  The discovery of two interstellar objects passing through the Solar System,
1I/`Oumuamua and 2I/Borisov, implies that a galactic population exists with a
spatial number density of order $\sim0.1$ au$^{-3}$. The forthcoming Rubin
Observatory Legacy Survey of Space and Time (LSST) has been predicted to detect
more asteroidal interstellar objects like 1I/`Oumuamua. We apply recently
developed methods to simulate a suite of galactic populations of interstellar
objects with a range of assumed kinematics, albedos and size-frequency
distributions (SFD). We incorporate these populations into the objectsInField
(OIF) algorithm, which simulates detections of moving objects by an arbitrary
survey. We find that the LSST should detect between $\sim 0-70$ asteroidal
interstellar objects every year (assuming the implied number density), with
sensitive dependence on the SFD slope and characteristic albedo of the host
population. The apparent rate of motion on the sky -- along with the associated
trailing loss -- appears to be the largest barrier to detecting interstellar
objects. Specifically, a relatively large number of synthetic objects would be
detectable by the LSST if not for their rapid sky-motion ($>0.5^\circ$
d$^{-1}$). Therefore, algorithms that could successfully link and detect
rapidly moving objects would significantly increase the number of interstellar
object discoveries with the LSST (and in general). The mean diameter of
detectable, inactive interstellar objects ranges from $\sim50 - 600$ m and
depends sensitively on the SFD slope and albedo.
