## 4 Conclusions  
The conducted numerical analysis was focused on the assessment of the viability of satellite targeting through a pointing system, with the ultimate goal of realizing autonomously guided ships. The required pointing accuracy to start the communication phase and, thus, the transition from the pointing stage to the satellite-tracking phase should be higher to 100 \(\upmu\)rad, and the system must ensure actual targeting even under different navigation conditions.  
The analysis, considering a two-degrees-of-freedom acquisition, tracking and pointing (ATP) system located on the ship's deck and, thus, subjected to the ship's motions, revealed an increase in accuracy when methodologies for reducing pointing errors were employed. Through the numerical analysis, the four analyzed ship motion scenarios led to the final consideration that the pointing phase is influenced less by ship motions and more by errors in satellite position and ship motions acquisition in the case in which a scanning methodology of the celestial vault is adopted.  
Between the two analyzed methodologies for improving pointing accuracy, the lemniscate scanning methodology proved to be more effective, showing a higher probability of achieving the required pointing accuracy.  
The higher scanning frequencies led to the choice of implementing the scanning methodology by deviating the laser beam through the swaying of the optical system mirror.  
The mirror swaying was realized through four actuators linked to the mirror, and the choice of actuators was evaluated through the actuators' characteristics of travel range and pull force.  
In order to ensure the feasibility of the system, a lemniscate scanning frequency \(\omega\) of 3500 Hz and a value \(a\) (half-width of the lemniscate) equal to 0.007 was chosen (the choice of \(\omega\) and \(\mathrm{r_{s}}\) parameters was made considering actuator specifications from the catalogue [31] using an iterative method). In the assessment, it was taken into account that the pull force is proportional to the square of the frequency, while the travel range is proportional to the scanning amplitude. The outcomes led to the selection of actuators with a travel range of 108 \(\upmu\)rad and a pull force of 125.7 N that ensure both a first satellite-targeting time of 0.25 s alongside the probability of hitting the target once every 0.0013 s (pointing accuracy greater than 100 \(\upmu\)rad).  
In this study, several sea conditions and the errors associated with the acquisition of ship motions and satellite coordinates were considered. Future developments concern the consideration of adverse weather conditions that may affect the pointing phase (e.g., fog or rain) and, thus, the system development to ensure communication in all sea and weather conditions. Additionally, geometric and installation errors should also be included in the numerical simulation to obtain a more realistic operation of the system.  
Methodology, F.D.M., S.S. and A.G.; Supervision, P.G. and R.T. All authors have read and agreed to the published version of the manuscript.  
The project received funding from European Space Agency (ESA) within the project \"A quantum-secured autonomous communication link for autonomous shipping--a feasibility study\" (project reference code: ESA-AO16373).  
The authors declare no conflict of interest.