We assess whether gravity darkening, induced by a tidal interaction during a
stellar fly-by, might be sufficient to explain the Great Dimming of Betelgeuse.
Adopting several simple approximations, we calculate the tidal deformation and
associated gravity darkening in a close tidal encounter, as well as the
reduction in the radiation flux as seen by a distant observer. We show that, in
principle, the duration and degree of the resulting stellar dimming can be used
to estimate the minimum pericenter separation and mass of a fly-by object,
which, even if it remains undetected otherwise, might be a black hole, neutron
star, or white dwarf. Our estimates show that, while such fly-by events may
occur in other astrophysical scenarios, where our analysis should be
applicable, they likely are not large enough to explain the Great Dimming of
Betelgeuse by themselves.