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Space-based direct imaging missions (HabEx, LUVOIR) would observe reflectedlight from exoplanets in the habitable zones of Sun-like stars. Theultimate---but not sole---goal of these concept missions is to characterizesuch planets. Knowing an exoplanet's orbit would help two-fold: (i) itssemi-major axis informs whether the planet might harbour surface liquid water,making it a priority target; and (ii) predicting the planet's future locationwould tell us where and when to look. The science yields of HabEx and LUVOIRdepend on the number, cadence, and precision of observations required toestablish a planet's orbit. We produce mock observations using realisticdistributions for the six Keplerian orbital parameters, experimenting with bothBeta and uniform eccentricity distributions, and accounting for imperfectastrometry ($\sigma$ = 3.5 mas) and obscuration due to the inner working angleof a high-contrast imaging system (IWA = 31 mas). Using Markov chain MonteCarlo methods, we fit the orbital parameters, and retrieve their averageprecisions and accuracies as functions of cadence, number of epochs, anddistance to target. Given the time at which it was acquired, each imageprovides two data: the $x$ and $y$ position of the planet with respect to itsstar. Parameter retrieval based on one or two images is formallyunder-constrained; yet the semi-major axis posterior can be obtainedsemi-analytically. For a planet at 1 AU around a star at a distance of 10 pc,three epochs constrain the semi-major axis to within $\lesssim$5\%, if eachimage is taken at least 90 days apart.

Three direct imaging epochs could constrain the orbit of Earth 2.0 inside the habitable zone