  Small bodies of the Solar system, like asteroids, trans-Neptunian objects,
cometary nuclei, planetary satellites, with diameters smaller than one thousand
kilometers usually have irregular shapes, often resembling dumb-bells, or
contact binaries. The spinning of such a gravitating dumb-bell creates around
it a zone of chaotic orbits. We determine its extent analytically and
numerically. We find that the chaotic zone swells significantly if the rotation
rate is decreased, in particular, the zone swells more than twice if the
rotation rate is decreased ten times with respect to the "centrifugal breakup"
threshold. We illustrate the properties of the chaotic orbital zones in
examples of the global orbital dynamics about asteroid 243 Ida (which has a
moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143
Itokawa.
