Measuring gravitational effects on antimatter in space

We propose an experimental test of the gravitational interaction with antimatter by measuring the branching fraction of the CP~violating decay $K_\mathrm{L} \to \pi^{+} \pi^{-}$ in space. We show that at the altitude of the International Space Station, gravitational effects may change the level of CP~violation such that a 5$\sigma$ discrimination may be obtained by collecting the $K_\mathrm{L}$ produced by the cosmic proton flux within a few years.