## 2 Materials and Methods
### Determination of the weight of fuel necessary to perform the Hohmann transfer  
Table 5 presents the parameters of the initial and target orbits, including orbital altitudes, corresponding orbital radii, and orbital velocities for both positions. Additionally, the velocities at the perigee and apogee of the transfer orbit are provided. Two velocity increments (\(\Delta\)v\({}_{1}\) i \(\Delta\)v\({}_{2}\)) were also calculated, which together constitute the total velocity \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Initial inclination of the orbit & i\({}_{\text{p}}\) & 97 & [\({}^{\circ}\)] \\ Orbit altitude & h & 482 & [km] \\ Acceleration of gravity & g & 8.49 & [\(\frac{m}{g}\)] \\ Orbital velocity & v\({}_{\text{o}}\) & 7.8 & [\(\frac{m}{g}\)] \\ Thrust force & F & 1 & [N] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Presentation of the fixed parameters used in the analysis of the possible change in inclination. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Fuel weight & m\({}_{\text{f}}\) & 0.5 & [kg] \\ Orbit altitude & h & 482 & [km] \\ Acceleration of gravity & g & 8.49 & [\(\frac{m}{g}\)] \\ Orbital velocity & v\({}_{\text{o}}\) & 7.8 & [\(\frac{m}{g}\)] \\ Thrust force & F & 1 & [N] \\ Weight of the fuel consumed to conduct the manoeuvre & m\({}_{\text{f}}\)spent & 0.5 & [kg] \\ Angle of inclination of the trajectory in reference to the equator at the orbit inclination of 97\({}^{\circ}\) & \(\theta\) & 0.655 & [rad] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Presentation of the fixed parameters used in the analysis of the duration of the satellite’s flight over Kampinos National Park for a variable weight of the satellite. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Initial weight of the satellite & m\({}_{\text{p}}\) & 15 & [kg] \\ Orbit altitude & h & 482 & [km] \\ Acceleration of gravity & h & 482 & [km] \\ Acceleration of gravity & g & 8.49 & [\(\frac{m}{g}\)] \\ Acceleration of gravity & g & 8.49 & [\(\frac{m}{g}\)] \\ Orbital velocity & v\({}_{\text{o}}\) & 7.8 & [\(\frac{m}{g}\)] \\ Thrust force & F & 1 & [N] \\ Weight of the fuel consumed to conduct the manoeuvre & m\({}_{\text{f}}\)spent & 0.5 & [kg] \\ Angle of inclination of the trajectory in reference to the equator at the orbit inclination of 97\({}^{\circ}\) & \(\theta\) & 0.655 & [rad] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Presentation of the fixed parameters used in the analysis of the duration of the satellite’s flight over Kampinos National Park for a variable fuel weight. increment (\(\Delta\)vtotal) required to perform the manoeuvre. The target orbit parameters reflect a typical Sun-synchronous orbit used in Earth observation missions, chosen to optimize coverage of the area of interest at specific times during the nanosatellite's passes. These parameters were determined based on mission requirements, particularly the frequency of passes over the area of interest (AOI), effective ground coverage, and ensuring adequate observation time. The first orbital manoeuvre (\(\Delta\)v1) was executed approximately two hours after the nanosatellite was placed in the initial orbit, initiating the Hohmann transfer manoeuvre. The main acceleration (\(\Delta\)v2) completing the transfer and shaping the target orbit was performed at the apogee of the transfer orbit, which occurred during the nanosatellite's second revolution. **Calculating the energy required to tilt the satellite**  
Table 6 presents the fixed parameters necessary for the analysis of the energy required to tilt the satellite. They include the satellite's weight without fuel, fuel weight, and the total weight of the satellite with fuel that influence the moment of inertia and motion dynamics. The parameters also include the slew rate that defines the rate of changing the orientation of the satellite.