Thirteen New Solutions to the Three-Body Problem Discovered
39 replies, posted
[quote]It's the sort of abstract puzzle that keeps a scientist awake at night: Can you predict how three objects will orbit each other in a repeating pattern? In the 300 years since this "three-body problem" was first recognized, just three families of solutions have been found. Now, two physicists have discovered 13 new families. It's quite a feat in mathematical physics, and it could conceivably help astrophysicists understand new planetary systems.[/quote]
[url]http://news.sciencemag.org/sciencenow/2013/03/physicists-discover-a-whopping.html[/url]
ArXiv preprint:
[url]http://arxiv.org/abs/1303.0181[/url]
I told my girlfriend I wanted to investigate solutions to the three-body problem and she slapped me.
I actually tried to implement the solution to the 2-body problem (or did I brute force it? Can't remember) in my "orbit" simulator a while ago. But I remember sucked so hard and and everything was wrong...
Three body problem is the stuff of nightmares.
So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?[/QUOTE]
No, they're supposed to orbit each other
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?[/QUOTE]
That's a ridiculous barycenter
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?[/QUOTE]
Well, actually, I am quite sure that would work if you had three exactly identical bodies moving at the exact same speed with the right vector starting in these equal distances.
When something is heavier and moves faster or in a different way (always), it sorta gets more complex.
[QUOTE=Awesomecaek;39857672]Well, actually, I am quite sure that would work if you had three exactly identical bodies moving at the exact same speed with the right vector starting in these equal distances.
When something is heavier and moves faster or in a different way (always), it sorta gets more complex.[/QUOTE]
Sorta being a gross understatement.
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?[/QUOTE]
they could be doing anything
they don't even have to be similar, you could have a planet and a moon but then something of negligible mass like a probe
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[IMG]http://i.imgur.com/MkMMCgj.png[/IMG]
Where three bodies all orbit around the same point?[/QUOTE]
This would be more representative, though shitty (MSPaint has its limitations).
[IMG]http://i.imgur.com/lWHa7qj.png[/IMG]
Think:
Moon orbits Earth, Earth orbits Sun.
The Moon would have tidal forces from the Earth.
The Earth would have tidal forces from the Moon.
The Moon would have tidal forces from the Sun.
The Earth would have tidal forces from the Sun.
The Sun would have tidal forces from the Moon.
The Sun would have tidal forces from the Earth.
[QUOTE=-TheWolf-;39856976]So let me get this straight. This is the type of problem they were trying to solve?
[img]http://i.imgur.com/MkMMCgj.png[/img]
Where three bodies all orbit around the same point?[/QUOTE]
No, that's a very simple problem. These are more complex orbits. We don't have any prescription in general for finding all possible orbits for systems of three or more bodies.
[QUOTE=JohnnyMo1;39859791]No, that's a very simple problem. These are more complex orbits. We don't have any prescription in general for finding all possible orbits for systems of three or more bodies.[/QUOTE]
I tried to see if Universe Sandbox held the solution.
[img]https://lh4.googleusercontent.com/-X7h_0Qk8wck/UTwUdskNyBI/AAAAAAAAJBo/cabeymWYIl0/s0/Universe%252520Sandbox%2525202013-03-09%25252023-53-11-38%252520big.gif[/img]
[QUOTE=mblunk;39861678]I tried to see if Universe Sandbox held the solution.
[img]https://lh4.googleusercontent.com/-X7h_0Qk8wck/UTwUdskNyBI/AAAAAAAAJBo/cabeymWYIl0/s0/Universe%252520Sandbox%2525202013-03-09%25252023-53-11-38%252520big.gif[/img][/QUOTE]
It's simple. We kill the third body.
[QUOTE=Bradyns;39859729]This would be more representative, though shitty (MSPaint has its limitations).
[IMG]http://i.imgur.com/lWHa7qj.png[/IMG]
Think:
Moon orbits Earth, Earth orbits Sun.
The Moon would have tidal forces from the Earth.
The Earth would have tidal forces from the Moon.
The Moon would have tidal forces from the Sun.
The Earth would have tidal forces from the Sun.
The Sun would have tidal forces from the Moon.
The Sun would have tidal forces from the Earth.[/QUOTE]
It's not the solution to the problem because the Sun doesn't orbit the Earth nor the Moon
[QUOTE=Laserbeams;39862900]It's not the solution to the problem because the Sun doesn't orbit the Earth nor the Moon[/QUOTE]
It doesn't really matter. Orbit is probably not being used in that sense. Either way, the earth-moon-sun system is not really an interesting system in terms of three body motion. I looks mostly like two two-body orbits without much three-way interaction.
And people want this sort of thing added into KSP :v:
How do we know these are all the solutions?
[QUOTE=Krinkels;39865778]How do we know these are all the solutions?[/QUOTE]
Nobody said these are all of them, these are just the ones we know so far.
would something like this work?
[img]http://filesmelt.com/dl/3body.png[/img]
or maybe this?
[img]http://filesmelt.com/dl/3body2.png[/img]
You solved it, congrats.
Here ya go:
[img]http://startswithabang.com/wp-content/uploads/2008/10/large-nobel.jpg[/img]
[QUOTE=Laserbeams;39862900]It's not the solution to the problem because the Sun doesn't orbit the Earth nor the Moon[/QUOTE]
What about Pluto + Charon + the other moons? Pluto and Charon orbit each other, and the moons orbit both of them.
The problem with half of these pics posted is that there's a central object that isnt orbiting.
All 3 are orbiting each other, not 2 around a static central object.
[QUOTE=SpartanXC9;39867402]would something like this work?
[img]http://filesmelt.com/dl/3body.png[/img]
or maybe this?
[img]http://filesmelt.com/dl/3body2.png[/img][/QUOTE]
The problem deals with equal masses.
The green would move towards the pink one.
It seems to me that some have failed to understand the problem.
What is sought after is simply a way to describe the velocities and positions of 3 bodies under influence of each other (without brute forcing). That's it.
[QUOTE=Swebonny;39867687]It seems to me that some have failed to understand the problem.
What is sought after is simply a way to describe the velocities and positions of 3 bodies under influence of each other (without brute forcing). That's it.[/QUOTE]
No idea how well this would work, but you could treat bodies A and B as one body, (by averaging their masses and positions), while computing C, then average A and C for B, and C and B for A, moving after all three have been computed.
I have a project for spring break next week, looks like!
Here I made an illustration in paint:
[IMG]http://i.imgur.com/4RiXOzz.png[/IMG]
[editline]10th March 2013[/editline]
they're in space btw
I would love to see some kind of animation to show how this could work.
Having a real hard time imagining how it might look.
[QUOTE=chimitos;39867862]No idea how well this would work, but you could treat bodies A and B as one body, (by averaging their masses and positions), while computing C, then average A and C for B, and C and B for A, moving after all three have been computed.
I have a project for spring break next week, looks like![/QUOTE]
I guess you could simulate it in that way, but imagine if I want to know where body A is after 103 hours. Now you'd have to run the simulation for 103 hours before getting the answer.
If you have the solution, you could just plug in the relevant numbers and you'd get it straight away.
[QUOTE=pansarkurt;39868073]I would love to see some kind of animation to show how this could work.
Having a real hard time imagining how it might look.[/QUOTE]
[url]http://suki.ipb.ac.rs/3body/[/url]
[editline]10th March 2013[/editline]
I like Moth III the best
[img]http://suki.ipb.ac.rs/3body/img/aB22.gif[/img]
[img]http://suki.ipb.ac.rs/3body/img/B22.zez.gif[/img]
[editline]10th March 2013[/editline]
Butteryfly IV is neat too
[img]http://suki.ipb.ac.rs/3body/img/aZZZZ.gif[/img]
[img]http://suki.ipb.ac.rs/3body/img/ZZZZ.zez.gif[/img]
[QUOTE=Swebonny;39868075]I guess you could simulate it in that way, but imagine if I want to know where body A is after 103 hours. Now you'd have to run the simulation for 103 hours before getting the answer.
If you have the solution, you could just plug in the relevant numbers and you'd get it straight away.[/QUOTE]
You wouldn't need it to run at real speed, I bet that it could be calculated quite a bit faster than that.
...but as for a general solution, that's a little out of my mathematical know-how.
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