Abstract: Shape based approach is a reverse design method by assuming a certain shape of the trajectory to find the parameters which fulfill the boundaryconditions. The inverse polynomial function provided a new shape-based method for the low thrust trajectory design and initial value selection for directoptimization solver. Coupled with the astrodynamics functions, the inverse polynomial shape-based method was derived and used to solve the low thrust transfer problem in a fixed time. The results demonstrate that the method presented is reasonable for the low trust trajectory design. Furthermore, thesolutions tend to be near optimal and are able to provide initial guess for direct optimizer.

Key words: Inverse polynomial, Transfer orbit , Optimal trajectory, Trajectory design, Spacecraft