3 Body problem: A stable binary system

[WhereToGoist]

i would really hate to be on that planet!

[FutileFreak]

I know this sounds like an ignorant question, But how exactly is this a "problem"

[TupoyVolk]

@FutileFreak Just a term. What is 2+2 is a "problem."

[timpanitimptim]

@FutileFreak Well, you have to figure out how to piece together the effect of each white planet on the green one, which depends on the distance and direction between them. No one knows how to make time go smoothly in computers, so you say "in this itty bitty time, it changes speed constantly" and "in the next itty bitty time it changes speed constantly, but at a slightly different rate" because the distances have changed a bit. So, you then approximate the speed like that. RK4 uses this idea.

[timpanitimptim]

@FutileFreak Oh, and there ain't no ignorant question.

[rottencranberry]

we can observe the transmigration phenomeno.

:O! Pretty well done.

[ManfredSupertyp]

its just a 2 body problem...

[cpaulof]

@ManfredSupertyp No, it's a restricted 3 body problem

[TriKri]

Is the solution obtained obtained analytical or numerically?

[cpaulof]

@TriKri If it was analytical, it should be stable. It is a numerical round off error that kills the stability

[TriKri]

@cpaulof What does the solution look like? I didn't know that there was an analytical solution to such a complicated problem. Do you use Euler's method? I think that you can make the system stable for a much longer time if you use another Runge-Kutta method. Interesting simulation though!

[cpaulof]

@TriKri Ups.. wrong comment on the wrong video.... This one probably hasn't a simple analytical solution, if it has at all .. my mistake, sorry. But this is an RK4. I' have here other video with the green body in the center that the planet should not move... but it moves! (Round off error) I forgot that i had uploaded this one also. This one is not supposed to be stable.. You're right!

[timpanitimptim]

@cpaulof Shouldn't it be possible to start off with a guessed Taylor polynomial and use an algorithm to converge that to an apt description? Do you know of anything like that?

[cpaulof]

@timpanitimptim With chaotic orbits, I don't know if we'll get "apt descriptions" . However your idea should be explored...

I don't think I know to do it (at least yet), but I can give it some tought.

Do you have some idea of how to do it?

[Hedgehogs4Me]

I think you're leaving out the gravitational effect the green circle has on the white circles.

[cpaulof]

@Hedgehogs4Me no no.. I assure you. Mass of the green circle=earth mass.

Mass of the white ones= Mass of the sun.

the orbit of the white circles (without the green mass) is circular.

the gravitational effects of the green circle are so low that you don't notice it.

[Orlor]

I wouldn't want to live on that planet.

[Theelectricgypsy]

what are your inits?

[Theelectricgypsy]

ok thanks alot. i saw your videos and i was intrigued, so i wrote my own little simulator. fun stuff

[cpaulof]

@Theelectricgypsy Mass of the green circle=earth mass.

Mass of the white ones= Mass of the sun.

the orbit of the white circles (without the green mass) is circular.

[cpaulof]

c++ compiler (g++) with the PNGwriter library

to generate the frames.

ImageMagik to join the frames in a file

The GIMP to optimize the file

[IoannesKomnenos]

what software did you use creating this?