Mechanisms of a-priori collision prediction of spacecraft in a circular Low Earth Orbit.

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. A metric has to be created, that determines when the risk of collision reaches a critical level. Two methodologies are investigated. The first one is ”covariance matrix propagation of position and velocity uncertainties” and the second methodology is the well-known ”Montecarlo Method”. Both of them are implemented in code and results are investigated in terms of different criteria like robustness, simulation time and quality of data. Simulations are carried out on two different types of deploy- ment (in-flight and out-of-plane direction). The outcome of the analysis demonstrates that satellites deployment can certainly be performed in the in-flight direction because it is the one associated with the lowest probability of collision. Conversely, out-of-plane deployment can dangerously bring to small relative distances among satellites and pos- sible collision. The spring energy of the deployment system, its uncertainties, and the mass of the payload to be deployed are the parameters that most affect the simulation. A correct selection and sizing allow the user to accomplish deployment in the best possible way, maximizing relative distances. In addition, boundaries curves of 3σ ellipsoid are suf- ficiently precise to be used as reference instead of Montecarlo simulation for preliminary analysis. All simulations were carried out for circular orbits in LEO, fixed number of orbits and the same simple deployment mechanism. For a generalization of the reported methods, non-circular orbits can be used for testing the boundaries and limitations of the model.