## 3 Results
### Analysis of the Weight of Fuel Necessary to Perform the Holmann Transfer  
The aim of the fourth analysis was to check the weight of fuel that is necessary to perform the Hohmann transfer. The analysis took into consideration two cases: (1) the weight of fuel is constant and is 0.5 kg, but the weight of the satellite, however, takes different values. Depending on the quality of the telescope, in may range from 8 to 18 kg. (2) the initial weight of the satellite is 15 kg, and the fuel weight ranges from 0.3 to 0.7 kg, at intervals of 0.05 kg.  
Table 10 presents the results of the analysis of the fuel weight required to perform the Hohmann transfer depending on the initial weight of the satellite and the specific impulse. As the specific impulse and effective exhaust velocity increase, a gradual decrease  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\
**Initial** & **End** & & & & & & & & & & & & & \\
**Weight** & **Weight** & **Weight** & **Specific** & **Effective** & **Increase** & **Possible** & **Passible** & **Target** & **Target** & **Target** & **Target** \\
**of the** & **of the** & **of the** & **of Fuel** & **Impulse** & **Ehausu** & **Inclici-** & **Change** & **Change** & **Inclina-** & **Inclina-** & **incina-** & **recase** & **Width** & **High** \\
**Satellite** & **Satellite** & **Satellite** & **m\({}_{t}\) [kg] & **I\({}_{up}\)** & **V\({}_{v}\)** [\(\frac{\pi}{2}\)] & **Av [\(\frac{\pi}{2}\)] & **Av [\(\frac{\pi}{2}\)] & **a** [\(\frac{\pi}{2}\)] & **a** [\(\frac{\pi}{  
in the required weight of fuel is observed, which means that the engine is more efficient at higher values.  
Figure 7 presents the Hohmann transfer, performed to raise the orbital altitude from 482 km to 550 km, resulting in a total increase of 68 km. The comparison of the results of analytical calculations and STK 12.7.1 simulations revealed that the values were very similar, where in the simulation for a satellite weighing 8 kg, the fuel consumption was 0.180 kg, while the result of analytical calculations was 0.194 kg. The difference between these results is only 0.014 kg. This slight difference may result from several factors. First and foremost, the simulation in the STK 12.7.1 environment accounts for more advanced gravitational models and perturbation effects significant for low Earth orbit, such as the Earth's ellipsoidal shape (J2), irregularities in the gravitational field, atmospheric drag, and potential third-body interactions from the Sun or Moon. On the other hand, analytical calculations are typically based on simplified assumptions, such as the spherical symmetry of the Earth and constant gravitational acceleration, and do not consider such perturbations. Additionally, differences may arise from numerical rounding in the STK 12.7.1 environment, which takes into account variable conditions during an actual manoeuvre, whereas analytical methods assume an impulsive manoeuvre executed instantaneously and precisely at a predetermined orbital point. The comparison of both approaches thus serves as an indirect assessment of the impact of orbital perturbations while maintaining the clarity and utility of the analytical model for preliminary mission planning. Detailed conclusions are presented in Section 4--Discussion.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Initial Weight of the** & **Specific Impulse** & **Effective Exhaust** & **Fuel Weight** \\
**Satellite** & **Is\({}_{\text{sp}}\) [s]** & **Velocity** & **Required** \\
**m\({}_{\text{p}}\) [kg]** & **Is\({}_{\text{sp}}\) [s]** & **v\({}_{\text{el}}\)[\(\frac{m}{s}\)]** & **m\({}_{\text{total}}\) [kg]** \\ \hline  
\hline \end{tabular}
\end{table}
Table 10: Presentation of the results of the analysis of the weight of fuel necessary to perform the Hohmann transfer.