# Solar Sail Transfer Trajectory Design for Comet 29P/Schwassmann-Wachmann 1 Rendezvous
## 1 Introduction
Bearing in mind that a rendezvous with the active comet SW1 is therefore a challenging scenario for a (photonic) solar sail-based spacecraft, this work aims to illustrate the results of a preliminary, orbit-to-orbit, heliocentric trajectory design by considering the (simplified) thrust vector that models the performance of a flat sail of assigned characteristics. In this context, the paper takes advantage of both the analytical model and the ad hoc automatic routines already implemented by the authors to study this specific mission scenario. In this sense, the contribution of this work is not to propose new optimization techniques or to refine the mathematical model for the solar sail-based trajectory design, but to collect and comment on the results of a simulation campaign aimed at estimating the potentialities of such a propellantless propulsion system in a challenging mission scenario such as the rendezvous with the comet SW1. In particular, taking the actual characteristics of the Earth and SW1 heliocentric orbits into account, the minimum flight time is evaluated by considering both an ideal force  
Figure 1: Sketch of the comet SW1 heliocentric orbit evaluated at 1 August 2023. The figure shows, for comparison purposes, the orbits of Mars, Earth, Jupiter, and Saturn. The star symbol indicates the perihelion point of the generic heliocentric orbit. model (i.e., a model in which the sail is assumed as a flat, perfectly reflecting, mirror) and an optical force model (i.e., a model in which the thermo-optical characteristics of the reflecting film are taken into account) to describe the solar sail thrust vector during the deep space flight [16; 17]. The numerical analysis presents a parametric study of the transfer time as a function of the sail typical performance parameter, i.e., the characteristic acceleration [18] defined as the maximum magnitude of the sail propulsive acceleration vector at a distance of 1 astronomical unit from the Sun. Finally, the numerical results obtained through a simplified, but less computationally demanding, two-dimensional approach to the preliminary trajectory design are discussed in the last part of the work. In this context, bearing in mind the orbital characteristics (i.e., the value of the eccentricity and the inclination) of both the starting (Earth) and target (SW1) orbit, the spacecraft heliocentric transfer is approximated through a classical circle-to-circle orbit raising [19] and the mission performance is obtained by using the typical approach discussed in the recent literature [20]. The numerical simulations will show that, even with a non-negligible value of the target orbit inclination over the Ecliptic (the value of that orbital inclination is about 9 degrees), the two-dimensional circle-to-circle approximation of the orbit transfer gives both a flight time and a shape of the transfer trajectory which are very close to those obtained with a three-dimensional approach. The paper is organized as follows. Section 2 briefly describes the mathematical model, that is, the three-dimensional spacecraft dynamics and the (rather classical) procedure which has been used to optimize the spacecraft trajectory during the interplanetary transfer. In particular, the aim of Section 2 is only to illustrates the main features of the mathematical model that, in its turn, has already been commented on in detail by the authors in the suggested references. Section 3 discusses the results of numerical simulations, in terms of a parametric study of the mission performance (i.e., the minimum flight time) as a function of the solar sail propulsive characteristics, and the results of a case study which refers to a specific value of the sail (reference) propulsive acceleration. A two-dimensional approach to the optimal trajectory design is then proposed in Section 4, whose aim is to obtain an approximate value of the optimal flight time with a reduced computation time. Finally, the concluding remarks are drawn in Section 5, as usual.