Editing Stellar dynamics (section)

== Connection with Kepler problem and 3-body problem ==
At a superficial level, all of stellar dynamics might be formulated as an N-body problem
by [[Newton's second law]], where the equation of motion (EOM) for internal interactions of an isolated stellar system of N members can be written down as,
<math display="block">m_i\frac{d^{2} \mathbf{r_i}}{dt^{2}} = \sum_{i=1 \atop i \ne j}^N \frac{G m_i m_j \left(\mathbf{r}_j - \mathbf{r}_i\right)}{\left\| \mathbf{r}_j - \mathbf{r}_i\right\|^3}. </math>
Here in the N-body system, any individual member, <math>m_i</math> is influenced by the gravitational potentials of the remaining <math>m_j</math> members.

In practice, except for in the highest performance computer simulations, it is not feasible to calculate rigorously the future of a large N system this way.  Also this EOM gives very little intuition. Historically, the methods utilised in stellar dynamics originated from the fields of both [[classical mechanics]] and [[statistical mechanics]]. In essence, the fundamental problem of stellar dynamics is the [[N-body problem]], where the N members refer to the members of a given stellar system. Given the large number of objects in a stellar system, stellar dynamics can address both the global, statistical properties of many orbits as well as the specific data on the positions and velocities of individual orbits.<ref name=":0" />