Rigorous Computation of Orbital Conjunctions

The manuscript addresses the problem of computing conjunctions either between Near Earth Objects and our planet or space debris and operative spacecraft. The problem is formulated as a global optimization problem, solved rigorously using Taylor models. With this technique, narrow bounds of the objective function are computed on sub-portions of the search space by combining high order Taylor approximations of the function with interval enclosures of the remainder terms. An algorithm based on differential algebra is then presented to nonlinearly describe the effect that uncertainties on the initial states produce on the time and distance of closest approach. This is represented with high order Taylor maps which can be potentially used for the implementation of innovative algorithms for risk assessment, avoiding the main assumptions of current approaches. Asteroid Apophis and a threatening condition between two geostationary satellites are considered as examples to analyze the features of the proposed methods.