# Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects

Colombo, C., Vasile, M. and Radice, G. (2009) Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects. Journal of Guidance, Control, and Dynamics, 32(3), pp. 796-809. (doi:10.2514/1.40363)

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Publisher's URL: http://dx.doi.org/10.2514/1.40363

## Abstract

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.

Item Type: Articles Published Yes Radice, Dr Gianmarco and Vasile, Dr Massimiliano Colombo, C., Vasile, M., and Radice, G. College of Science and Engineering > School of Engineering > Aerospace Sciences Journal of Guidance, Control, and Dynamics American Institute of Aeronautics and Astronautics 0731-5090 1533-3884

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
363731Optimal interception and deviation of potentially hazardous near earth objectsGianmarco RadiceEngineering & Physical Sciences Research Council (EPSRC)GR/S83999/01Aerospace Sciences