With the increasing number of objects orbiting and the construction of the International Space Station (ISS), the prediction of close approaches between objects in space has become a crucial aspect of satellite operations. The main objective of this thesis is to investigate the behaviour of an Orbital Transfer Vehicle (OTV) deploying a small satel- lite. The primary focus is to identify any critical situations or potential collisions between the satellite and the OTV by propagating the Yamanaka equations for relative motion forward in time. At each time step, the collision probability is evaluated and compared to a predetermined threshold. Conjunction analyses typically assess the risk posed to a specific object of interest, known as the primary objects, by all other orbiting objects, referred to as the secondary objects.