1. Two-body problem

The two-body problem (or Kepler's problem) consists in studying the relative motion of two particles, exerting between them the force of gravitational attraction, to the exclusion of any other force.

This problem is formulated in a galilean reference frame. The two point bodies have masses m ₁ and m ₂ respectively and positions ${\overrightarrow{r}}_1$ and ${\overrightarrow{r}}_2$ respectively.

Body 2 attracts body 1 with the gravitational force...