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The recently discovered population of interstellar objects presents us withthe opportunity to characterize material from extrasolar planetary and stellarsystems up close. The forthcoming Vera C. Rubin Observatory Legacy Survey ofSpace and Time (LSST) will provide an unprecedented increase in sensitivity tothese objects compared to the capabilities of currently operationalobservational facilities. We generate a synthetic population of `Oumuamua-likeobjects drawn from their galactic kinematics, and identify the distribution ofimpact parameters, eccentricities, hyperbolic velocities and sky locations ofobjects detectable with the LSST, assuming no cometary activity. Thispopulation is characterized by a clustering of trajectories in the direction ofthe solar apex and anti-apex, centered at orbital inclinations of$\sim90^\circ$. We identify the ecliptic or solar apex as the optimal skylocations to search for future interstellar objects as a function of surveylimiting magnitude. Moreover, we identify the trajectories of detectableobjects that will be reachable for \textit{in-situ} rendezvous with a dedicatedmission with the capabilities of the forthcoming \textit{Comet Interceptor} orproposed \textit{Bridge} concept. By scaling our fractional populationstatistics with the inferred spatial number density, we estimate that the LSSTwill detect of order $\sim 15$ interstellar objects over the course of its$\sim10$ year observational campaign. Furthermore, we find that there should be$\sim1-3$ and $\sim0.0007-0.001$ reachable targets for missions with propulsioncapabilities comparable to \textit{Bridge} and \textit{Comet Interceptor},respectively. These numbers are lower limits, and will be readily updateablewhen the number density and size frequency distribution of interstellar objectsare better constrained.

The Population of Interstellar Objects Detectable with the LSST and Accessible for $\textit{In Situ}$ Rendezvous with Various Mission Designs