Securing the legacy of TESS through the care and maintenance of TESS planet ephemerides

TESS has begun fulfilling its promise of delivering thousands of new transiting planets orbiting nearby bright stars. The mission's legacy will fuel exoplanet science for many years to come, but much of this science relies on precisely predicted transit times that are needed for many follow-up characterization studies. We investigate the severity of ephemeris deterioration for TESS planets, and find that most will have uncertainties greater than 1 hour just one year after their TESS observations. It is the mission's relatively short observing baseline that drives this fast deterioration. We identify the parameters that have the strongest impact on this deterioration. We recommend that one or two follow-up transits be observed three and/or nine months after the end of a planet's TESS observations, in order to refresh its ephemeris for two years past the follow-up observations. We find that the longer the baseline between the TESS and the follow-up observations, the longer the ephemerides will stay fresh, facilitating the scheduling of future observations with expensive facilities such as the Hubble Space Telescope, the James Webb Space Telescope, the ELTs, and Ariel.