Hill's Problem as a Dynamical Billiard

A problem of a mass point movements in gravitation field of two selestial body, one of which has small size and mass with respect to the other and is situated in its immediate proximity, is considered in the paper. Substantively, such model can describe movement of an apparatus in Mars-Fobos system. Movement of robot near the surface of a satellite in its umbilical orbit plane has been numerically analyzed by means of Poincare cut method within the scope of classical Hill problem. The domains of chaotic movements of the problem have been found and new periodical orbits have been shown.