for "perturbations" are the idealized motions themselves. They don't "nullify" them.

Neptune was discovered by the perturbation of the orbit of Uranus by an unseen object.   Uranus had an expected motion. It was the observed deviations from that expected motion that led to the prediction of another unseen body that ultimately turned out to be Neptune.

Perturbations are not an end unto themselves. They don't "nullify" laws of motion. They are modifiers.

About time for Tom to link to this, http://www.sacred-texts.com/earth/za/za60.htm I think.

[RonJ]

What I see here is the implementation of the successive approximation model.  The first step is to gather all the information you have about something you need to investigate.  Next is the formulate a theory about what needs to be done.  After that you take some actions based upon your theory and see what happens.  You expect to make errors.  Very few do something new perfectly the first time.  After you analyze the errors maybe it will point you to some new information you didn't have previously.  Using that new information you can modify your theory and again take some actions.  You keep repeating this process until you are successful.  In the link provided I did read the story about Le Verrier.  This was an application of the successive approximation model.  Le Verrier probably did apply the principles of Newtonian mechanics and did locate the planet but made some errors in the paths.  These errors probably were not a problem with the theory, but more likely a problem with the initial assumptions made.  Maybe Le Verrier used some data from another source that wasn't quite accurate.  Maybe he didn't quite understand something about Newtonian mechanics correctly, or maybe he made a stupid error in calculation.  I think it wasn't a problem with the theory, it more likely was a problem with best guess data.  Sometimes a theory just doesn't work at all no matter what you try.  At that point nothing at all will make sense.  All I can say about that is some theories are from Mars, and other are from Uranus.   

[Tom Bishop]

Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.

https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/

Perhaps the most important application of the three-body 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.

The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.

The biggest problem in astronomy is getting it to work!

[Curious Squirrel]

Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.

https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/

Perhaps the most important application of the three-body 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.

The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.

The biggest problem in astronomy is getting it to work!

I *might* be reading this wrong but it sounds to me that what they are creating/finding here are equations that they can use that will simulate a stable orbit for an extended period without modification. However that's NOT how they calculate the movements for the eclipse tables. I'll try and dig it up when I have more time, but it might also be in one of the quotes already and I'm missing it. But the movements of the Earth/Moon/Sun system (and the solar system in general) aren't done via a specific solution to the three body problem. They're done by an iterative solving of all the effects on a body repeatedly.

You take a snapshot of where all the bodies appear at T=0. You calculate all the acting effects on every body and apply them to your next snapshot at T=1. You then do this again for every interval of T. There's no need to have a solution for a 3-body problem (which the Earth/Moon/Sun very likely isn't anyway) as you aren't attempting to solve it via a singular equation. This is likely how such software as the 'Universe Sandbox' works, or at least similarly.

[RonJ]

http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003#tab1

Well the discussion subroutine has come full circle back to near the start again.  The OP Bobby was hypothesizing that you would need more than just pattern based descriptions to accurately predict eclipses.  My link points to a researcher that has all the equations using strictly Newtonian mechanics that accomplishes that objective.  The three body diversion was tried. It didn't fly far.  Now it's time to 'square yourself in the hatch' and illustrate just what the problems are with the equations proffered in the paper pointed to in the link.  They sure look OK to me.  Can I expect another diversionary tactic or a useful criticism that can be objectively discussed?   

[Tom Bishop]

Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.

https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/

Perhaps the most important application of the three-body 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.

The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.

The biggest problem in astronomy is getting it to work!

I *might* be reading this wrong but it sounds to me that what they are creating/finding here are equations that they can use that will simulate a stable orbit for an extended period without modification. However that's NOT how they calculate the movements for the eclipse tables. I'll try and dig it up when I have more time, but it might also be in one of the quotes already and I'm missing it. But the movements of the Earth/Moon/Sun system (and the solar system in general) aren't done via a specific solution to the three body problem. They're done by an iterative solving of all the effects on a body repeatedly.

You take a snapshot of where all the bodies appear at T=0. You calculate all the acting effects on every body and apply them to your next snapshot at T=1. You then do this again for every interval of T. There's no need to have a solution for a 3-body problem (which the Earth/Moon/Sun very likely isn't anyway) as you aren't attempting to solve it via a singular equation. This is likely how such software as the 'Universe Sandbox' works, or at least similarly.

It sounds pretty clear to me:

“This is kind of the zeroth step. Then the question becomes, how is the space of all possible positions and velocities filled up by solutions?” says Richard Montgomery at the University of California, Santa Cruz. “These simple orbits are kind of like a skeleton to build the whole system up from.”

They are at the zeroth step: The Stone Age.

They are going to use these orbits like a skeleton to "build the whole system up from."

The following quote says it all:

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.

Why didn't the supercomputer find possible orbits for bodies of slightly different masses? Because they can't exist.

[Tom Bishop]

The above is in line with my post a few days ago on the subject:

I assume you're referring to FET when saying, " General application of the Three Body Problem are, in fact, impossible". Because in this day and age it's very simple.

"They could predict the eclipses thousands of years into the future". This statement is contradiction of the former.

Prediction of three or more orbiting bodies under the Newtonian System is impossible. Literally impossible. It is one of the greatest problems of astronomy, mathematics, and classical mechanics. They can't get the heliocentric system to work.

Take a look at the existing Three Body Problem solutions. The bodies are either all of the same mass, or some of them are mass-less. The applications are very limited.

The famous physicist Henri Poincare studied the Three Body Problem. Here is a quote from 'Mathematics Applied to Deterministic Problems in Natural Sciences' about Poincare's discoveries:

As Poincare experimented, he was relieved to discover that in most of the situations, the possible orbits varied only slightly from the initial 2-body orbit, and were still stable, but what occurred during further experimentation was a shock. Poincare discovered that even in some of the smallest approximations some orbits behaved in an erratic unstable manner. His calculations showed that even a minute gravitational pull from a third body might cause a planet to wobble and fly out of orbit all together.

The available solutions to the Three Body Problem, beyond looking unlike anything seen in Heliocentric Theory, are so sensitive that the slightest change or imperfection will tear the entire system apart. As a very illustrative demonstration, take a look at this online Three Body Problem simulator that uses the simplest possible figure eight pattern, which requires three identical bodies of equal mass that move at very specific momentum and distance in relation to each other.

Demo: Figure-Eight Three Body Problem



Adjust the slider values in the upper left to something very slight to find what happens. What you will see is a demonstration of Chaos Theory. Any slight modification to the system creates a chain reaction of random chaos.

This is precisely the issue of modeling the Heliocentric System, and why the fundamental systems as depicted in popular astronomy cannot exist. Only very specific and very sensitive configurations may exist. The slightest deviation, such as with a system with unequal masses, or the minute influence from a gravitating body external to the system will, as Poincare found, cause the entire system to fly apart!

Play the demo. Adjust the sliders to something very slight. We can see that that only very specific configurations could exist.

Again, I ask, why did the supercomputer not find orbits with different masses?

Why do the bodies need to be of exactly the same mass, or one of the bodies mass-less?

These questions will ignored, in favor of ignorance, because of a refusal to accept that Copernicus was wrong.

[garygreen]

They cannot simulate it at all.

lol that's nonsense.

A three million year integration of the earth's orbit
describes a numerical simulation of all nine planets carried out by integrating newton's equations of motion.  it says that explicitly in the paper and describes the method of integration.

La2010: A new orbital solution for the long term motion of the Earth
some book-nerd frenchman named jacques laskar loves making long-term models of the solar system.  here's his most recent one.

also you evidently don't understand that "chaotic" motion does not imply that everything flies apart.  that's not even what your article says.  the motion of the objects in the solar system can be (and is) chaotic without ejecting all the planets in it.

https://www.nature.com/articles/338237a0

The solution is chaotic, with a maximum Lyapunov exponent that reaches the surprisingly large value of ∼ 1/5 Myr–1. The motion of the Solar System is thus shown to be chaotic, not quasiperiodic. In particular, predictability of the orbits of the inner planets, including the Earth, is lost within a few tens of millions of years. This does not mean that after such a short timespan we will see catastrophic events such as a crossing of the orbits of Venus and Earth; but the traditional tools of quantitative celestial mechanics (numerical integrations or analytical theories), which aim at unique solutions from given initial conditions, will fail to predict such events.

again i'd like to point out that you should follow your own advice and demonstrate an accurate understanding of the subject you are criticizing.  otherwise it's just vapid.

[Bobby Shafto]

Why didn't the supercomputer find possible orbits for bodies of slightly different masses? Because they can't exist.

"And yet we see the bumblebee CAN fly."

Position + Motion + Perturbations => Ephemerides

Ephemerides + Spherical Geometry => Besselian Elements

Not patterns.

Thinking that proving a globe earth model isn't possible somehow proves the flat earth model correct is poor critical reasoning.

Thinking that the N-body problem somehow means ephemerides are "pattern-based" is poor critical reasoning.

Predictions of when, where, how long, type, swath are not only NOT pattern-based, they also only work within the spherical geometry of a globe earth. Unless, that is, you have a comparable model that can make similarly accurate predictions. I don't know how that can be possible when there isn't even a flat earth map.

Erroneously claiming predictions are pattern-based and that an expert in calculating the Besselian Elements of future (and past) solar eclipses is speaking nonsense and is not really applying spherical geometry in producing his outputs is not a logical way to defend a flat earth model. The first step ought to be to develop a flat earth model that can show some alternative success.

I grow so weary watching flat earth advocates taking the approach that "globebusting" somehow bolsters a flat earth argument, as if the flat earth stands in default if the globe is refuted. Adding misunderstanding and erroneous claims to the mix only makes it worse. I've stated my criticism of the wiki article. I'll bow out.

[Tom Bishop]

No, Gary. Answer the question. You did just as I stated. The question was ignored.

Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?

Your links are clearly talking about something else, such as an analysis of the perturbations and statistical analysis that constitutes current planetary prediction methods, not n-body solutions and simulations.

Answer the question:

Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?

[garygreen]

The question was ignored.

nice goalposts.  i wasn't replying to a question.  i replied to your statement that there do not exist any numerical simulations of the solar system based on its geometry and newton's equations of motion.  you described it as "not possible."  i provided you with two important ones.

Your links are clearly talking about something else, such as an analysis of the perturbations and statistical analysis that constitutes current planetary prediction methods, not n-body solutions and simulations.

lol so in other words you didn't bother to even attempt to read or understand any of it.  nice.  why do i even bother.

Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?

this is something like me asking "UA is dumb because how can the earth go faster than the speed of light???" and you correctly answering "your question is based on a false premise.  you fundamentally misunderstand the position you are criticizing."

me shouting just answer the question!!! at you would be pretty disingenuous.

it is not the case that those are the only solutions to the three-body problem.  your own source says that there are lots of periodic solutions to the three-body problem, even for unequal masses.

[Tom Bishop]

Lets see these orbits with unequal masses, Gary. Here is a recent paper on unequal masses and the Three Body Problem by the people with the supercomputer:

Over a thousand new periodic orbits of a planar three-body system with unequal masses

Abstract

The three-body problem is common in astronomy, examples of which are the solar
system, exoplanets, and stellar systems. Due to its chaotic characteristic, discovered by
Poincare, only three families of periodic three-body orbits were found in 300 years, until ´
2013 when Suvakov and Dmitra ˇ sinovi ˇ c ( ´ 2013, Phys. Rev. Lett., 110, 114301) found 13 new
periodic orbits of a Newtonian planar three-body problem with equal mass. Recently,
more than 600 new families of periodic orbits of triple systems with equal mass were
found by Li and Liao (2017, Sci. China-Phys. Mech. Astron., 60, 129511). 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. None of the families have ever been
reported, except the famous “figure-eight” family. In particular, 1223 among these 1349
families are entirely new, i.e., with newly found “free group elements” that have been
never reported, even for three-body systems with equal mass. It has been traditionally
believed that triple systems are often unstable if they are non-hierarchical. However,
all of our new periodic orbits are in non-hierarchical configurations, but many of them
are either linearly or marginally stable. This might inspire the long-term astronomical
observation of stable non-hierarchical triple systems in practice. In addition, using these
new periodic orbits as initial guesses, new periodic orbits of triple systems with three
unequal masses can be found by means of the continuation method, which is more
general and thus should have practical meaning from an astronomical viewpoint.

Their supercomputer found three body problem solutions where two of the bodies had exactly the same mass and one of the masses was different.

Hence, we see that our position is entirely vindicated. The possibilities of these orbits are very limited. None of this is anything like the imaginary astronomy proposed by Copernicus.

[RonJ]

I did some research on statistics and chaos theory a while back.  Just because there’s chaos doesn’t mean a solution can’t be found.  Scientists studying planetary motion have already figured this out.  Last year I was able to calculate Pi to about 4 figures to the right of the decimal place just using about 100 million random numbers generated by my Python program.  Talk about chaos!  My program did require about 8 hours of run time to complete.

The research papers I read had a program that could calculate planetary motions of the entire known solar system including the moon and accounting for 5 different asteroids.  It took over a year of processing time on a desk top computer, but the results modeled everything back for millions of years. Yes, they did say that the accuracy of the data started to decline the further out they went. My other readings did indicate that the Lyapunov time for a solar system was about 50 million years so the results I read about were not too surprising.

Now maybe you have come across an example of what doesn’t work, but there are examples of what does work out there.  Yes, the Newtonian equations do work.  Yes, multi-body solutions can be accurately calculated.  Eclipses can be predicted accurately using just Newtonian equations.  All the information is at your disposal if you choose to access it.  Of course, you can also access all the failures as well and use them to your advantage.  I fully understand that you have the flat earth ball & chain firmly wrapped around your neck and that limits your options.  At least this response will put another mark on the wall for you, and that’s the good news.

[Rounder]

Tell Fred that response is nonsense.

Tell him yourself.  I would love to read the correspondence between the two of you.

[garygreen]

Lets see these orbits with unequal masses, Gary.

i posted two already.  the first two links describe two independent n-body simulations of the solar system (here, n=9 and all the masses are different).  these models numerically integrate newton's laws of motion for all 8 planets plus pluto.

Hence, we see that our position is entirely vindicated. The possibilities of these orbits is very limited.

your authors don't say anything like that.

tbh you obviously don't understand what your authors are even talking about.  they're looking for analytic solutions.  they're looking for sets of initial conditions that create periodic orbits.  these cases are special because if you know the initial conditions at t=0, then you have a single expression to tell you the positions of the objects at t=whenever.

but that doesn't have anything to do with numerical integration.  literally no one but you is claiming that anyone has an analytic model of the solar system.