Analytical formulation of impulsive collision avoidance dynamics |
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Authors: | Claudio Bombardelli |
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Affiliation: | 1. Research Associate, ETSI Aeronauticos, Technical University of Madrid, Plaza Cardenal Cisneros 3, 28040?, Madrid, Spain
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Abstract: | The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form analytical expressions are provided that accurately predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the analytical expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation. |
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