Problem on Maintaining Contact of a Low-Mass Research Probe with Asteroid

 The problem on maintaining contact of a body of small mass with the surface of a homogeneous, symmetrical asteroid rotating by inertia is investigated. Two opposite forces: the holding gravitational force of the asteroid and the repulsive centrifugal force act on the body. The problem is considered in a restricted formulation. Critical contact points are investigated for on a number of surfaces with an axis of symmetry. It is also shown that the movement of the body over the surface of the asteroid can contribute to its more reliable contact with the asteroid.