Abstract:

In this talk we will give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equal masses when two of the masses are sufficiently small. In particular, for this particular 4-body problem we prove the following two conjectures:

1) "There is a unique convex planar central configuration of the 4-body problem for each ordering of the masses in the boundary of its convex hull" and

2) "There is a unique convex planar central configuration having two pairs of equal masses located at the adjacent vertices of the configuration and it is an isosceles trapezoid".