  Understanding the evolution of satellite galaxies of the Milky Way (MW) and
M31 requires modeling their orbital histories across cosmic time. Many works
that model satellite orbits incorrectly assume or approximate that the host
halo gravitational potential is fixed in time and is spherically symmetric or
axisymmetric. We rigorously benchmark the accuracy of such models against the
FIRE-2 cosmological baryonic simulations of MW/M31-mass halos. When a typical
surviving satellite fell in ($3.4-9.7$ Gyr ago), the host halo mass and radius
were typically $26-86$ per cent of their values today, respectively. Most of
this mass growth of the host occurred at small distances, $r\lesssim50$ kpc,
opposite to dark-matter-only simulations, which experience almost no growth at
small radii. We fit a near-exact axisymmetric gravitational potential to each
host at $z=0$ and backward integrate the orbits of satellites in this static
potential, comparing against the true orbit histories in the simulations.
Orbital energy and angular momentum are not well conserved throughout an
orbital history, varying by 25 per cent from their current values already
$1.6-4.7$ Gyr ago. Most orbital properties are minimally biased, $\lesssim10$
per cent, when averaged across the satellite population as a whole. However,
for a single satellite, the uncertainties are large: recent orbital properties,
like the most recent pericentre distance, typically are $\approx20$ per cent
uncertain, while earlier events, like the minimum pericentre or the infall
time, are $\approx40-80$ per cent uncertain. Furthermore, these biases and
uncertainties are lower limits, given that we use near-exact host mass profiles
at $z=0$.
