  We combine orbital information from N-body simulations with an analytic model
for star formation quenching and SDSS observations to infer the differential
effect of the group/cluster environment on star formation in satellite
galaxies. We also consider a model for gas stripping, using the same input
supplemented with HI fluxes from the ALFALFA survey. The models are motivated
by and tested on the Hydrangea cosmological hydrodynamical simulation suite. We
recover the characteristic times when satellite galaxies are stripped and
quenched. Stripping in massive ($M_\mathrm{ vir}\sim
10^{14.5}\,\mathrm{M}_\odot$) clusters typically occurs at or just before the
first 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 lines
typically fade $\sim3.5\,\mathrm{Gyr}$ ($5.5\,\mathrm{Gyr}$) after first
pericentre in clusters (groups), followed a few hundred $\mathrm{Myr}$ later by
reddenning in $(g-r)$ colour. These `delay timescales' are remarkably constant
across the entire satellite stellar mass range probed
($\sim10^{9.5}-10^{11}\,\mathrm{M}_\odot$), a feature closely tied to our
treatment of `group pre-processing'. The lowest mass groups in our sample
($\sim10^{12.5}\,\mathrm{M}_\odot$) strip and quench their satellites extremely
inefficiently: typical timescales may approach the age of the Universe. Our
measurements are qualitatively consistent with the `delayed-then-rapid'
quenching scenario advocated for by several other studies, but we find
significantly longer delay times. Our combination of a homogeneous analysis and
input catalogues yields new insight into the sequence of events leading to
quenching across wide intervals in host and satellite mass.
