  We extract the antikaon potential from differential data on elastic $K^-A$
scattering within Glauber theory at an antikaon momentum of 800 MeV/c. The
$K^-N$ cross section at densities up to 0.1 $fm^3$ is found to be close to the
value given in free space $K^-p$ and $K^-n$ interactions (averaged over the
number of protons and neutrons) whereas the ratio $\alpha$ of the real to
imaginary part of the forward scattering amplitude $f(0)$ differs from the
ratio $\alpha$ in free space indicating a dropping of $Re f(0)$ at finite
nuclear density. The extrapolated $K^-$ potential at a momentum of 0.8 GeV/c
amounts to $\approx $--28 MeV at density $\rho_0$ which is substantially less
than the values extracted from kaonic atoms at zero momentum or heavy-ion data
at 300 MeV/c${\leq}p_K{\leq}$600 MeV/c. We, furthermore, investigate the
perspectives of scattering experiments on $^{12}C$ at low ($\approx$300 MeV/c)
and high ($\approx$1.2 GeV/c) momenta.
