  Target of NASA's DART mission, the system of Didymos and Dimorphos will once
again be visited by a space mission -- ESA's Hera mission, scheduled to be
launch in 2024. Hera will arrive in the system approximately 4 years after the
DART impact, a long period compared to Dimorphos' orbital period (about 12
hours). It is therefore imperative to understand the dynamics of material in
this environment on a long timescale. Here, we explore the long-term dynamics
of the binary system (65038) Didymos, in the context of the perturbed, planar,
circular and restricted 3-body problem. We design an analytical description for
a symmetrical top-shaped object, the shape assumed for the Didymos, while the
Dimorphos is considered an ellipsoid. In the absence of external effects, we
identify seven stable equatorial regions where particles persist for more than
a decade. However, in the presence of the solar radiation effect, the lifetime
of small particles (<mm) is in the order of days, being unlikely that Hera
spacecraft will encounter clusters of millimetre and sub-millimetre particles
in stable equatorial orbits. Nonetheless, large objects may reside in the
region for some years, particularly in quasi-satellite orbits, the most stable
orbits in the system. Additionally, interplanetary dust impacts onto Didymos
populate the region, extending up to a distance of approximately 1500 meters
from the primary center, with young dust. These impacts are responsible for a
transfer of dust mainly from Didymos to Dimorphos. If the interplanetary dust
impacts generate metric-sized boulders, they may persist in the system for
years, in first sort orbits around Didymos.
