On the symmetric central configurations for the planar \(1+5\)-body problem with small arbitrary masses (Q2159141)

For the 1+5-body problem, the authors studied the relationship between the masses of 5 satellites (subject to their mutual Newtonian gravitational interaction) and given symmetric configuratios, where the symmetry axis contain one satellite. They found analytically some central configurations for suitable positive masses, under certain assumptions. The authors proved, also, for certain symmetric configuration of these satellites, there exists a one-parameter family of mass vectors for which such configuration is a central configuration. Some numerical results for configurations are presented and the positive masses of these satellites are derived, such that these configurations to be central configurations.