What is N-body problem: Definition and 17 Discussions

In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem. The n-body problem in general relativity is considerably more difficult to solve.
The classical physical problem can be informally stated as the following:

Given the quasi-steady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times.
The two-body problem has been completely solved and is discussed below, as well as the famous restricted three-body problem.

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  1. SemM

    A Wavefunction for n-particles

    Hi, in Bohm's "Quantum Theory" David Bohm writes: for n-particles the wavefunction is:\begin{equation} G (_{N}) = Ae^{ip \eta /\hbar} + B e^{-ip \eta /\hbar} \end{equation} But this is the same as a wavefunction in one dimension (x) given in Atkins and Friedman "Molecular Quantum Mechanics"...
  2. astrof

    A Numerical simulation the n-body problem under SR model

    The problem is a simple n-body problem: there is n charged particles - electrons, protons, or other particles; we have the initial parameters: a mass, charge, position, velocity, at a time t = 0. In a standard (classical) numerical computation of the n-body problem I can use any numerical...
  3. S

    C/C++ Runge-Kutta methond for n body C++

    Hi! I am trying to simulate the rotation of a planet around a star, using the 2nd order Runge-Kutta method (I am starting with this and I will try 4th order later, I am new to this topic). I have this code but it doesn't work. When I plot y(x) I should get a circle, but I don't get it. Any idea...
  4. olgerm

    Analogues between QM- and CM N-body problem

    In CM general formulation of N-body problem is: x(N;D;T) = \iint \sum_{n=0}^{N_{max}} (\frac {(x(N;D;t)-x(n;D;t))*(m_N*m_n*G+q_N*q_n/(4*π*ε_0))}{(\sum_{d=0}^{D_{max}}((x(N;d;t)-x(n;d;t))^2))^{3/2}*m_N}) \, dt^2 Where x(N;D;T) is D´th coordinate of N´th body at time T. But to get equation of...
  5. M

    C# 3D N-Body Problem (Solar System) C#

    Hey there, first time posting, I have casually browsed this forum for a while. Anyway on to the question, I am trying to solve in the best way possible the N-Body problem, I am at a complete loss, I have no idea what I can do, I have tried figuring out my self different integrators such as...
  6. P

    N-Body Problem - Initial Values

    Hello everyone, I'm new here so let me introduce myself first: I'm a games engineering student and my main field is programming Right now I'm struggeling with the N-Body Problem, well I think actually solved parts of it: I've implemented the basic equations with a leapfrog algorithm...
  7. E

    How to Solve N-body Problem with Python using Euler's Method?

    I was wondering if anyone could by any chance give me some help. I used Euler's method and the program runs, however, it doesn't give the correct solution. I honestly have no idea what's happening in the program, the problem has to be in the way I implemented Euler's Method. But I can't seem to...
  8. C

    Could Virtual Particles Solve the N-Body Problem?

    N-Body Problem -- ideas? First of all I would like some explanation on why one can't find a GENERAL solution for the N-body problem, and what exactly we have to use in its place. Secondly, I want to know if anybody understands these vague ideas of mine and how they would work... Let's...
  9. T

    Explore the N-Body Problem for Chaos

    When looking for chaos in the n body problem what should i do?
  10. A

    N-body problem simulation and relativity

    Do you happen to know about any resources on the gravitational N-body problem and general relativity? Ideally some open-source implementations or pseudo code. I'm doing a N-body simulator for my bachelor's thesis and my advisor was wondering if I could add some algorithms that take general...
  11. P

    Yet-another RK4 n-body problem

    Homework Statement Implementing the 4th order Runge-Kutta method for an n-body problem Homework Equations The RK4 method for the IVP y' = f(t,y), y(t0) = y0, is given by y_(n+1) = y_n + (1/6)(k1 + 2 k2 +2 k3 + k4) t_(n+1) = t_n + h where k1 = h f(t_n,y_n) k2 = h f(t_n+ h/2, y_n + k1/2) k3...
  12. kjohnson

    Programming Efficiency N-body problem

    I am currently in the process of writing a program in VBA that will numerically "solve" a given n-body gravitational problem. I'm doing this pretty much just for fun and am by no means a programmer (had a 1 semester course in c++). The question I have is something that seems to keep coming into...
  13. G

    Best Book on the N-Body Problem?

    What is the best book on the n-body problem, one that would cover all the different numerical and analytic methods of solving it? I am looking for something http://www.amara.com/papers/nbody.html" but more comprehensive, e.g., perhaps with quantum n-body methods, too.
  14. A

    Runge kutta 4 & N-body problem

    Hello ppl, I'm new here. I'm trying to compute RK4 for N-body problem. But after computing I'm getting strange numbers. So here are the formulas for these problem. Start from two differential equations of first order: [1] d\vec{r}/dt = \vec{v_i} [2] \frac{d\vec{v_i}}{dt} = \gamma...
  15. Y

    Static n-Body Problem: Definition and Explanation

    What does it mean for an n-body problem to be static? I come from a mathematics background, so I don't know much about relativity, and I can't seem to find a clear, detailed definition of what a static n-body configuration is. If anyone can explain this to me, I would be very grateful. Thanks.
  16. L

    RK4 in solar system simulation (n-body problem)

    [SOLVED] RK4 in solar system simulation (n-body problem) Hi, I'm making a simulation of the solar system and have so far been using euler's method to integrate my equations of motion - and i'd like to upgrade to a 4th order runge-kutta method. I'm having a lot of trouble understanding the...
  17. L

    Help Needed: Solving the N-Body Problem in 3 Dimensions

    i am attempting to find a solution for the n-body problem, but i don't know the equations for gravity in three dimensions. if someone could post them for me, i would be most appreciative. thank you also, any advice as to how to approach this problem would be appreciated as well