Planar central configurations of some restricted (4 + 1)-body problems

Abstract

We start with the 13 central configurations of the restricted (4 + 1) body problem having four primaries with equal masses at the vertices of a square. Then, we describe the evolution of these central configurations when some of the masses of the four primaries tend to zero and the remainder ones keep constant. More precisely, we consider the cases where one of the masses tends to zero, where either two adjacent or two opposite equal masses tend to zero simultaneously, and where three equal masses tend to zero simultaneously. Here, simultaneously means that the masses that go to zero take the same value at any moment.