Hodographic-Shaping Method for Low-Thrust Interplanetary Trajectory Design

A novel low-thrust trajectory design method is developed based on the velocity hodograph of a spacecraft. The trajectory design is done by shaping the velocity components during the transfer. For this purpose, velocity functions are used that consist of a sum of simple base functions. These base functions can be integrated analytically, such that the change in position can be obtained analytically. Doing so, the departure and rendezvous conditions on position and velocity can be solved very easily without the need of iterative computations. Extra parameters can be added to make the transfer design more flexible and optimize the trajectory. Two different methods have been developed: one that shapes the velocity as a function of time and another one that shapes as a function of the polar angle. To obtain minimum-ΔV trajectories, the free parameters in the velocity functions have been optimized and the search for the optimal departure date and time of flight is done by stepping through the flight window using a grid. Both hodographic-shaping methods have been tested for missions to Mars, the near-Earth asteroid 1989ML, comet Tempel 1, and Mercury and have been compared with results of other shape-based methods.