This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple analytical formulas are derived from proximal motion equations. The proposed analytical formulation allows for an analysis of the optimal direction of the deviating impulse transferred to the asteroid. This ideal optimal direction cannot be achieved for every asteroid at any time; therefore, an analysis of the optimal launch opportunities for deviating a number of selected asteroids was performed through the use of a global optimization procedure. The results in this paper demonstrate that the proximal motion formulation has very good accuracy in predicting the actual deviation and can be used with any deviation method because it has general validity. Furthermore, the characterization of optimal launch opportunities shows that a significant deviation can be obtained even with a small spacecraft. Copyright © 2007 by Massimiliano Vasile and Camilla Colombo. Published by the American Institute of Aeronautics and Astronautics, Inc

In this paper, a comparative assessment of the effectiveness of different deviation methods for near-Earth objects is presented. Specifically, a solar collector, nuclear interceptor, kinetic impactor, low-thrust propulsion, mass driver, and gravity tug are modeled and compared. For each method, a mathematical model is developed to compute the achievable deviation. A multicriteria optimization method is then used to construct the set of Pareto-optimal solutions, minimizing the mass of the spacecraft at departure from the Earth and the warning time (i.e., the time from launch to the foreseen impact of the asteroid with the Earth), while maximizing the deviation. A dominance criterion is defined and used to compare all of the Pareto sets for all of the various mitigation strategies. Finally, a technology readiness level factor is associated with each strategy to estimate the required technological development

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth-centered orbits for swarms of microscale " smart-dust" devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified in which sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the nonconservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such higharea- to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris. © 2011 by Camilla Colombo and Colin McInnes. Published by the American Institute of Aeronautics and Astronautics, Inc