  The orbital parameters of dark matter (DM) subhaloes play an essential role
in determining their mass-loss rates and overall spatial distribution within a
host halo. Haloes in cosmological simulations grow by a combination of
relatively smooth accretion and more violent mergers, and both processes will
modify subhalo orbits. To isolate the impact of the smooth growth of the host
halo from other relevant mechanisms, we study subhalo orbital evolution using
numerical calculations in which subhaloes are modelled as massless particles
orbiting in a time-varying spherical potential. We find that the radial action
of the subhalo orbit decreases over the first few orbits, indicating that the
response to the growth of the host halo is not adiabatic during this phase. The
subhalo orbits can shrink by a factor of $\sim$1.5 in this phase. Subsequently,
the radial action is well conserved and orbital contraction slows down. We
propose a model accurately describing the orbital evolution. Given these
results, we consider the spatial distribution of the population of subhaloes
identified in high-resolution cosmological simulations. We find that it is
consistent with this population having been accreted at z < 3, indicating that
any subhaloes accreted earlier are unresolved in the simulations. We also
discuss tidal stripping as a formation scenario for NGC1052-DF2, an ultra
diffuse galaxy significantly lacking DM, and find that its expected DM mass
could be consistent with observational constraints if its progenitor was
accreted early enough, z > 1.5, although it should still be a relatively rare
object.
