## 3 Results
### Selection of the Optimum Nanosatellite Dedicated to Maximise the Specific Operational Task  
Based on the previous analyses, the authors decided to select the optimum nanosatellite dedicated to capture images of a specific area of interest. The sample calculations provided below are based on the values of specific parameters of the M6P satellite from NanoAvionics [30]. The analysis of the manoeuvre of transfer onto a higher orbit was conducted with great precision and an accuracy of up to 1 m, which will enable a precise determination of the influence of changes in the orbital parameters on the efficiency of the mission. Figure 8: Visualisation of the tilt of the sensor with the satellite platform and of the coverage of Kampinos National Park. (Source: STK 12.7.1). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tilt Angle** & \begin{tabular}{c} **Duration of the** \\ **Manoeuvre** \\ **t [s]** \\ \end{tabular} & \
\begin{tabular}{c} **Energy Consumed by** \\ **Reaction Wheels** \\ **E [J]** \\ \end{tabular} &
\begin{tabular}{c} **Charging Time** \\ **t [s]** \\ \end{tabular} \\ \hline
15 & 3.00 & 1.35 & 0.01929 \\
16 & 3.20 & 1.44 & 0.02057 \\
17 & 3.40 & 1.53 & 0.02186 \\
18 & 3.60 & 1.62 & 0.02314 \\
19 & 3.80 & 1.71 & 0.02443 \\
20 & 4.00 & 1.80 & 0.02571 \\
21 & 4.20 & 1.89 & 0.02700 \\
22 & 4.40 & 1.98 & 0.02829 \\
23 & 4.60 & 2.07 & 0.02957 \\
24 & 4.80 & 2.16 & 0.03086 \\
25 & 5.00 & 2.25 & 0.03214 \\
26 & 5.20 & 2.34 & 0.03343 \\
27 & 5.40 & 2.43 & 0.03471 \\
28 & 5.60 & 2.52 & 0.03600 \\
29 & 5.80 & 2.61 & 0.03729 \\
30 & 6.00 & 2.70 & 0.03857 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._The force of atmospheric drag acts on the satellite that is moving on a low Earth orbit (LEO) in the rarefied atmosphere. The formula to calculate drag is derived from basic fluid dynamics:  
\[F_{D}=\frac{1}{2}\rho\cdot v^{2}\cdot C_{D}\cdot A=0.00000135\;\mathrm{N}, \tag{28}\]  
where \(\rho\) is the density of the atmosphere at the altitude h. This parameter describes the number of molecules that interact with the satellite in a unit of volume. Atmospheric density decreases exponentially with increasing altitude. At the altitude h = 500 km, in the thermosphere, air density is extremely low. The atmospheric density at 500 km is \(10^{-12}\;\frac{\mathrm{kg}}{\mathrm{m}^{3}}\). This value is comparable to that of the density in the vacuum in outer space. v is the orbital speed. On a low Earth orbit, the orbital speed is approx. v = 7.8 \(\frac{\mathrm{km}}{\mathrm{s}}\). The force of drag increases with the square of velocity, as higher velocity means stronger collisions with atmospheric particles. C\({}_{\mathrm{D}}\) is aerodynamic drag coefficient. This is a dimensionless coefficient that determines how an object reacts to a flow of gas (e.g., atmosphere). For typical satellites on low Earth orbits, this coefficient is C\({}_{\mathrm{D}}\) = 2.2. The value C\({}_{\mathrm{D}}\) = 2.2 was obtained from research on the aerodynamic drag of CubeSats on low Earth orbits. A is the frontal surface of the satellite. This surface interacts with the flow of the atmosphere. It is assumed that the frontal surface of the satellite is A = 0.02 m\({}^{2}\), as the analysed satellite has the dimensions of 0.1 \(\times\) 0.2 \(\times\) 0.3 m, and the smallest possible frontal surface is assumed by default, so as to minimise the drag. Then, the loss of orbital energy was calculated, from the formula to calculate energy loss that results from the work of the drag force. \[\Delta E=F_{D}\cdot v\cdot\Delta t=27307\;\mathrm{J}, \tag{29}\]  
where F\({}_{\mathrm{D}}\) = 0.00000134 N, v is orbital velocity. On a low Earth orbit, the orbital speed is approx. v = 7.8 \(\frac{\mathrm{km}}{\mathrm{s}}\). The force of drag increases with the square of velocity, as higher velocity means stronger collisions with atmospheric particles. \(\Delta t\) is time [s] for a month. The next step consisted of calculating the decrease in altitude \(\Delta h\).