  We study a 2-body problem given by the sum of the Newtonian potential and an
anisotropic perturbation that is a homogeneous function of degree $-\beta$,
$\beta\ge 2$. For $\beta>2$, the sets of initial conditions leading to
collisions/ejections and the one leading to escapes/captures have positive
measure. For $\beta>2$ and $\beta\ne 3$, the flow on the zero-energy manifold
is chaotic. For $\beta=2$, a case we prove integrable, the infinity manifold of
the zero-energy level is a disconnected set, which has heteroclinic connections
with the collision manifold.
