The work is devoted to the development of the methods for studying the trajectories of multi-orbit low-thrust transfers. A mathematical model of the averaged orbital motion of a spacecraft with low thrust is proposed. Approximate solutions for the evolution of a nearly circular orbit under periodic perturbative acceleration are obtained. Based on the averaged model, a new methodology to obtain optimal multi-turn orbital transfers is developed. The presented methodology is applied in a preliminary ballistic analysis of a promising mission to study the Earth magnetosphere (based on a PhD dissertation)