## 4 Discussion
### Discussion of the Results of the Analysis of the Possible Change in Inclination
37.56 \(\frac{\mathrm{m}}{\mathrm{s}}\), which is a relatively low \(\Delta\)v, considering the analysed change in the altitude of the orbit. Specific impulse (Isp) is another key parameter that influences the efficiency of fuel consumption. For the specific impulse of 180 s, the effective exhaust velocity is 1527.69 \(\frac{\mathrm{m}}{\mathrm{s}}\). A higher specific impulse means lower fuel consumption at the same \(\Delta\)v, which enables to use the resources of the satellite more economically. The semi-major axis of the transfer orbit (which is approx. 6887 km in the analysis) influences the velocity in the perigee and apogee of the transfer orbit. These values indicate the difference in velocities that the satellite must achieve to perform a successful transfer. In conclusion, a larger amount of fuel allows to perform larger manoeuvres to change the orbit altitude. However, even for a relatively small increase in velocity (37.56 \(\frac{\mathrm{m}}{\mathrm{s}}\)), the difference in the required amount of fuel is significant for heavier satellites. A higher specific impulse means lower fuel consumption, which is crucial for satellite missions where saving weight is important. The value of 1527.69 \(\frac{\mathrm{m}}{\mathrm{s}}\) of effective exhaust velocity means that every change in \(\Delta\)v requires a significant amount of fuel. The analysis reveals that the increases in velocity must be calculated precisely in order to avoid situations when the planned manoeuvres will become impossible with the available resources. Even slight differences in \(\Delta\)v may have a great influence on mission planning. Efficient fuel management is crucial, in particular for missions that require multiple manoeuvres. The possibility to change the orbit with limited resources is important for the achievement of the satellite's long-term goals, such as the observation of the Earth or adjusting the orbit to changing needs. In conclusion, it is possible to perform the Hohmann transfer in order to change the altitude of the orbit, yet only with correct fuel management and a proper understanding of the influence of specific impulse on propulsion efficiency. The results of the analysis reveal the total increase in velocity \(\Delta\
u_{\text{total}}=37.56\ \frac{\text{m}}{\text{s}}\). These are significantly lower values in comparison, for example, to the Hohmann transfer, such as the example provided in [35], where the first increase in velocity was \(\Delta\
u_{1}=2.25\ \frac{\text{km}}{\text{s}}\), the second increase was \(\Delta\
u_{2}=1.46\ \frac{\text{km}}{\text{s}}\), and the total increase was \(\Delta\
u_{\text{total}}=3.71\ \frac{\text{km}}{\text{s}}\). The duration of the Hohmann transfer was 3 h and 56 min, which also differs from the impulsive nature of the analysis, where the manoeuvres only take seconds. Similarly, for the data of SpaceX [36], the first impulse for the F9-25 Thiacom 8 mission was \(\Delta\
u_{1}=2.25\ \frac{\text{km}}{\text{s}}\), while for F9-70 Nusantara \(\Delta\
u_{1}=2.74\ \frac{\text{km}}{\text{s}}\), with the manoeuvre lasting for approximately 5 h.  
The differences mainly result from the smaller scale of the orbit changes in the analysis and the differences in the weight and characteristics of the satellites, which influence both the required increases in velocity, and the duration of the manoeuvres. In the context of the Hohmann transfer, it is possible to apply simple optimisation methods, such as minimising fuel consumption while maintaining the required parameters of orbital transfer. An example may be selecting the specific impulse and \(\Delta\
u\) so as to achieve the fuel efficiency within the limits of the available resources. It is recommended for future analyses to apply such optimisation methods that might additionally improve the efficiency of the manoeuvre. Conclusions:  
* The weight of the necessary fuel increases with the increase in the initial weight of the satellite. Heavier satellites require more fuel to generate the same increase in velocity.