Restricted three body problem (numerical simulation of gravitational attraction)

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Discussion Overview

The discussion revolves around the numerical simulation of the restricted three-body problem, where two massive bodies influence the motion of a third negligible mass. Participants explore the behavior of the third body under various initial conditions and seek to prolong its simulation time for presentation purposes.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant describes their implementation of the restricted three-body problem and notes that the third body is ejected to infinity too quickly for their presentation needs.
  • Another participant suggests that there is no general method for determining suitable initial conditions and recommends experimenting with different parameters.
  • A third participant raises the concern that simulations may be sensitive to rounding or truncation errors and suggests using higher precision in calculations.
  • A fourth participant expresses a desire for assistance in creating a similar simulation, indicating interest in the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to effectively choose initial conditions for the simulation, and multiple viewpoints regarding the sensitivity of simulations and the need for experimentation remain present.

Contextual Notes

Participants acknowledge the randomness of the system and the challenges associated with initial conditions, but do not resolve the specifics of how to achieve longer-lasting simulations.

Who May Find This Useful

Individuals interested in numerical simulations of dynamical systems, particularly in the context of celestial mechanics and the restricted three-body problem.

Silviu
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Hello! I am implementing the three body restricted problem numerically (2 of them are massive and the 3rd one is not affecting them, so it is just moving in the potential created by them). I implemented it and if I put the 3rd one close to one of the big ones it moves in circles around it, while the big one moves around the center of mass of the 2 big ones, as expected. However I want to show the randomness of the system, but for all the initial conditions of the 3rd one (position, momentum and mass), it gets thrown out to infinity too fast (the ones I saw on the internet evolve for quite a while). I understand that this is random, but how can I choose the initial conditions so that it lasts longer (I actually need it for a presentation and I want to show it for half a minute or so). Thank you!
 
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I'm afraid there is no general method to find the initial conditions. You need to play with the parameters. How about this?
 
I think these types of simulations can be very sensitive to rounding/truncation errors in the math. You might try using the highest precision available, if you're not doing that already.
 
Hello. Can you help me with creating such a simulation? I'm trying to create one myself.
 

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