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  • Optimal Trajectories for NEO Deflection

    Paper number



    Ms. Camilla Colombo, University of Glasgow, United Kingdom


    Dr. Massimiliano Vasile, University of Glasgow, United Kingdom



    Near Earth Objects (NEOs) interception and hazard mitigation has been recognised as a key issue for the safety of life on Earth. The threat posed by Apophis sparked unprecedented attention towards NEOs and any possible strategy for deflection. Missions aiming at tracking asteroids or at characterising their shape and composition have become increasingly important with time (for example the European Space Agency‘s Don Quijote, current under study).
    In this paper we propose an approach to the design of optimal trajectories for NEO interception and deflection missions. The maximum deviation problem is formulated as an optimisation problem in which the objective function is the achievable displacement of the asteroid at the point of minimum orbit interception distance. The displacement, after a deviation action, is computed analytically by means of the proximal motion equations expressed as a function of the orbital elements through Gauss’ equations.  A simple analytical formulation was derived both in the case of an impulsive deviation action and in the case of a low-thrust one. 
    For the case in which a continuous low thrust is applied to the asteroid, a set of semi-analytical equations have been derived by averaging Gauss’ planetary equations over one revolution period of the NEO. Averaged equations provide a fast estimation of the achievable deviation compared to a full numerical integration of the osculating elements.  
    In this paper the formulas for impulsive deviations were applied to the analysis of kinetic impactors and nuclear blasts while fomulas for low-thrust were applied to the analysis of solar sublimation systems and of low-thrust propulsion device anchored to the surface of the asteroid. The accuracy and general applicability of the proposed formulation is illustrated through some sample cases.
    Furthermore we derived an analytical solution for the optimal directions of the deviating action, depending on the time to impact. Finally, families of optimal solutions for a potential deflection mission, found through a global search over a wide range of launch opportunities, will be presented both in the case of low-thrust action and kinetic impact.
    Abstract document


    Manuscript document

    IAC-07-C1.4.02.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.