Feasibility analysis of the angular momentum reversal trajectory via hodograph method for high performance solar sails

In this paper a new phase space of hodograph method is adopted to investigate and better understand the two-dimensional angular momentum reversal (H-reversal) trajectories for high performance solar sails within a fixed cone angle. As the hodograph method and the H-reversal trajectory are not very common, both of them are briefly introduced. The relationship between them are constructed and addressed with a sample trajectory. How the phase space varies according to the sail quality and the fixed sail cone angle is also studied. Through variation of the phase space, the minimum sail lightness number can be obtained by solving a set of algebraic equations instead of a parameter optimization problem. For a given sail lightness number, there are three types of the two-dimensional possible heliocentric motion, including the spiral inward trajectories towards the Sun, the H-reversal trajectories and the directly outward escape trajectories. The boundaries that separate these different groups are easily determined by using the phase space. Finally, the method and procedures to achieve the feasible region of the H-reversal trajectory with required perihelion distance are presented in detail.