N-body problem

N-body problem is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The $N$-body problem is an inherent feature of a physical description of mechanical system of $N$ interacting objects. The system is described by Newton's Law

${\vec {F}}=m_{i}{\frac {d^{2}{\vec {r}}_{i}}{dt^{2}}},i=1..N$

with continious combined force from other bodies

$F_{i}=\sum _{j}^{}F_{ij},i=1..N$

Exact formulation of first mechanical problem is, given initial coordinates and velocities $t=0$, to find coordinates and velocities at $t=t_{0}$ with accuracy more then given relative value $\epsilon ={\frac {{\vec {r}}-{\vec {r}}'}{|{\vec {r}}|}}$

As well known from physical background, only the choice of N=2 can be analytically solved.