## 4 Conclusions and Future Work  
The proposed methodology of dividing a planar SALT trajectory into several parts with different dynamics is analogous to the patched conic approximation concept for high-energy trajectories. It appears fruitful in classifying SALT trajectories, identifying basic features (TLI burn magnitudes and phases, initial solar phase values, etc.), and quantifying the perturbing effect due to the Sun's gravity to rigorously prove the quadrant rule. The \(L_{2}\) lunar gateway is a convenient tool for targeting specific capture conditions. In the next step of the study, we will examine several gateways with other Jacobi integral values in order to fully understand the behavior of SALT trajectories of all three types. It opens the road to the semianalytical design of planar SALT trajectories: by properly setting the departure parameters, one will be able to generate an excellent initial guess from which the multiple-shooting procedure could rapidly converge to a planar BR4 BP trajectory with the desired characteristics.  
The numerically observed similarity of planar and spatial SALT trajectories (in terms of their geometric shapes and principal parameters) gives us a reasonable hope that most of the results obtained in the planar case could be transferred (or naturally extended) to the spatial BR4 BP model. Ideally, a unified multiple-shooting method and the general rules of choosing  
Figure 23: A sample SALT trajectory of the third type (with a retrograde lunar flyby): the patched three-body approximation (thin) and upon adaptation to the BR4 BP (bold). As earlier, the adapted trajectory segments corresponding to the departing, arriving, and exterior legs, are colored the same (red, green, and black, respectively). Upon adaptation, the TLI burn has decreased from 3149 m/s to 3147 m/s. The burn phase has changed from 296.84 deg to 293.88 deg. The apogee TCM of 34.5 m/s has been added.  
the initial conditions should be developed for both planar and spatial SALT trajectories. The transition from the BR4 BP to the ephemeris model would then be a simple final step.  
Conceptualization, S.T.; methodology, A.T. and S.T.; software, A.T. and M.S.; validation, S.T. and M.S.; investigation, A.T. and S.T.; writing--original draft preparation, A.T. and S.T.; writing--review and editing, S.T.; visualization, A.T. and S.T.; supervision, S.T. and M.O.; project administration, M.O.; funding acquisition, M.O. All authors have read and agreed to the published version of the manuscript.  
This study was funded by the Russian Science Foundation (RSF) grant 19-11-00256.  
Not applicable.  
The authors declare no conflict of interest.  
The following acronyms and abbreviations are used in this manuscript:  
\begin{tabular}{l l} BLT & Ballistic lunar transfer \\ BR4 BP & Bicircular restricted four-body problem \\ CAPSTONE & Cislunar Autonomous Positioning System Technology Operations and Navigation \\  & Experiment \\ CR3 BP & Circular restricted three-body problem \\ EQUULEUS & EQUilibriUm Lunar-Earth point 6U Spacecraft \\ GRAIL & Gravity Recovery and Interior Laboratory \\ LOI & Lunar orbit insertion \\ LOP-G & Lunar Orbital Platform-Gateway \\ RoP & Region of prevalence \\ SALT & Sun-assisted lunar transfer \\ SMART-1 & Small Missions for Advanced Research in Technology-1 \\ TCM & Trajectory correction maneuver \\ TLI & Translunar injection \\ WSB & Weak stability boundary \\ \end{tabular}