  The Galactic Center black hole Sgr A* is the archetypical example of an
underfed massive black hole. The extremely low accretion rate can be understood
in radiatively inefficient accretion flow models. Testing those models has
proven to be difficult due to the lack of suitable probes. Radio and submm
polarization measurements constrain the flow very close to the event horizon.
X-ray observations resolving the Bondi radius yield an estimate roughly four
orders of magnitude further out. Here, we present a new, indirect measurement
of the accretion flow density at intermediate radii. We use the dynamics of the
gas cloud G2 to probe the ambient density. We detect the presence of a drag
force slowing down G2 with a statistical significance of approx 9 {\sigma}.
This probes the accretion flow density at around 1000 Schwarzschild radii and
yields a number density of approx. 4 x 10^3 cm^-3. Self-similar accretion
models where the density follows a power law radial profile between the inner
zone and the Bondi radius have predicted similar values.
