### N-body problem

(calculating the paths of gravitationally-interacting celestial objects)

The **N-body problem** is the mathematical/dynamical problem
of describing the course of multiple celestial bodies interacting
via gravity (or more generally, via any type of force interacting
between the bodies). The term is generally used for the "difficult"
case of N greater than two, since the **two-body problem** has its
own specific analytical solution. Three or more bodies generally
requires the use of a **Taylor series** or N-body simulation, i.e.,
calculating the motions in small steps.
The case of interacting orbits has some specialized solutions: some
generalized information can be calculated such as whether the orbits
are likely to remain stable (a planet thrown out of the system would
imply instability, for example) or become chaotic, i.e.,
perturbation theory.
The Jacobi integral is another method addressing
**three-body problems**.

The term **many-body problem** is used for interactions where
the number of objects has made the computation difficult,
and is seen in relation to quantum mechanicses.

The **million-body problem** is currently (2018) barely within reach
of (pure) n-body simulations but remains impractical.
A specific reason for interest is that a million is the
order-of-magnitude of sizeable globular clusters.
Ways have been
devised to make it more practical by incorporating various Monte Carlo methods,
one approach being to use the MC method for **weak interactions**
(i.e., that only slight perturbations in velocity) but simulate the
**strong interactions** in detail.
Galaxies such as the Milky Way have
far more stars and are not close to being simulated in such a manner.
Open clusters are generally smaller, on the order of 10,000
stars, and can be simulated.

(*mathematics,dynamics*)
**Further reading:**

http://en.wikipedia.org/wiki/N-body_problem

**Referenced by pages:**

adaptive refinement tree (ART)

Jacobi integral

N-body simulation

quantum Monte Carlo (QMC)

Index