## 4 Discussion
### Discussion of the Results of the Analysis of the Possible Change in Inclination
The value of cos\(\theta\) decreases with the increase in the angle of inclination. As a result, the satellite's velocity in reference to the surface of the Earth diminishes. In this specific case, this means that only approx. 22.6% of the total velocity of the satellite (7800 \(\frac{\mathrm{m}}{\mathrm{s}}\)) is translated into motion in reference to the surface of the Earth. This significantly reduces the velocity relative to the Earth's surface, which prolongs the duration of flight over a given area. In this case, the flight duration is 8.22 s, being significantly longer than the neighbouring options, where the angle of inclination is smaller and the velocity relative to the surface of the Earth is higher. It results in an extended duration of flight over the given area, which may be beneficial for certain missions, e.g., for observation purposes, where it is required for the satellite to spend more time over a specific area. However, the need to process data and maintain contact with the satellite for a longer time during such a flight may generate increased energy costs. Through the comparison of the results of the conducted analysis of the change in orbit inclination with examples of orbital manoeuvres provided in the literature, one may notice significant differences in the required \(\Delta\)v, duration of the manoeuvre, and fuel consumption. An example presented in the literature, where changing the inclination by 2.17\({}^{\circ}\) requires \(\Delta\)v = 4.22 \(\frac{\mathrm{km}}{\mathrm{s}}\), points to high energy requirements for short impulsive manoeuvres [7]. In a different case, at low thrust, changing the inclination by 5.6\({}^{\circ}\) required \(\Delta\)v = 1.18, but at the expense of the long duration of the manoeuvre (54 days) and consuming 25.8 kg of fuel by a satellite of the initial weight of 367 kg [34]. Conclusions:
* The ability to change orbital inclination is strongly dependent on both fuel mass and specific impulse. Even a slight increase in available \(\Delta\)v allows for more advanced manoeuvres. * An increase in specific impulse by 10 s results in an increase in exhaust gas velocity by approximately 85 \(\frac{\mathrm{m}}{\mathrm{s}}\), improving fuel utilisation efficiency. * Even small changes in inclination (\(\approx\)0.5-0.8\({}^{\circ}\)) may significantly influence the coverage of the target area. * A longer duration of flight over the given area may be beneficial for observation missions, but it requires more precise manoeuvres. * The optimum orbit should take into account the compromise between the amount of fuel, efficiency of the manoeuvre, and the required duration of the flight over the area. Discussion of the Results of the Analysis of the Weight of Fuel Necessary to Perform the Hohmann Transfer  
Now let us move on to the conclusions from the data provided in Table 10, taking into account specific key parameters, such as the initial and end weight of the satellite, increase in velocity, as well as the amount of fuel necessary to perform the Hohmann transfer. The influence of the initial weight and amount of fuel should be analysed. The amount of fuel required to perform the manoeuvre increases with the increasing initial weight of the satellite. The analysis reveals that for a satellite of the initial weight of 8 kg, the amount of fuel necessary to change the orbit from 482 km to 550 km is approx. 0.194 kg, whereas a satellite of the initial weight of 15 kg requires 0.300 kg of fuel to perform the same orbital transfer. Then, the increase in velocity was analysed. The values of \(\Delta\)v\({}_{1}\) and \(\Delta\)v\({}_{2}\) are essential to calculate the amount of energy that must be provided to change the orbit. In the calculations, the increases in velocity remain relatively stable for different weights of the satellite, which means that the increase in weight influences, first of all, the necessary amount of fuel. The total increase in velocity is approx.