  We study the linear stability of $(1+n)$-gon elliptic relative equilibrium
(ERE for short), that is the Kepler homographic solution with the $(1+n)$-gon
central configurations. We show that for $n\geq 8$ and any eccentricity
$e\in[0,1)$, the $(1+n)$-gon ERE is stable when the central mass $m$ is large
enough. Some linear instability results are given when $m$ is small.
