# Solar Sail Transfer Trajectory Design for Comet 29P/Schwassmann-Wachmann 1 Rendezvous
## 1 Introduction  
This paper investigates the performance of a solar sail-based spacecraft in a classical, orbit-to-orbit, three-dimensional heliocentric transfer from Earth to comet 29P/Schwassmann-Wachmann 1 (SW1) [1, 2, 3]. Comet SW1, which was discovered on 15 November 1927 by German astronomers [PERSON] and [PERSON], currently covers a nearly circular orbit between Jupiter and Saturn with a small inclination to the Ecliptic [4], as sketched in Figure 1. This periodic and active comet, whose orbital period is roughly 15 years, is an interesting and still unexplored small body that has been regarded as an object of the Centaurs group [5, 6, 7], that is, a celestial body originating from the Kuiper belt and then moved to the inner region of the Solar System. Thanks to its (relative) accessibility if compared with the Kuiper belt objects, comet SW1 has been proposed as a potential target for a robotic exploration mission [8]. In particular, the aim of the proposed missions was both to obtain in situ physical measurements of such a primordial celestial body [9, 10] and to collect the particles ejected by the comet during its frequent outbursts [11, 12]. In this paper, the capability of a spacecraft equipped with a photonic solar sail to perform a rendezvous of the SW1 orbit is investigated from an optimal viewpoint. In fact, the specific characteristics of the SW1 heliocentric orbit, which can be roughly approximated with a circular orbit of radius 6 au, make the solar sail transfer a challenging problem, due to the fact that the maximum magnitude of the sail propulsive acceleration is inversely proportional to the square of the solar distance. Accordingly, and as also highlighted in the next section, just before the cometary rendezvous the propellants propulsion system can give only a small fraction (about \(1/6^{2}\simeq 3\%\)) of the total thrust available just after the launch from the Earth, that is, when the Sun-spacecraft distance is roughly 1 au. Indeed, a solar sail-based propulsion system is rarely considered in a heliocentric mission scenariowhich requires the thrust vectoring at a solar distance greater than 5 au, that is, beyond the typical Jupiter distance from the Sun. However, the photonic solar sail can be still effective even beyond a radial distance of 5 au, as highlighted by the numerical results discussed later in this paper. In fact, the (rather) common assumption that a solar sail should be jettisoned, or the solar sail-induced propulsive acceleration should be neglected, when the solar distance is greater than 5 au, originates from the interesting work by [PERSON] [13] that analyzes the photonic solar sail performance in a Solar System escape (more precisely, the term used in [13] is 'interstellar') mission scenario. In particular, according to [13], in the last paragraph of p. 9 [PERSON] substantially affirms that \"_...the effectiveness of the sail in reducing flight time is minimal..._\" when the solar distance of the spacecraft is in the range [5; 10] au, so that the primary propulsion system (i.e., the solar sail) is jettisoned at 5 au \"_...to allow the acquisition of science data without possible interference from the sail_\". This conclusion is, indeed, absolutely acceptable in a Solar System escape trajectory such as that analyzed in the second part of [13], because such a specific trajectory uses a pass close to the Sun (i.e., a sort of'solar photonic assist maneuver' as named by [PERSON] and [PERSON] [14] and [PERSON] [15] in their fine paper of 2004) to reach the required value of the hyperbolic excess speed. On the other hand, in a Solar System escape scenario the use of a solar sail-based propulsion system at a distance greater than 5 au is still possible, but the reduction in the total flight time (in that case, the flight times are of the order of decades) is marginal when compared to the increase in difficulty to actively change the sail attitude at such great solar distances.