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We measure the star formation quenching efficiency and timescale in clusterenvironments. Our method uses N-body simulations to estimate the probabilitydistribution of possible orbits for a sample of observed SDSS galaxies in andaround clusters based on their position and velocity offsets from their hostcluster. We study the relationship between their star formation rates and theirlikely orbital histories via a simple model in which star formation is quenchedonce a delay time after infall has elapsed. Our orbit library method isdesigned to isolate the environmental effect on the star formation rate due toa galaxy's present-day host cluster from `pre-processing' in previous grouphosts. We find that quenching of satellite galaxies of all stellar masses inour sample ($10^{9}-10^{11.5}\,{\rm M}_\odot$) by massive ($> 10^{13}\,{\rmM}_\odot$) clusters is essentially $100$ per cent efficient. Our fits show thatall galaxies quench on their first infall, approximately at or within a Gyr oftheir first pericentric passage. There is little variation in the onset ofquenching from galaxy-to-galaxy: the spread in this time is at most $\sim 2$Gyr at fixed $M_*$. Higher mass satellites quench earlier, with very littledependence on host cluster mass in the range probed by our sample.

Satellite quenching timescales in clusters from projected phase space measurements matched to simulated orbits