Real 3-Body Systems Initial Value Problem Data

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In summary: In other words, it is possible to prove that, under given conditions, the three body problem will always converge to a solution that is not measure zero.Wallace
  • #1
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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.
 
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  • #2
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?
 
  • #3
I guess these values are always constrained by The Uncertainty Principle.
 
  • #4
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.)
 
  • #5
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" [Broken] site.
 
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  • #6
Thank you, Wallace. I have contacted him already.
 
  • #8
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.
 
  • #9
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.
 

1. What is a real 3-body system initial value problem?

A real 3-body system initial value problem refers to a scenario in which three objects interact with each other through gravitational forces. These objects can be planets, stars, or any other massive bodies. The initial value problem refers to the equations that govern the motion of these objects and the initial conditions that determine their positions and velocities at a certain time.

2. How is the data for a real 3-body system initial value problem collected?

The data for a real 3-body system initial value problem is typically collected through observations and measurements from astronomical instruments such as telescopes and satellites. This data includes the masses, positions, and velocities of the three objects involved in the system.

3. What is the significance of studying real 3-body system initial value problems?

Studying real 3-body system initial value problems allows scientists to better understand the laws of physics, specifically the effects of gravity on multiple objects. This can also provide insight into the formation and evolution of planetary systems and other celestial bodies.

4. Are there any challenges in solving real 3-body system initial value problems?

Yes, there are several challenges in solving real 3-body system initial value problems. One major challenge is the complexity of the equations involved, which often require numerical methods to solve. Another challenge is the uncertainty in the initial conditions and the potential for chaotic behavior, making it difficult to accurately predict the long-term behavior of the system.

5. How are real 3-body system initial value problems used in other fields of study?

Real 3-body system initial value problems have applications in various fields such as astronomy, physics, and engineering. They can be used to model the motion of celestial bodies in space, study the dynamics of molecules in chemistry, and even simulate the behavior of particles in computer graphics and simulations.

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