Offline BRrollin

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3 Body Solution Simulations
« on: May 09, 2020, 09:49:38 PM »
I ran across a cute Java script from a student at Monash Center for Astrophysics, that plots the numerical solutions of the differential equations that describe central force from gravity on three bodies. Enjoy!

https://evgenii.com/blog/three-body-problem-simulator/

The solutions are found using the well-established Runge-Kutta method in mathematics. For details, see:

http://calculuslab.deltacollege.edu/ODE/7-C-3/7-C-3-h.html
« Last Edit: May 09, 2020, 09:53:22 PM by BRrollin »
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

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Offline ChrisTP

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Re: 3 Body Solution Simulations
« Reply #1 on: May 10, 2020, 12:46:35 AM »
I found this one a while back where you can even change the path of the bodies mid sim and watch in realtime as it changes;

https://phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and-orbits_en.html

I actually linked this to Tom and his answer wwas something along the lines of "it' doesn't count cause it's educational" which is funny cause that was the whole point in showing him . :P
Tom is wrong most of the time. Hardly big news, don't you think?

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Offline Tom Bishop

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Re: 3 Body Solution Simulations
« Reply #2 on: May 10, 2020, 01:09:20 AM »
Are you guys aware that you are posting things from random blogs ("I am Evgenii, I like to sleep, listen to Harry Potter books and play Fortnite."), and science teaching resource for elementary schools (PHet)?

Teacher Resources - Copeland Elementary School

"PHet Interactive: This amazing site offers math and science principals explained in colorful simulations which allow students to see and experiment with the math and science concepts."

How does that compare to the citations of physcists and mathematicians who directly state that the three body problems are insoluable and only stable in symmetric conditions?
« Last Edit: May 10, 2020, 01:39:00 AM by Tom Bishop »

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Offline JSS

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Re: 3 Body Solution Simulations
« Reply #3 on: May 10, 2020, 01:36:07 AM »
Are you guys aware that you are posting things from blogs ("I am Evgenii, I like to sleep, listen to Harry Potter books and play Fortnite."), and teaching resource organizations for elementary and middle schools (phet)?

How does that compare to the citations of physcists and mathematicians who directly state that the three body problems are insoluable and only stable in symmetric conditions?

I'd say it holds up pretty well, as none of those citation say we can't use Newtons laws to do real work and calculate real solutions. Write to any of them and ask if their work is stating that we can't use Newtons math to calculate the orbits of planets and spacecraft and comet impacts and launch probes to every planet in the solar system.

Just because a math problem doesn't have an algebraic solution doesn't mean we can't use numerical methods to get our answers, and we do, every day.

And just because a math problem is taught in high school doesn't mean it can't be used for real, practical applications.

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Offline Tom Bishop

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Re: 3 Body Solution Simulations
« Reply #4 on: May 10, 2020, 01:48:36 AM »
You guys are citing gravity learning resources for children.  PHet made a 'gravity simulation' for elementary school teachers to show how gravity makes the Earth go around the Sun. I would recommend finding better evidence for this.

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Offline JSS

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Re: 3 Body Solution Simulations
« Reply #5 on: May 10, 2020, 02:07:43 AM »
You guys are citing gravity learning resources for children.  PHet made a 'gravity simulation' for elementary school teachers to show how gravity makes the Earth go around the Sun. I would recommend finding better evidence for this.

I'm still curious what physicists and mathematicians directly state that we can't use n-body calculations to predict orbits or plat spacecraft trajectories. Can you cite those sources?

Offline BRrollin

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Re: 3 Body Solution Simulations
« Reply #6 on: May 10, 2020, 02:12:28 AM »
You guys are citing gravity learning resources for children.  PHet made a 'gravity simulation' for elementary school teachers to show how gravity makes the Earth go around the Sun. I would recommend finding better evidence for this.

Well, I cannot speak to the phet sim thing, but the java script I posted is from a graduate student in one of the top astrophysics programs. Of course, it isn’t published work - and I never meant for it to be interpreted that way. But why does that mean it’s for children?

You’ll probably be hard pressed to find this stuff that’s published, because it doesn’t seem to be a topic that is of publishable difficulty - as you see, this graduate student did it for their webpage.

What I like about it is if you scroll down, the author details the calculations that go into the code, and even gives the code.

I think that’s pretty neat! And it shows mathematically how you can start from Newton’s gravity and plot actual orbits.

I dunno what top math minds say it isn’t possible, but it seems pretty possible to me. I mean, it’s staring me in the face :)
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

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Offline ChrisTP

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Re: 3 Body Solution Simulations
« Reply #7 on: May 10, 2020, 02:20:15 AM »
Quote
You guys are citing gravity learning resources for children.
Yea it's pretty crazy that we have to resort to showing you childrens resources. In other news, toddlers are just learning 1+1=2 but this super simple stuff isn't wrong just because it's early education material.
Tom is wrong most of the time. Hardly big news, don't you think?

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Offline Tom Bishop

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Re: 3 Body Solution Simulations
« Reply #8 on: May 10, 2020, 02:39:04 AM »
Well, I cannot speak to the phet sim thing, but the java script I posted is from a graduate student in one of the top astrophysics programs. Of course, it isn’t published work - and I never meant for it to be interpreted that way. But why does that mean it’s for children?

On that website it says on that page: "This work is based on Rosmary’s ideas and code."

It's not even that person's ideas or code. They copied code from another author, who may be using it for a different purpose than a true simulation of the n-body problems.

You know that we have an established body of science for the n-body problems, and the study of gravity isn't taking place on blogs with essentially plagiarized code with vague descriptions, right?
« Last Edit: May 10, 2020, 03:14:45 AM by Tom Bishop »

Offline BRrollin

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Re: 3 Body Solution Simulations
« Reply #9 on: May 10, 2020, 02:45:06 AM »
Well, I cannot speak to the phet sim thing, but the java script I posted is from a graduate student in one of the top astrophysics programs. Of course, it isn’t published work - and I never meant for it to be interpreted that way. But why does that mean it’s for children?

On that website it says right ton that page: "This work is based on Rosmary’s ideas and code."

It's not even that person's ideas or code. They copied code from another author, who may be using it for a different purpose than a true simulation of the n-body problems.

You know that we have an established body of science for the n-body problems and the study of gravity isn't taking place on blogs with plagiarized code, right?

Oh yeah, I saw that. It doesn’t bother me though - proper credit was given to the original author, so it isn’t plagiarized.

This doesn’t strike me as a “study of gravity.” The published works on n body simulations I’ve read are on a different level of difficulty and sophistication.

This student took Newton’s second law for each body, solved the differential equations using the Runga-Kutta method, and plotted the resulting orbits.

I think it’s cute, but it’s okay to disagree.

I still don’t see how the basic mathematics required could ever be found in a published article though...it seems more like a homework problem given to students, or something.
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

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Offline Tom Bishop

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Re: 3 Body Solution Simulations
« Reply #10 on: May 10, 2020, 02:52:13 AM »
Quote
Oh yeah, I saw that. It doesn’t bother me though - proper credit was given to the original author

So you are championing a blog post by someone who basically copied random code from github to show larange points, and are telling us that it's a proof of the stability of the n-body problems.

Can you point out the part where he calls it a proof for the stability of the n-body problems? How can you be so sure that it is the purpose of the code? This is something you are inferring.

Quote
I still don’t see how the basic mathematics required could ever be found in a published article though

It's called peer review. It would be reviewed by peers as an established solution to the n-body problem, which physcists and mathematicians would point to as the established method.

Rather than relying on science you guys rely on random simulations you find that may not have been designed for the purpose of proving the stability of the n-body problems.
« Last Edit: May 10, 2020, 02:54:42 AM by Tom Bishop »

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Offline JSS

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Re: 3 Body Solution Simulations
« Reply #11 on: May 10, 2020, 02:54:10 AM »
Quote
I still don’t see how the basic mathematics required could ever be found in a published article though

It's called peer review. It would be reviewed by peers as an established solution to the n-body problem, which physcists and mathematicians would point to as the established method.

Rather than relying on science you guys rely on random simulations you find that may not have been designed for the purpose of proving the stability of the n-body problems.

I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds. I would like to see some of these.

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Offline Tom Bishop

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Re: 3 Body Solution Simulations
« Reply #12 on: May 10, 2020, 02:57:07 AM »
The author does not call it a proof of the stability for the n-body problems and I see no reason to assume that it is. There is a body of science for the n-body problems and this isn't it. I would suggest citing that science in the future.

Quote
I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds

There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.

This is the response to that, to post random found simulations which do not state that they are solving the stability issues of the n-body problems. We must "infer" that this is the purpose or feature of the simulation.
« Last Edit: May 10, 2020, 03:20:34 AM by Tom Bishop »

Offline ChrisTP

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Re: 3 Body Solution Simulations
« Reply #13 on: May 10, 2020, 03:10:48 AM »
Quote
The author does not call it a proof of the stability for the n-body problems and I see no reason to assume that it is.
While I don't particularly care much for the N-body topic I find it pretty funny that you would say this, since you like to cherrypick from scientific papers/research where the authors don't call it proof of a flat earth but you're happy to take that research and use it as evidence of a flat earth. It seems you have a very high standard for anything that will prove your points wrong and an extremely low standard for any snippet of information that sounds like it proves your points right.  ??? I would suggest in the future maybe never cite any scientific paper to use as flat earth evidence if the author doesn't specificially say the research shows a flat earth, otherwise you'd be quite the hypocrite. Maybe you could also start by going through the flat earth's iki and removing anything based on your standards you've shown here (which is most of it).
Tom is wrong most of the time. Hardly big news, don't you think?

Offline BRrollin

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Re: 3 Body Solution Simulations
« Reply #14 on: May 10, 2020, 04:10:51 AM »
The author does not call it a proof of the stability for the n-body problems and I see no reason to assume that it is. There is a body of science for the n-body problems and this isn't it. I would suggest citing that science in the future.

Quote
I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds

There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.

This is the response to that, to post random found simulations which do not state that they are solving the stability issues of the n-body problems. We must "infer" that this is the purpose or feature of the simulation.

I agree that the author does not claim to address chaotic systems. It looks like precise initial conditions are inputted - so there would be no chaotic dynamics to analyze.

I agree and have also read about the inability to find analytical solutions to the differential equations. But I’m confused why this is being raised - this isn’t the topic of the post.

The topic is numerical solutions using a known mathematical process. They show the orbits that follow from the equations when solved using this method. Do you dispute any of the mathematics on the webpage?

It is convincing to me that the numerical method used is accurately applied. So I take this as computational evidence that Newton’s gravity can depict orbits.

However, this doesn’t mean I think you are wrong in your replies. The chaotic dynamics and variations using initial conditions are interesting, and arise when perturbation analytical methods are used to try to find closed form solutions for the differential equations.

I would enjoy discussing that in a new thread, but that is not what THIS thread is about.

Lastly, I respectfully object to statement that this post was a response to Poincare’s work and the chaotic dynamics. It was not, and I never said this. I fear it would “poison the well” to hold this numerical solution to an analytical standard. They are different things.
« Last Edit: May 10, 2020, 04:15:19 AM by BRrollin »
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

- Parsifal


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- totallackey

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Offline JSS

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Re: 3 Body Solution Simulations
« Reply #15 on: May 10, 2020, 11:17:34 AM »
Quote
I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds

There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.

You post lots of quotes of physicists and mathematicians that state there are no closed solutions to the 3 body problem, but none of them are calming that we can't use numerical solutions to do real work and get real answers and predictions.

Poincare is great and all but we didn't even have computers back then. Poincare himself wouldn't have agreed with you, as much of his work involved using relativity to correct for Newton's limitations, and led directly to the formation of the special theory of relativity.

Can you give me your best source for why you think n-body simulations can't simulate real-world problems correctly? One that was written after we had computers capable of solving them.

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Offline AATW

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Re: 3 Body Solution Simulations
« Reply #16 on: May 10, 2020, 06:43:02 PM »
There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.
Yes. And do any of them say that it means the globe earth or heliocentric model is incorrect?
No, they don't. This is the trouble with cherry picking.

Whenever you post those quotes you get the same explanation. There are no ANALYTICAL solutions. That means there is no equation where you can put in the initial conditions and in the equation there's a 't' variable where you can put in time and it will spit out a result which will match observations no matter how far t is in the future. That is a failure of mathematics, not physics.

But there ARE numerical solutions. That means you can take the initial conditions and find what the conditions will be in a small time increment later. You then take the results and repeat the process. There is an inherent problem with this though. If the initial conditions aren't perfectly known - which they can't be - then errors will start to build up and over long timescales the results will no longer match observations. And because it's an iterative process then rounding errors will be a factor too.

But in this case the timescales are pretty long, we can use our models to land craft on Mars or fly a probe past Pluto or tour the outer planets. No model is going to be perfect, it's impossible to account for every moon, every asteroid, every comet. But a model doesn't have to be perfect to be useful. It isn't a point for FE that the RE model is imperfect, especially when the FE model cannot make a single prediction which matches observations.

None of the people who you cherry pick quotes from and misunderstand what those quotes mean are flat earthers. None of them see it as a problem because they understand the above. Is it really so difficult to understand?
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

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Offline BRrollin

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Re: 3 Body Solution Simulations
« Reply #17 on: May 10, 2020, 07:41:50 PM »
There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.
Yes. And do any of them say that it means the globe earth or heliocentric model is incorrect?
No, they don't. This is the trouble with cherry picking.

Whenever you post those quotes you get the same explanation. There are no ANALYTICAL solutions. That means there is no equation where you can put in the initial conditions and in the equation there's a 't' variable where you can put in time and it will spit out a result which will match observations no matter how far t is in the future. That is a failure of mathematics, not physics.

But there ARE numerical solutions. That means you can take the initial conditions and find what the conditions will be in a small time increment later. You then take the results and repeat the process. There is an inherent problem with this though. If the initial conditions aren't perfectly known - which they can't be - then errors will start to build up and over long timescales the results will no longer match observations. And because it's an iterative process then rounding errors will be a factor too.

But in this case the timescales are pretty long, we can use our models to land craft on Mars or fly a probe past Pluto or tour the outer planets. No model is going to be perfect, it's impossible to account for every moon, every asteroid, every comet. But a model doesn't have to be perfect to be useful. It isn't a point for FE that the RE model is imperfect, especially when the FE model cannot make a single prediction which matches observations.

None of the people who you cherry pick quotes from and misunderstand what those quotes mean are flat earthers. None of them see it as a problem because they understand the above. Is it really so difficult to understand?

I agree with all of the above. And I would add that the instability of orbits predicted by chaotic dynamics doesn’t bother me. As far as I can tell, there is a scientific consensus that the solar system is not in a stable configuration, and over long timescales the orbits will not remain.

Those timescales are very long though, so we have other problems before that happens :)
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

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“I hang out with sane people.”

- totallackey

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Offline Tim Alphabeaver

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Re: 3 Body Solution Simulations
« Reply #18 on: May 25, 2020, 11:27:12 PM »
The author does not call it a proof of the stability for the n-body problems and I see no reason to assume that it is. There is a body of science for the n-body problems and this isn't it. I would suggest citing that science in the future.

Quote
I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds

There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.

This is the response to that, to post random found simulations which do not state that they are solving the stability issues of the n-body problems. We must "infer" that this is the purpose or feature of the simulation.
The OP even stated that this is a numerical solution, not 'solving the stability issues of the n-body problems'. Why you feel the need to infer that the simulation is inferring anything other than its actual stated purpose is confusing to me.
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Offline TomInAustin

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Re: 3 Body Solution Simulations
« Reply #19 on: May 26, 2020, 09:07:49 PM »
How does that compare to the citations of physcists and mathematicians who directly state that the three body problems are insoluable and only stable in symmetric conditions?

Or the citations of physicists and mathematicians who directly state that the Earth is round?
Do you have a citation for this sweeping generalisation?