2. The potential

  Stipulate the repulsion potential at center-of-mass mass is zero, and at the distance r from the center is

                                                                                        ( 3 )

 The gravitational potential of a homogenous solid sphere, of radius  a ,  is

                                   (  r < a  )

                                         (  r > a  )

This is solution of  Poissons  equation.