  Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario,
we consider a particular modification of standard gravity, which manifests as
an imperfect low pressure fluid. While practically indistinguishable from a
collection of non-relativistic weakly interacting particles on cosmological
scales, it leaves drastically different signatures in the Solar system. The
main effect stems from gravitational focusing of the flow of Imperfect Dark
Matter passing near the Sun. This entails strong amplification of Imperfect
Dark Matter energy density compared to its average value in the surrounding
halo. The enhancement is many orders of magnitude larger than in the case of
Cold Dark Matter, provoking deviations of the metric in the second order in the
Newtonian potential. Effects of gravitational focusing are prominent enough to
substantially affect the planetary dynamics. Using the existing bound on the
PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique
constant of the model.
