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We combine orbital information from N-body simulations with an analytic modelfor star formation quenching and SDSS observations to infer the differentialeffect of the group/cluster environment on star formation in satellitegalaxies. We also consider a model for gas stripping, using the same inputsupplemented with HI fluxes from the ALFALFA survey. The models are motivatedby and tested on the Hydrangea cosmological hydrodynamical simulation suite. Werecover the characteristic times when satellite galaxies are stripped andquenched. Stripping in massive ($M_\mathrm{ vir}\sim10^{14.5}\,\mathrm{M}_\odot$) clusters typically occurs at or just before thefirst pericentric passage. Lower mass ($\sim10^{13.5}\,\mathrm{M}_\odot$)groups strip their satellites on a significantly longer (by$\sim3\,\mathrm{Gyr}$) timescale. Quenching occurs later: Balmer emission linestypically fade $\sim3.5\,\mathrm{Gyr}$ ($5.5\,\mathrm{Gyr}$) after firstpericentre in clusters (groups), followed a few hundred $\mathrm{Myr}$ later byreddenning in $(g-r)$ colour. These `delay timescales' are remarkably constantacross the entire satellite stellar mass range probed($\sim10^{9.5}-10^{11}\,\mathrm{M}_\odot$), a feature closely tied to ourtreatment of `group pre-processing'. The lowest mass groups in our sample($\sim10^{12.5}\,\mathrm{M}_\odot$) strip and quench their satellites extremelyinefficiently: typical timescales may approach the age of the Universe. Ourmeasurements are qualitatively consistent with the `delayed-then-rapid'quenching scenario advocated for by several other studies, but we findsignificantly longer delay times. Our combination of a homogeneous analysis andinput catalogues yields new insight into the sequence of events leading toquenching across wide intervals in host and satellite mass.

A homogeneous measurement of the delay between the onsets of gas stripping and star formation quenching in satellite galaxies of groups and clusters