  A system of N points, each having mass m, and a central mass M forming a
planar central configuration, is considered. The equations of motion of a test
particle are given and compared using different coordinates. For large values
of N, even or odd, the equations are given too. The method used for the
computation of some relevant sums can be important for practical applications.
It is shown that the stationary solutions (libration points) can be determined
from an algebraic equation of 5-th degree. If the mass of the particles is
large, the outer libration points disappear. For the inner libration points the
limit minimal distance has been detected. If m=M is small the solution obtained
for the libration has as limit a solution similar to the for 3-body collinear
points. We have also constructed a central configuration with 2N + 1 bodies, in
which N new particles, each of mass m1= m, are placed at the libration points
of our first system.
