We study the planar central conﬁgurations of the 1 + n body problem where
one mass is large and the other n masses are inﬁnitesimal and equal. We ﬁnd
analytically all these central conﬁgurations when 2 ≤ n ≤ 4. Numerically, ﬁrst
we provide evidence that when n ≥ 9 the only central conﬁguration is the regular
n–gon with the large mass in its barycenter, and second we provide also evidence
of the existence of an axis of symmetry for every central conﬁguration.