  Context: Various ideas have been proposed to explain the formation of the
Geminid meteoroid stream from the asteroid (3200) Phaethon. However, little has
been studied about the Geminid formation based on the assumption that mass
ejection happened from this asteroid via rotational instability. Aims: Here, we
present the first dynamical study of the Geminid formation, taking account of
low-velocity mass ejection as a result of Phaethon's rotational instability.
Methods: We conducted numerical simulations for 1 mm and 1 cm particles ejected
in a wide range of ejection epochs (10$^3$--10$^5$ years ago). We computed the
minimum orbital intersecting distance (MOID) of the dust particles as the
realistic condition, that is, the Earth's radius and the Earth-Moon distance to
be observed as the Geminid meteoroid stream. Results: We found that the
low-velocity ejection model produced the Geminid-like meteoroid stream when the
dust particles were ejected more than $\sim$2,000 years ago. In this case,
close encounters with terrestrial planets would transport some dust particles
from the Phaethon orbit (the current MOID is as large as $\sim$460 Earth
radius) to the Earth-intersecting orbits. The optimal ejection epoch and the
estimated mass were 18\,000 years ago and $\sim 10^{10} - 10^{14}$ g (<0.1 \%
of the Phaethon mass). Conclusions: Our results suggest that the JAXA's
DESTINY\textsuperscript{+} mission has the potential to find evidence of recent
rotational instability recorded on the Phaethon's surface.

Earth and Planetary Astrophysics