  We present a semi-analytic model of satellite galaxies, SatGen, which can
generate large samples of satellite populations for a host halo of desired
mass, redshift, and assembly history. The model combines dark-matter halo
merger trees, empirical relations for the galaxy-halo connection, and analytic
prescriptions for tidal effects, dynamical friction, and ram pressure
stripping. SatGen emulates cosmological zoom-in hydro-simulations in certain
aspects. Satellites can reside in cored or cuspy DM subhaloes, depending on the
halo response to baryonic physics that can be formulated from hydro-simulations
and physical modeling. The subhalo profile and the stellar mass and size of a
satellite evolves depending on its tidal mass loss and initial structure. The
host galaxy can include a baryonic disc and a stellar bulge, each described by
a density profile that allows analytic orbit integration. SatGen complements
simulations by propagating the effect of halo response found in simulated field
galaxies to satellites (not properly resolved in simulations) and outperforms
simulations by sampling the halo-to-halo variance of satellite statistics and
overcoming artificial disruption due to insufficient resolution. As a first
application, we use the model to study satellites of Milky Way sized hosts,
making it emulate simulations of bursty star formation and of smooth star
formation, respectively, and to experiment with a disc potential in the host
halo. Our model reproduces the observed satellite statistics reasonably well.
Different physical recipes make a difference in satellite abundance and spatial
distribution at the 25% level, not large enough to be distinguished by current
observations given the halo-to-halo variance. The MW disc depletes satellites
by 20% and has a subtle effect of diversifying the internal structure of
satellites, important for alleviating certain small-scale problems.
