The three-body problem wiki article
« on: April 23, 2019, 08:53:43 PM »
This is altogether a terrible article. Here's a breakdown of everything it gets wrong:

Quote from: wiki
which has its roots in the unsuccessful attempts to simulate a heliocentric Sun-Earth-Moon system.
The model isn't wrong—in fact, it actually simulates the Sun/Earth/Moon system quite well.

Quote from: wiki
Due to the nature of Newtonian Gravity, a three body system inherently prefers to be a two body orbit and will attempt to kick out the smallest body from the system—often causing the system to be destroyed altogether.
The keyword there is attempt—it's not guaranteed to break the system. The Earth and Moon have far more binding energy than can be supplied by tidal forces from the Sun.

Quote from: wiki
There are a limited range of scenarios in which three body orbits may exist. It is seen that those configurations require at least two of the three bodies to be of the same mass, can only exist with specific magnitudes in specific and sensitive configurations, … The slightest imperfection, such as with bodies of different masses, or the effect of a gravitational influence external to the system, causes a chain reaction of random chaos which compels the entire system to fall apart
The differential equation has unstable equilibria. Shocker.

Quote from: wiki
"Describing the motion of any planetary system (including purely imaginary ones that exist only on paper) is the subject of a branch of mathematics called celestial mechanics. Its problems are extremely difficult and have eluded the greatest mathematicians in history." — Paul Trow, Chaos and the Solar System (Archive)
Eluded the mathematicians, but not the physicists.

Quote from: wiki
Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.
An unsolvable differential equation can still describe reality. Is there a point to the quote?

Sections 2-3
The important thing to remember is that, for a long time—maybe a billion or two years—the solar system was unstable. If a body had a close encounter with a much larger mass, it had 3 possible outcomes: colliding with the larger mass, deflection into a more eccentric orbit, and acceleration into a larger orbit. Eventually most bodies either hit a planet, get too much eccentricity and falls into the Sun, or get ejected into the Kuiper Belt, resulting in the modern set of planets in orbits too far apart for any close encounters.

Also, minor gravitational interactions between planets are observed as slight orbital changes over decades or centuries. Even if a planet had enough energy to eject an adjacent planet (I haven't done the math yet but I doubt it), it would take hundreds of millions of years or more for perturbations to lead to encounters.

Quote from: wiki
The problem with the 3-body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).
Again conflating unsolvable equations with bad models.

Quote from: wiki
This is precisely the issue of modeling the Heliocentric System, and why its fundamental system cannot exist.
This issue relies on the assumption that there are no setups that can last long periods of time without being the equal-mass solution that I've already dismissed as irrelevant.

Quote from: wiki
Programming students participated in the New Mexico Supercomputing Challenge to simulate the solar system and found issues with creating basic orbits:

Simulation of Planetary Bodies in the Universe (N-Body) (Archive) (Source Code)
I recognize that algorithm, having used it myself. One thing I can say is: this algorithm leaves out a key invariant, and that can cause instability in close encounters between objects, or even just over time.

Quote from: wiki
It has often been claimed that this simulation provides evidence that the Sun-Earth-Moon System and the Solar System are able to be simulated with Newtonian Gravity.
Universe Sandbox doesn't use Newtonian gravity. It uses general relativity.

Kidding. While it isn't technically using the Newtonian model, it's close enough at the scale of the solar system that it might as well be. Anyway, the quoted passage goes into how the simulation uses a set of 2-body problems between bodies and their main attractors. The bolded phrases seem to be cherrypicked to indicate that the simulation uses this alternative model because using the normal model would reveal the inherent instability of an incorrect system. This is entirely wrong, it's a problem of time complexity.


In conclusion:
Every part of this article is either wrong or irrelevant, and it should be deleted.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #1 on: April 23, 2019, 08:59:34 PM »
No one has solved the three body problems of astronomy.

"It actually simulates the Sun-Earth-Moon system quite well" is not evidence, or an argument. Your opinion is not an argument.

The Three Body Problem remains unsolved. See: https://wiki.tfes.org/Three_Body_Problem
« Last Edit: April 23, 2019, 09:08:00 PM by Tom Bishop »

Re: The three-body problem wiki article
« Reply #2 on: April 23, 2019, 09:10:02 PM »
No one has solved the three body problems of astronomy.

"It actually simulates the Sun-Earth-Moon system quite well" is not evidence, or an argument. Your opinion is not an argument.

The Three Body Problem remains unsolved. See: https://wiki.tfes.org/Three_Body_Problem
Tell me, what do you think "solve" means in this context? Hint: it has nothing to do with testing the equations against reality.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #3 on: April 23, 2019, 09:13:42 PM »
Quote from: 9 out of 10 doctors agree
Quote
Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.

An unsolvable differential equation can still describe reality. Is there a point to the quote?

"An unsolvable differential equation can still describe reality"

An interesting string of sentences, but I don't really see anything to discuss on the matter. Is there an argument somewhere? If you want to know what the three body problem is and its goals then I would suggest you do some research on the matter.
« Last Edit: April 23, 2019, 09:27:39 PM by Tom Bishop »

Re: The three-body problem wiki article
« Reply #4 on: April 23, 2019, 09:37:46 PM »
Quote from: 9 out of 10 doctors agree
Quote
Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.

An unsolvable differential equation can still describe reality. Is there a point to the quote?

"An unsolvable differential equation can still describe reality"

An interesting string of sentences, but I don't really see anything to discuss on the matter. Is there an argument somewhere? If you want to know what the three body problem is and its goals then I would suggest you do some research on the matter.
Well, the argument seemed to be that since nobody has solved it, it can't be a working model. Which is wrong.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #5 on: April 23, 2019, 09:39:46 PM »
If no one has solved it, it means that they don't have a working model.

Re: The three-body problem wiki article
« Reply #6 on: April 23, 2019, 10:07:40 PM »
If no one has solved it, it means that they don't have a working model.
You're quite obviously conflating terms.

This is an example of a model (actually, most are second order, but this one is first order):



To solve this model means to find the set of functions that comprise solutions for any initial conditions, like so:



A working model means that the differential equation matches observations.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #7 on: April 23, 2019, 10:16:55 PM »
If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions  and scenarios are extremely sensitive look nothing like heliocentric astronomy.
« Last Edit: April 23, 2019, 10:21:07 PM by Tom Bishop »

Re: The three-body problem wiki article
« Reply #8 on: April 23, 2019, 10:27:48 PM »
If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions and scenarios are extremely sensitive look nothing like heliocentric astronomy.
We haven't been searching for a simulation method for 4 centuries, we knew how to the whole time.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #9 on: April 23, 2019, 10:52:21 PM »
The "Euler method" is shown in the article:

https://wiki.tfes.org/Three_Body_Problem#Poliastro

Quote
Poliastro, an astrodynamics software developer, shares several numerical methods for the restricted three body problem:

https://twitter.com/poliastro_py/status/993418078036873216?lang=en (Archive)

  “ Look at this beautiful plot of several numerical methods for the restricted three body problem taken from Harier et al. "Solving Ordinary Differential Equations I". The use of high order Runge-Kutta methods is pervasive in Celestial Mechanics. Happy Monday! ”


Re: The three-body problem wiki article
« Reply #10 on: April 23, 2019, 11:06:48 PM »
The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?

Also, the simulation in the image doesn't use the orbit that the Moon has.
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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #11 on: April 23, 2019, 11:32:47 PM »
The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?

I don't see a simulation of the heliocentric sun-earth-moon system. Do you?

The restricted three body problem also assumes that one of the bodies, the moon in this case, is massless. That's the best they can do.

Quote
Also, the simulation in the image doesn't use the orbit that the Moon has.

Do you think that they were trying to simulate an incorrect model of the moon's orbit?

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Online markjo

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Re: The three-body problem wiki article
« Reply #12 on: April 23, 2019, 11:41:57 PM »
If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model.
Tom, would you care to elaborate as to what you mean by "working model"?
Abandon hope all ye who press enter here.

Science is what happens when preconception meets verification.

If you can't demonstrate it, then you shouldn't believe it.

Re: The three-body problem wiki article
« Reply #13 on: April 23, 2019, 11:51:02 PM »
The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?

I don't see a simulation of the heliocentric sun-earth-moon system. Do you?
Universe Sandbox is mentioned in the article.

The restricted three body problem also assumes that one of the bodies, the moon in this case, is massless. That's the best they can do.
Is that restriction necessary for an approximation though?

Quote
Also, the simulation in the image doesn't use the orbit that the Moon has.

Do you think that they were trying to simulate an incorrect model of the moon's orbit?
Funny thing, I looked up the orbit listed on the image, and it turns out it's not even an orbit for the Moon at all.
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Re: The three-body problem wiki article
« Reply #14 on: April 24, 2019, 02:51:09 AM »
If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions  and scenarios are extremely sensitive look nothing like heliocentric astronomy.

Hi Tom,

I’ve found for you some resources that detail central force problems and how we solve them to explain dynamics in the solar system.

https://courses.physics.ucsd.edu/2010/Fall/physics110a/LECTURES/CH09.pdf

I will track down a few more for your purview just to present a range of options for study.

Let me know if I might be of assistance in understanding them.
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

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Offline QED

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Re: The three-body problem wiki article
« Reply #15 on: April 24, 2019, 03:13:29 AM »
A few more resource for varied audiences:

1. Reduction of differential equations and modeling using simulations:

https://www.google.com/amp/s/www.wired.com/2016/06/way-solve-three-body-problem/amp

2. A more detailed analysis:

https://arxiv.org/pdf/physics/0410149.pdf

3. Numerical estimates of 3 body problem before computers:

http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/ThreeBodyProblem.pdf

4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sun-earth-Moon system easily.

https://arxiv.org/pdf/1508.02312.pdf

5. A older numerical solution to the three body problem which does not constrain the masses or shapes of the orbits:

http://adsbit.harvard.edu//full/1967AJ.....72..876S/0000876.000.html

6. An example which demonstrates that we give our students this problem to solve as homework:

https://physics.stackexchange.com/questions/185555/solving-the-three-body-problem-numerically

7. A science article which details the variety of solutions found for the three-body problem. Not only have they found the rather trivial case of the earth-moon-sun system, but can also describe rather exotic and complicated orbits, demonstrating the sophistication of our knowledge in this area:

https://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem

8. The earth-moon-sun calculations in particular:

http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node100.html

9. Finally, a 300 page manuscript which covers in brutal detail the different solutions to the three body problem:

http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf

This all took me 15 minutes to find.
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

- Tom Bishop

We try to represent FET in a model-agnostic way

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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #16 on: April 24, 2019, 04:34:03 AM »
4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sun-earth-Moon system easily.

https://arxiv.org/pdf/1508.02312.pdf

Stop lying QED. It says in the first sentence:

" Abstract. The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. "

Quote
This all took me 15 minutes to find.

If you have any input then we expect you to quote your sources directly rather than spamming articles that show you to be wrong. I would suggest reading the articles before posting them. 15 minutes to collect those links? That is just spam. We want quality posts.

The rest of those articles talk about two body approximations as a "solution" to the three body problem. No one found a "rather trivial" three body problem solution for the Sun-Earth-Moon system. I would suggest you read your sources, since you admit that you do not. All sources will tell you that it is not really solvable or stable except with some very special and absurd scenarios.
« Last Edit: April 24, 2019, 06:53:07 AM by Tom Bishop »

Offline ChrisTP

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Re: The three-body problem wiki article
« Reply #17 on: April 24, 2019, 10:47:54 AM »
The three body problem shouldn't even be on the FE wiki. Three body problem has absolutely nothing to do with proving flat earth or disproving a spheroid earth. Humans lack of ability to simulate the solar system with perfect accuracy doesn't mean the solar system doesn't exist, nor does it mean the earth is flat. The fact is there needs to be a better model, one that works better than what we understand now, to prove spheroid earth wrong.

Tom, you should be trying to work out a flat earth model that's better rather than silly attempts at poking holes in our understanding of the solar system. It's a childish endeavour. You're bringing strawman problems to another table rather than working solutions to your own and it's not a productive way to prove the earth is flat. If anything, by trying to find issues with current models and understandings it seems you're simply trying to buy time with strawmen to avoid coming to the inevitable truth that you could be wrong about the shape of the earth.

So by all means start working on a functional model before anything else. Separate yourself from trying to disprove spheroid earth and come up with actual, functional solutions to the flat earth. Currently you really have none. All I see is a bunch of 'what ifs' that don't work together to form a working model of the flat earth. Why is that? Maybe start with working out the three body problem for a flat earth? I look forward to your solution to the flat earth three body problem, Tom. Good luck!
Tom is wrong most of the time. Hardly big news, don't you think?

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Offline QED

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Re: The three-body problem wiki article
« Reply #18 on: April 24, 2019, 11:08:17 AM »
4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sun-earth-Moon system easily.

https://arxiv.org/pdf/1508.02312.pdf

Stop lying QED. It says in the first sentence:

" Abstract. The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. "

Quote
This all took me 15 minutes to find.

If you have any input then we expect you to quote your sources directly rather than spamming articles that show you to be wrong. I would suggest reading the articles before posting them. 15 minutes to collect those links? That is just spam. We want quality posts.

The rest of those articles talk about two body approximations as a "solution" to the three body problem. No one found a "rather trivial" three body problem solution for the Sun-Earth-Moon system. I would suggest you read your sources, since you admit that you do not. All sources will tell you that it is not really solvable or stable except with some very special and absurd scenarios.

I encourage you to read the source. I know that it what it says in the abstract, but that is simply the stronger focus. If you follow the equations, it is shown blatantly that no conditions are imposed on the masses either. They do not specify this in the abstract because it is uninteresting - the problem is easy to solve without this constraint. This is precisely the information you were requesting.

My intent was not to spam, but to provide a sample of the wealth of sources which detail how we describe orbits.

I do not really feel inclined to complete your homework for you, and I suppose you are free to ignore all of this if you wish. But I hope that you do not. It may take some time, but here is a wealth of learning that will assist you in formulating better arguments against REers.

I know you probably don’t believe that is what I am trying to help you do, but it truly is!

The smoking gun evidence is right here, staring you right in the face. Let me know if I can be of any assistance understanding the mathematics. It can be daunting to the untrained, and it would be my pleasure to help.

All the best in your search for truth :)
« Last Edit: April 24, 2019, 11:50:36 AM by QED »
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

- Tom Bishop

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Offline Tom Bishop

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Re: The three-body problem wiki article
« Reply #19 on: April 24, 2019, 01:56:34 PM »
Quote from: QED
I encourage you to read the source. I know that it what it says in the abstract, but that is simply the stronger focus.

Quote
If you follow the equations, it is shown blatantly that no conditions are imposed on the masses either. They do not specify this in the abstract because it is uninteresting

Very funny. First you admit to only a cursory glance at the articles, as it only took you '15 minutes' to find them, and now you claim to have read them and that it's abstractly 'in the equations' and never stated anywhere, and that the abstract makes a similar statement about the positions and velocities, but it was only a coincidence. You often rely on "it's too simple" and "everyone knows..."

Please quote your sources directly if you are going to make an argument. "My argument is buried in this paper somewhere and somehow" is an invalid debate tactic.
« Last Edit: April 24, 2019, 02:18:36 PM by Tom Bishop »