Real 3-Body Systems Initial Value Problem Data

[Version 7]

Hi everybody,

I'm looking for initial value problem data for real
three-body systems.
I.e., three point-like (or physically nearly equivalent)
body systems for which the masses of the bodies and their
positions and velocities are known for a given instant;
either in the system's centre of mass frame of reference
or in one of the particle's coordinate frame.

I would be grateful to anybody who could provide me with
this kind of data.

 

[Wallace]

I think you imply more than you are asking. Any set of masses, positions and velocities for the three particles are perfectly reasonable initial conditions. On the other hand, if you want initial conditions for a bound, stable 3 body interaction, then it is much more tricky. Is this what you want?

 

[Hippasos]

I guess these values are always constrained by The Uncertainty Principle.

 

[Version 7]

Wallace,

The question was made as short as possible. Of course, I can input (make up) any initial conditions, but I will not be able to verify whether or not the numerical solution is to any accuracy correct. As such, I am more interested if it happens that those conditions in fact mirror a real system at any given time, e.g., Earth-Moon-Sun system.

I make no other requirements (as for stability), for the three-body problem does not have "classical" analytical solutions as its two-body counterpart. (And thinking of the three-body problem in terms of its two-body counterpart is maybe not very helpful.)

Of course, although it is not at all necessary for the system to be bound, the 3 bodies should nevertheless move only -or very closely- under their mutual gravitational interactions.

Hippasos, I am referring to the three-body problem gravitational case. I apologize if I wasn't clear enough.

Thank you very much for your replies. Is there any data available? Any comments or suggestions will be welcome.


(PS.: I may not be able to reply immediately.)

 

[Wallace]

Sorry, there is still something fundamental missing in your question. You say

Of course, I can input (make up) any initial conditions, but I will not be able to verify whether or not the numerical solution is to any accuracy correct.

I think (though I'm not sure) you are asking whether someone has the initial conditions and data about the subsquent evolution of a 3 body system, so that you can compare to your calculations? You may find some usefull things on http://www.ast.cam.ac.uk/~sverre/web/pages/nbody.htm" site.

 

[Version 7]

Thank you, Wallace. I have contacted him already.

 

[Bob S]

This site:http://en.wikipedia.org/wiki/N-body_problem#Three-body_problem
implies that the evolution of the general 3-body system is chaotic. The attached article references work done by Newton and others.

 

[Hippasos]

Hi Bob,

In what stage of the 3 body system's evolution You think the system begins to behave chaotically?

I personally think that "in real life" there are only chaotically behaving systems of which initial value data can not be exactly acquired (excluding less or more accurate computer simulations).

Correct me if I am somehow fundamentally wrong about this.

 

[D H]

The three body problem is almost always chaotic. "Almost always" has a specific mathematical meaning: It means for all cases but a set of measure zero.