  The stability and topological structure of equilibrium points in the
potential field of the asteroid 101955 Bennu have been investigated with a
variable density and rotation period. A dimensionless quantity is introduced
for the nondimensionalization of the equations of motion, and this quantity can
indicate the effect of both the rotation period and bulk density of the
asteroid. Using the polyhedral model of the asteroid Bennu, the number and
position of the equilibrium points are calculated and illustrated by a contour
plot of the gravitational effective potential field. The topological structure
and the stability of the equilibrium points are also investigated using the
linearized method. The results show that there are nine equilibrium points in
the potential field of the asteroid Bennu, eight in the exterior of the body
and one in the interior of the body. Moreover, bifurcation will occur with a
variation of the density and rotation period. Different equilibrium points will
encounter each other and mix together. Thus, the number of equilibrium points
will change. The stability and topological structure of the equilibrium points
will also change because of the variation of the density and rotation period of
the asteroid. When considering the error of the density of Bennu, the range of
the dimensionless quantity covers the critical values that will lead to
bifurcation. This means that the stability of the equilibrium points is
uncertain, making the dynamical environment of Bennu much more complicated.
These bifurcations can help better understand the dynamic environment of an
irregular-shaped asteroid.
