NASAs Transiting Exoplanet Survey Satellite (TESS) mission is expected to discover hundreds of planets via single transits first identified in their light curves. Determining the orbital period of these single transit candidates typically requires a significant amount of follow-up work to observe a second transit or measure a radial velocity orbit. In Yao et al. (2019), we developed simulations that demonstrated the ability to use archival photometric data in combination with TESS to precover the orbital period for these candidates with a precision of several minutes, assuming circular orbits. In this work, we incorporate updated models for TESS single transits, allowing for eccentric orbits, along with an updated methodology to improve the reliability of the results. Additionally, we explore how radial velocity (RV) observations can be used to follow up single transit events, using strategies distinct from those employed when the orbital period is known. We find that the use of an estimated period based on a circular orbit to schedule reconnaissance RV observations can efficiently distinguish eclipsing binaries from planets. For candidates that pass reconnaissance RV observations, we simulate RV monitoring campaigns that enable one to obtain an approximate orbital solution. We find this method can regularly determine the orbital periods for planets more massive than 0.5 M_J with orbital periods as long as 100 days.
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