Three body problem and numerical method

[Rothiemurchus]

What is meant by " a numerical method to solve a three body problem?"

 

[neurocomp2003]

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).

 

[Cyrus]

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.

 

[Sean Torrebadel]

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.

 

[Rothiemurchus]

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?