Application of pseudo-equinoctial shaping to Near-Earth asteroid orbital transfer

This paper determines the near-optimal transfer trajectory of a Near-Earth Asteroid (NEA) to an orbit in the Earth-Moon system through the use of an ion beam redirection method. The ion beam method is a hovering approach to asteroid redirection. The method operates through the use of two diametrically opposed thrusters. The redirection mission targets Arjuna-type asteroids, and uses a sample asteroid, 2013 RZ53, to demonstrate the applicability of the pseudo-equinoctial shaping to asteroid orbital transfer. The asteroid transfer from its initial orbit about the Sun to its final orbit in the Earth-Moon system is divided into two phases using a patched conics approximation. The first phase includes the transfer of the asteroid from its initial orbit to an optimized rendezvous point with Earth. The second phase begins as soon as the asteroid arrives within the Earth's sphere of influence and ends with the transfer of the asteroid into a stable orbit about Earth and Moon. The pseudo-equinoctial shaping approach is employed during each phase, and determines the near-optimal solution for the lowest combined delta-v required to complete the orbital transfer. The pseudo-equinoctial method is a shape-based approach to trajectory design which assumes the trajectory transfer can be modelled as a variation of a conic arc. The transfer considers the eccentricity, inclination, and semi-major axis, as well as optimizes several free parameters, such as the thrust, the start of transfer and the rendezvous point with Earth. The optimization is completed using a genetic algorithm, and the results of the optimization are presented in terms of time of flight, thrust, number of revolutions, and delta-v. Lastly, the results are detailed and the feasibility of a redirection mission for an Arjuna-type asteroid is discussed.