Semi-Analytical Method for the Analysis of Solar Sail Heliocentric Orbit Raising

L OW-THRUST trajectories are usually investigated within an optimal framework by minimizing a suitable scalar performance index, like the total mission time or the propellant mass consumption. Very often a preliminary mission analysis requires a considerable amount of simulation time to investigate the effect of different parameters on mission performance; therefore the availability of simple analytical and/or graphical means to describe the orbit evolution is very useful. These simplified tools are of great importance formission-design concepts and tradeoff studies because they can provide good estimates of fundamental mission parameters, like the total velocity increment, with a reduced computational effort. In this regard, a famous method was developed by Edelbaum [1] for the study of a circle-to-circle transfer under the effect of a constant and freely steerable propulsive acceleration. This method, especially in the variant proposed by Kechichian [2–4], has been succeedingly extended to deal with more complex mission scenarios [5–7]. An interesting alternative to Edelbaum’s approach is provided by the so-called Alfano transfer [8]. Assuming that the spacecraft is subjected to a constant propulsive thrust, the Alfano transfer basically uses the calculus of variations to minimize the flight time t required for a circle-to-circle transfer as a function of the initial and final orbit radii (r0 and r1, respectively) and of the propulsion system characteristics (in terms of initial acceleration a0 and constant propellant mass flow rate _ mp). Because, by assumption, the thrust acts continuously without any coasting phase, the minimum-time transfers coincide with minimum propellant mass consumption trajectories. The results of the optimization process are then collected into charts [9] that simplify the flight time evaluation as a function of themission characteristics for a number of parameters combinations, like r1=r0, a0, and _ mp=m0, where m0 is the initial spacecraft mass. The aim of these charts is twofold. On one side, they allow the designer to quickly obtain, in a graphical form, the optimal transfer performance, to estimate the sensitivity to a mission parameter variation, and to automatize his/her analysis with the aid of simple interpolations [10]. The second and more intriguing aim is to detect possible relationships to describe the variation of the performance index as a function of the mission parameters. Such information is useful both for validating already available analytical models [5] and to suggest new approximations. According toAlfano [10], in hismethod theflight time is not given explicitly, but it is represented in terms of total accumulated velocity change Va, that is