| Contents |
| The planar central configurations are configurations of a finite number of gravitating points in a relative equilibrium. They are obtained by solving a system of algebraic equations. This is one of the most natural systems having configurations as roots. By looking at the set of solutions we observe very simple facts, which we are unable to prove. For example, whatever be the masses, there are at most 50 planar central configurations of 4 bodies. We will analyse results by Marshall Hampton, Rick Moeckel, Carles Sim\'o and Zhihong Xia which point toward an interesting conjecture about a general lower bound. |
|