B-plane orbital resonance analysis and applications

Sammanfattning: Many space engineering and orbital mechanics applications seek for the usage of focused mathematical models, capable of providing useful insight onto particular phenomena or exploiting some theoretical and physical tools to reduce the computational costs and/or increase the level of accuracy reached. Orbital resonances are one of the phenomena that needs to be properly modelled, both for exploiting such features in the mission design phase and to predict possible resonant returns of threatening objects closely approaching a specified planet. This work deals indeed with one of the possible models of orbital resonances, representing such a physical phenomenon in the B-plane reference frame with an analysis on the resonant trajectories performed at the moment of close encounter. Before this, flybys are an important source of uncertainty in the numerical simulations, which then need to be as accurate as possible to be used as benchmark. To this extent, a highly efficient method to account for general relativity effects in the N-body propagation is developed, tested and validated, to be then used as precise benchmark for the resonance analysis and application. The B-plane resonance model is a strictly patched conics theory which does not account for perturbations. A semi-analytical extension of the current B-plane resonance model is proposed to account for perturbing effects inside the planet’s sphere of influence. Introducing a set of perturbing coefficients brings the model to match the simulation results at the B-plane point where such coefficients are computed, as well as to be a highly reliable approximation in its vicinity, performing a validation with Monte-Carlo simulated data. An extension of the validation proposed would lead to a complete planetary protection or defence application, whereas in its final part the work will show the flexibility of the model by looking at it from a different perspective. A ballistic resonant flyby design application will be implemented by solving a multi-level optimisation problem, to modify an initial trajectory into a new one on the same Tisserand level. Without dealing with the specific case of resonances, the B-plane reference frame embeds a smart geometrical framework where to express and design flyby deflections, whose power will be shown in terms of accuracy achieved and computational cost required. Once completed by detaching from the patched conics approximation, such a model could bring remarkable simplifications in planetary protection applications, reducing the need of propagating a high number of Monte Carlo samples, and would increase the precision of the defence analyses against impacts from near-Earth threatening asteroids. About the application proposed here, internal and/or external integration could eventually lead to an enhanced efficiency of the current mission design strategies and could widen the internal proposed capabilities, providing high precision and almost optimal results with lowered computational costs.