  We define scattering data for the Newton equation in a potential $V\in
C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some
$\alpha\in (0,1]$. We provide estimates on the scattering solutions and
scattering data and we prove, in particular, that the scattering data at high
energies uniquely determine the short range part of the potential up to the
knowledge of the long range tail of the potential. The Born approximation at
fixed energy of the scattering data is also considered. We then change the
definition of the scattering data to study inverse scattering in other
asymptotic regimes. These results were obtained by developing the inverse
scattering approach of [Novikov, 1999].
