About the values of the parameters that describe the Newtonian problem of the eight bodies

Abstract

We consider the Newtonian restricted eight bodies problem with incomplete symmetry. We investigate the stability of some configurations of this problem. The values of the parameters that describe the Newtonian problem of the eight bodies are investigate by some numerical methods. For geometric parameter the intervals of linear stability and instability are found. All relevant and numerical calculation are done with the computer algebra system Mathematica.