  Physical processes regulating star formation in satellite galaxies represent
an area of ongoing research, but the projected nature of observed coordinates
makes separating different populations of satellites (with different processes
at work) difficult. The orbital history of a satellite galaxy leads to its
present-day phase space coordinates; we can also work backwards and use these
coordinates to statistically infer information about the orbital history. We
use merger trees from the MultiDark Run 1 N-body simulation to compile a
catalog of the orbits of satellite haloes in cluster environments. We
parameterize the orbital history by the time since crossing within 2.5 rvir of
the cluster centre and use our catalog to estimate the probability density over
a range of this parameter given a set of present-day projected (i.e.
observable) phase space coordinates. We show that different populations of
satellite haloes, e.g. infalling, backsplash and virialized, occupy distinct
regions of phase space, and semi-distinct regions of projected phase space.
This will allow us to probabilistically determine the time since infall of a
large sample of observed satellite galaxies, and ultimately to study the effect
of orbital history on star formation history (the topic of a future paper). We
test the accuracy of our method and find that we can reliably recover this time
within +/-2.58 Gyr in 68 per cent of cases by using all available phase space
coordinate information, compared to +/-2.64 Gyr using only position coordinates
and +/-3.10 Gyr guessing 'blindly', i.e. using no coordinate information, but
with knowledge of the overall distribution of infall times. In some regions of
phase space, the accuracy of the infall time estimate improves to +/-1.85 Gyr.
Although we focus on time since infall, our method is easily generalizable to
other orbital parameters (e.g. pericentric distance and time).
