  We study the problem of planar central configurations with $N$ heavy bodies
and $k$ bodies with arbitrary small masses. We derive the equation which
describe the limit of light masses going to zero, which can be seen as the
equation for central configurations in the anisotropic plane. Using computer
rigorous computations we compute all central configurations for $N=2$ and
$k=3,4$ and for the derived limit problem. We show that the results are
consistent.
