This paper considers two objects moving by inertia in gravitational space. The goal of the first object (Pursuer) is to reach the second object (Evader) at a certain specified distance. To solve this problem, depending on the awareness of the Pursuer, two solution approaches are proposed. In the first approach, the Pursuer has information about the current control of the Evader and builds its interception strategy (in short, \(\Pi\) -Strategy). Using the \(\Pi\) -Strategy, the conditions for the solvability of the problem (the Pursuit Problem) are determined. In real applied problems it is difficult to have information about the current control of the Evader. However, the first approach points the way to the second approach. In this case, the Pursuer knows, with some slight delay, the discrete locations of the Evader. In the second approach, the \(\Pi\) -Strategy also plays a key role. For the real applied problems, the second approach is more acceptable, since it is not difficult to obtain information about the location of the opponent. For both approaches, a guaranteed process completion time was found.
