Abstract:In this paper, for the initial design of spacecraft transfer trajectory via small thrust, a third-order Fourier series design method is proposed to realize multi-turn transfer of spacecraft via small thrust. Based on the shape-based method of finite Fourier series, the trajectory of spacecraft via small thrust with multiple constraints is optimized. The initial and terminal positions in the two-point boundary value problem are selected from coplanar, coaxial and same eccentric orbits, then the proposed method is verified by simulation. The results show that the proposed method can decrease nearly 75% of velocity increase and greatly reduce the needed value of maximum thrust compared with the modified fifth-order inverse polynomial shape-based method when spacecraft transfer 5 turns and the finite Fourier series has 10 terms.