# Solar Sail Transfer Trajectory Design for Comet 29P/Schwassmann-Wachmann 1 Rendezvous
## 5 Conclusions  
A solar sail-based rendezvous with comet 29P/Schwassmann-Wachmann 1 requires a flight time of about two decades when a medium-high performance sail is considered in the orbital simulations. Accordingly, such a complex mission scenario can be considered a typical application of a high performance sail, which could give a flight time less than ten years, even with a realistic optical force model. In this respect, the numerical results discussed in this paper can be used to obtain a fast estimation of the characteristics of the optimal transfer trajectory with a reduced computation time. A possible extension of this work is to consider a cometary flyby mission, instead of a rendezvous scenario, in order to reduce the required flight time for a given value of the characteristic acceleration. In fact, a flyby mission has a less constrained terminal condition, so that the flight time is surely lesser than the time obtained in the paper. Accordingly, for example, if the scientific mission requires a cometary flyby and not an in situ study, the flight time can be significantly less than the decades obtained in the previous section, the value of the characteristic acceleration being the same.  
Figure 16: Polar form of the optimal transfer trajectory (black line) for an optical force model, when \(a_{c}\in\{0.5,0.7,1,1.2,1.5,2\}\) mm/s\({}^{2}\). Black circle \(\rightarrow\) start; square \(\rightarrow\) arrival; orange circle \(\rightarrow\) Sun; blue line \(\rightarrow\) Earth’s orbit; red line \(\rightarrow\) comet SW1 orbit.  
**Author Contributions:** Conceptualization, A.A.Q.; methodology, A.A.Q.; software, A.A.Q.; writing--original draft preparation, A.A.Q.; writing--review and editing, A.A.Q., K.A.S., and G.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Abbreviations**  
\begin{tabular}{l l} JPL & Jet Propulsion Laboratory \\ MEOE & modified equinoctial element \\ RTN & radial--tangential--normal \\ SW1 & 29P/Schwassmann--Wachmann 1 \\ TPBVP & two-point boundary problem \\ \(a\) & semimajor axis [au] \\ \(a_{c}\) & characteristic acceleration [mm/s\({}^{2}\)] \\ \(a\) & propulsive acceleration vector [mm/s\({}^{2}\)] \\ \(\mathbb{A}\) & matrix, see Equation (11) \\ \(\{b_{1},b_{2},b_{3}\}\) & force coefficients, see Table 1 \\ \(d\) & vector, see Equation (11) \\ \(e\) & eccentricity \\ \(\mathcal{H}\) & Hamiltonian function \\ \(i\) & orbital inclination [deg] \\ \(\mathfrak{z}_{\mathfrak{z}}\) & radial unit vector \\ \(\mathfrak{z}_{\mathfrak{z}}\) & transverse unit vector \\ \(\mathfrak{z}_{\mathfrak{z}_{\mathfrak{z}}}\) & normal unit vector \\ \(\mathfrak{z}\) & performance index [days] \\ \(\hat{\mathfrak{n}}\) & normal unit vector \\ \(\{p,f,g,h,k,L\}\) & MEOEs \\ \(r\) & Sun--spaecraft distance [au] \\ \(\boldsymbol{r}\) & position vector [au] \\ \(\boldsymbol{\hat{r}}\) & Sun--spaecraft unit vector \\ \(r_{\infty}\) & reference distance [1 au] \\ \(t\) & time [days] \\ \(\boldsymbol{x}\) & spacecraft state vector \\ \(\Delta t\) & flight time [days] \\ \(\Lambda\) & adjoint vector \\ \(\lambda_{y}\) & generic adjoint variable \\ \(\mu_{\infty}\) & Sun's gravitational parameter [km\({}^{3}\)/s\({}^{2}\)] \\ \(\omega\) & argument of periapse [deg] \\ \(\Omega\) & right ascension of the ascending node [deg] \\ \(\mathit{Subscripts}\) & \\ \(0\) & initial, Earth's heliocentric orbit \\ \(f\) & final, comet SW1 heliocentric orbit \\ \(\mathit{Superscripts}\) & derivative with respect to time \\ \end{tabular}