Abstract: Lawden's equations are firstly established to investigate the model error. By comparing the relative trajectory calculated by the Lawden's equations and that by numerical integral method, it is concluded that the homogenous solutions of Lawden's equations are non-periodical, and the initial condition, which is selected to satisfy the periodical solutions, is a compulsory one irrelevant to the condition of long-term formation flying. The precision of the equations' solutions is specified by calculating the energy variation of the follower satellite, and a method that guarantees the design precision by constraining the size of the relative trajectory is proposed. The simulation results show that the proposed method is effective.