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The addition of an external starshade to the {\it Nancy Grace Roman SpaceTelescope} will enable the direct imaging of Earth-radius planets orbiting at$\sim$1 AU. Classification of any detected planets as Earth-like requires bothspectroscopy to characterize their atmospheres and multi-epoch imaging to tracetheir orbits. We consider here the ability of the Starshade Rendezvous Probe toconstrain the orbits of directly imaged Earth-like planets. The target list forthis proposed mission consists of the 16 nearby stars best suited for directimaging. The field of regard for a starshade mission is constrained by solarexclusion angles, resulting in four observing windows during a two-yearmission. We find that for habitable-zone planetary orbits that are detected atleast three times during the four viewing opportunities, their semi-major axesare measured with a median precision of 7 mas, or a median fractional precisionof 3\%. Habitable-zone planets can be correctly identified as such 96.7\% ofthe time, with a false positive rate of 2.8\%. If a more conservative criteriais used for habitable-zone classification (95\% probability), the falsepositive rate drops close to zero, but with only 81\% of the truly Earth-likeplanets correctly classified as residing in the habitable zone.

Starshade Rendezvous: Exoplanet Orbit Constraints from Multi-Epoch Direct Imaging