Deviation iterating approach for transfer orbit design with J2 perturbation

Referring to the process of shooting algorithm, this paper advances a new analytical method named deviation iterating approach to design transfer orbits when J₂ perturbation is taken into account. The convergence of the approach is analyzed theoretically, and the transfer angle equals π is found to be a singularity. After being verified by numerical studies, the singularity is discussed again from the uniqueness of the solution of motion equations, and two treatments are proposed for practical space missions. The deviation iterating approach calculates almost analytically and converges rapidly, resulting in a great decrease in computing time. The procedure could perform well with an onboard processor, and hence can facilitate the implementation of on-line tasks, such as explicit guidance and onboard path programming.