A particle P of mass m can move under the gravitational attraction of two particles, of equal mass M, fixed at the points (0,0,±a). Show that the origin O is a position of equilibrium, but that it is not stable. [This illustrates the general result that no free-space static gravitational field can provide a position of stable equilibrium.] Please draw the diagram for this problem.

A particle P of mass m can move under the gravitational attraction of two particles, of equal mass M, fixed at the points (0,0,±a). Show that the origin O is a position of equilibrium, but that it is not stable. [This illustrates the general result that no free-space static gravitational field can provide a position of stable equilibrium.] Please draw the diagram for this problem.