  It is well known that a planar central configuration of the $n$-body problem
gives rise to solutions where each particle moves on a specific Keplerian orbit
while the totality of the particles move on a homographic motion. When the
eccentricity $e$ of the Keplerian orbit belongs in $[0,1)$, following Meyer and
Schmidt, we call such solutions elliptic relative equilibria (shortly, ERE). In
order to study the linear stability of ERE in the near-collision case, namely
when $1-e$ is small enough, we introduce the collision index for planar central
configurations. The collision index is a Maslov-type index for heteroclinic
orbits and orbits parametrised by half-lines that, according to the Definition
given by authors in [16], we shall refer to as half-clinic orbits and whose
Definition in this context, is essentially based on a blow up technique in the
case $e=1$. We get the fundamental properties of collision index and
approximation theorems. As applications, we give some new hyperbolic criteria
and prove that, generically, the ERE of minimal central configurations are
hyperbolic in the near-collision case, and we give detailed analysis of Euler
collinear orbits in the near-collision case.
