  The equilibrium points of the gravitational potential field of minor
celestial bodies, including asteroids, comets, and irregular satellites of
planets, are studied. In order to understand better the orbital dynamics of
massless particles moving near celestial minor bodies and their internal
structure, both internal and external equilibrium points of the potential field
of the body are analyzed. In this paper, the location and stability of the
equilibrium points of 23 minor celestial bodies are presented. In addition, the
contour plots of the gravitational effective potential of these minor bodies
are used to point out the differences between them. Furthermore, stability and
topological classifications of equilibrium points are discussed, which clearly
illustrate the topological structure near the equilibrium points and help to
have an insight into the orbital dynamics around the irregular-shaped minor
celestial bodies. The results obtained here show that there is at least one
equilibrium point in the potential field of a minor celestial body, and the
number of equilibrium points could be one, five, seven, and nine, which are all
odd integers. It is found that for some irregular-shaped celestial bodies,
there are more than four equilibrium points outside the bodies while for some
others there are no external equilibrium points. If a celestial body has one
equilibrium point inside the body, this one is more likely linearly stable.
