Three body problem and numerical method

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Discussion Overview

The discussion revolves around the concept of the three body problem and numerical methods used to solve it. Participants explore the complexities involved in modeling three interacting bodies under physical forces, particularly gravitational interactions, and the challenges of deriving numerical solutions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about the meaning of "numerical method" in the context of the three body problem, suggesting it involves numerical integrators that evolve the system based on physical forces.
  • Others explain that the three body problem cannot be easily separated into explicit equations of motion, necessitating iterative methods like Euler's method for solutions.
  • One participant notes the difficulty of applying numerical methods to the three body problem, emphasizing that solutions typically involve gravitational forces and may require vector analysis.
  • There is a discussion on specific examples, such as the Sun, Earth, and Moon, highlighting the complexity of interactions, including gravitational attraction and electron-electron repulsion in atomic systems like Helium.
  • A participant raises questions about simplifying assumptions, such as treating the Sun as a fixed point in a solar system model, and whether large distances can reduce a three body problem to a two body problem.
  • There is curiosity about the criteria for determining when a three body problem can be simplified and whether physical contact between bodies alters their classification.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the nature of the three body problem and the applicability of numerical methods, indicating that multiple competing views remain without a consensus on specific criteria for simplification or the nature of numerical solutions.

Contextual Notes

Participants highlight the complexity of the three body problem and the need for clarity on which specific scenario is being discussed, as well as the limitations of numerical methods in capturing all interactions involved.

Rothiemurchus
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What is meant by " a numerical method to solve a three body problem?"
 
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3-body usually means based on some physical force...numerical method i would assume to be the numerical integrator that maintains/evolves the system (eg integrator for gravity or potential).
 
it means the equation is not separable for the equations of motion to get an explicit equation. You have to iterate to find the solution using eulers method.
 
Typically, a three body problem is extremely hard to put into numerical form. If someone has a numerical solution for a three body problem it would have to involve one force, where vectors would be used to solve the problem. The Sun, Earth and moon are a three body problem. The force involved in each case is that of gravitation. Trying to describe the motion of the Earth with a numerical solution is not straight forward. In the case of Hydrogen, one electron orbits a proton- a two body system. Bohr's theory was a solution to this two body problem, it equated electrostatic force or coulomb's law with an inward centripetal force. In the case of Helium, we have two electrons and one nucleus, a three body problem. In this case a solution is extremely difficult, because we have to consider not only the attraction between the electrons and the proton, but also electron-electron repulsion.
In order to be relevant we really need to know what three body problem you are referring too.
 
If we had a solar system with a sun and just one planet, with one moon going around this planet, this would be a three body problem.Can we assume that because the sun is large it is a fixed point,and that the moon is small and does not affect the motion of the planet too much, the movement of the planet around the sun is a two body problem?Does a large distance between some masses reduce a problem from being three body to two body? How do we decide when a three body problem has become a two body problem?
Is there some equation that tells us this or is it a subective judgement?
If the planet and moon physically touch one another do they become one body?
 

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