Logarithmic spiral-based Non-Keplerian orbit design

Shape-based method is a brand-new and feasible method for Non-Keplerian orbit design. Interception trajectories are designed, while the trajectory shape is assumed as a logarithmic spiral. At the beginning, the relation between the differentiations of radius as well as polar angle with respect to the normalized time and alterable parameter q for orbital design are derived by non-dimensional processing. And then in combination with the equations of motion both the magnitude and direction of acceleration are specified as functions of q when the spacecraft's trajectory is the logarithmic spiral. Moreover, the trajectory design is focused on for initial circular and elliptical orbits. Finally, a range of initial elliptical orbit's phase angle which enabled the method to be more effective is discussed. The analysis demonstrates that the logarithmic spiral is feasible for interception trajectory design; when the spacecraft maneuvers in a certain range of phase angle on the initial highly eccentric orbit, the flight time and fuel consumption could meet the design requirements.