  Some low-mass planets are expected to be ejected from their parent planetary
systems during early stages of planetary system formation. According to
planet-formation theories, such as the core accretion theory, typical masses of
ejected planets should be between 0.3 and 1.0 $M_{\oplus}$. Although in
practice such objects do not emit any light, they may be detected using
gravitational microlensing via their light-bending gravity. Microlensing events
due to terrestrial-mass rogue planets are expected to have extremely small
angular Einstein radii (< 1 uas) and extremely short timescales (< 0.1 day).
Here, we present the discovery of the shortest-timescale microlensing event,
OGLE-2016-BLG-1928, identified to date ($t_{\rm E} \approx 0.0288\ \mathrm{day}
= 41.5 \mathrm{min}$). Thanks to the detection of finite-source effects in the
light curve of the event, we were able to measure the angular Einstein radius
of the lens $\theta_{\rm E} = 0.842 \pm 0.064$ uas, making the event the most
extreme short-timescale microlens discovered to date. Depending on its unknown
distance, the lens may be a Mars- to Earth-mass object, with the former
possibility favored by the Gaia proper motion measurement of the source. The
planet may be orbiting a star but we rule out the presence of stellar
companions up to the projected distance of 8.0 au from the planet. Our
discovery demonstrates that terrestrial-mass free-floating planets can be
detected and characterized using microlensing.
