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The two dimensional heliocentric trajectories for fixed Sun-angle solar sails are examined. The objective of this work is to completely classify all possible motion in this framework. This is achieved via a mathematical reduction which results in a two dimensional phase space interpretation of the problem.

In this thesis, a selection of numerical optimisation methods were developed for application to realistic solar sail heliocentric trajectory optimisation problems. A Non-Linear Programming method based on Sequential Quadratic Programming was developed, with the sail controls parameterised in time. This method was hybridised with Genetic Algorithms or locally-optimal analytical control laws to generate an initial guess, where required. The goal of this thesis is to create a detailed catalogue of trajectories to a broad range of heliocentric targets, subject to realistic constraints on trip-time, sail performance, and thermal-limited solar approach. This thesis illustrates the wide range of targets in the solar system that can be reached with solar sailing. In addition, the trajectory problems for which solar sailing is not attractive are also identified. Trajectory analysis of sample return missions to the terrestrial planets, Mars, Venus and Mercury, has been conducted. Extensive depmiure date scans were perfOlmed, where it was found that there are minima and maxima in trip-time, separated by discontinuities, providing effective launch windows. Roundtrip optimal launch dates were identified, after combining outbound and return departure date scans. For Mercury rendezvous, the application of positive launch excess velocity and a Venus gravity assist was investigated, where a small trip-time saving can be made. Trajectories to rendezvous with the Short Period Comet Wirtanen have been optimised, where it was found that a significant reduction in trip time and launch mass could have been realised, relative to a conventional mission. An investigation of using higher performance sails to flyby Long Period Comets has also been conducted, to demonstrate that solar sailing could be used to reach newly discovered comets soon after first discovery, such as the previous Hale-Bopp apparition. It is also shown that solar sailing could be used, instead of solar electric propulsion, to rendezvous with two Main-Belt asteroids, with a reduction in launch mass. The open ended nature of solar sailing was used to show that rendezvous with two further asteroids is also possible. It is also shown that a three-phase trajectory concept, utilising an inclination cranking manoeuvre, could be used to return a sample from a high inclination Near-Earth Asteroid, that would be essentially impossible to reach using conventional propulsion. It is demonstrated that flyby missions to the outer planets, such as Pluto are feasible in reasonable timescales using a solar photonic assist concept. However, due to the faint solar radiation pressure at Jupiter, only flyby missions are practical to the Jovian system with solar sails. An extensive trade-off between launch hyperbolic excess energy, Jupiter arrival velocity, hip-time, and the number of photonic assist loops has been conducted. By contrast, solar sailing appears to be the only feasible option for missions to the Heliopause at 200 AD. Heliopause trajectory analysis included investigation of the number of loops, and the effect of thermallyconstrained closest solar approach on escape velocity and trip-time. It was found that, in order to reach the Heliopause in 25 years, a solar sail of characteristic acceleration of order 1.5 mm S-2 would be required, executing a thermally constrained solar photonic assist at 0.25 AD. Investigation of the effect of positive launch energy is also conducted for Heliopause trajectOlies. A key near-term mission application for solar sails is a Solar Polar Orbiter. Trajectory analysis has revealed that a solar sail transfer to a true solar polar orbit, Earth resonant at 0.48 AU, in 5 years would require a characteristic acceleration of 0.42 nun S-2. In the course of the parametric analysis, two-phase and three-phase scenarios were investigated, with an assessment of the effect of spiralling down to a close cranking orbit radius from positive launch excess energy. Finally, new transfers to exotic, displaced Non-Keplerian Orbits have been optimised for a range of final orbit dimensions among one family of these unique orbits. For lower performance sails, transfers to artificial Lagrange points have been optimised, in the context of the Geostorm and Polar Observer missions.