Analytical three-phase transfer to a solar polar orbit using solar sail propulsion

A general solution for a 3-phase transfer trajectory from the Earth to a solar polar orbit using solar sail propulsion is presented, deriving for the first time the optimal trajectory architecture without the need for engineering assumptions and numerical analysis. The 3-phase transfer presented involves spiralling in close to the Sun, performing a rapid inclination increase, and spiralling back out to the final target orbit. The general perturbation solution allows the split of inclination change per phase to be optimised for the minimum transfer duration, negating the need for assumptions used in previous numerical optimisations. This method offers significant advantages over the numerically optimised solutions currently available as it allows for a complete understanding of the optimal structure of the trajectory to be gained. These results show that the 3-phase transfer can offer time savings of approximately 30% when compared with a 2-phase transfer. By further sub-dividing the spiral phases into shorter sections it is found that it is possible to further optimise the trajectory; this approach could theoretically be extended to approximate an optimal transfer trajectory. The simplest of these extensions, the 5-phase transfer, is found to offer only a 1% time saving compared with the 3-phase transfer, suggesting that further optimisation beyond the 3-phase transfer may yield only minor improvements. Comparison with existing numerical solutions shows the general perturbation solution to offer a 10% reduction in transfer time due to the optimisation of the amount of inclination change per phase. Thus, this analytical description of the time-optimal transfer trajectories for a mission to a solar polar orbit offers significant advantages for system design trade studies and future mission design