We consider some classical problems of Celestial Mechanics assotiated with the study of mutual distance between Keplerian orbits. The space of the pairs of Keplerian orbits has a nontrivial topology and some funtions on this space like mutual distance function play very important role in classical theory of perturbations. We present some recent results about mutual distance function, linking coeffitient and natural metrics on the space of orbits. These results were obtained using Groebner bases technique and give us most effective methods to study closed mutual approaches of planets and asteroids.