Motivated by the study of the controlled Kepler problem, we analyze the controllability properties of some classes of mechanical systems. Consider a control system with drift. Our aim is to determine if, given a pair of initial states at a fixed initial time, assuming that the controller acts only on one of the two corresponding trajectories, it is possible for the controlled trajectory to reach the uncontrolled one in finite time. We prove that this is the case for the controlled Kepler

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... , taking into account both elliptic and non-elliptic orbits. We extend the result to other classes of mechanical controlled systems. T being free, such that q(0) = q 0 and q(T ) = φ(T, q 1 ,ū), where t → φ(t, q 1 ,ū) is the solution ofq = f (q,ū) such that φ(0, q 1 ,ū) = q 1 . Control problems for which the controller's goal is to perform such kind of rendez-vous arise naturally, and are in fact currently handled. We can think, for instance, of any control system where uncontrolled trajectories are determined by some drift. The problem of reaching an "object" moving according to the dynamics determined by such drift is of intrinsic rendez-vous nature. Rendez-vous controllability problems can be seen as classical controllability problems by adding the time as an extra