On safe orbits of a space station tethered to a precessing asteroid by two cables

We study the problem of existence of safe motion for a space station tethered to a small planet by two cables. We consider the case of the dynamically symmetric asteroid and of the cables which opposite ends are fixed to the poles of the small planet. We establish that the station equilibria with respect to axes of precession and of dynamical symmetry are the safe orbits if gravitation of the asteroid satisfy some restrictions. We illustrate these restrictions by geometrical diagrams. Also, we deduce general conditions for existence of the safe orbits of other types.