  We prove a meromorphic integrability condition at order 2 near a homothetic
orbit for a meromorphic homogeneous potential of degree -1, which extend the
Morales Ramis conditions of order 1. Conversely, we prove that if this
criterion is satisfied, then the Galois group of second order variational
equation is abelian and we compute explicitly the Galois group and the
Picard-Vessiot extension.
