  We are interested in stable periodic orbits for spacecrafts in the
gravitational field of minor celestial bodies. The stable periodic orbits
around minor celestial bodies are useful not only for the mission design of the
deep space exploration, but also for studying the long-time stability of small
satellites in the large-size-ratio binary asteroids. The irregular shapes and
gravitational fields of the minor celestial bodies are modeled by the
polyhedral model. Using the topological classifications of periodic orbits and
the grid search method, the stable periodic orbits can be calculated and the
topological cases can be determined. Furthermore, we find five different types
of stable periodic orbits around minor celestial bodies: A) Stable periodic
orbits generated from the stable equilibrium points outside the minor celestial
body, B) Stable periodic orbits continued from the unstable periodic orbits
around the unstable equilibrium points, C) Retrograde and nearly circular
periodic orbits with zero-inclination around minor celestial bodies, D)
Resonance periodic orbits, E) Near-surface inclined periodic orbits. We take
asteroid 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley
for examples.
