Chaotic Zones around Rotating Small Bodies

Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and. planetary satellites, with diameters smaller than 1000 km 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 10 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.