## 4 Results
Based on the calculations above, it is recommended to use 500 km orbits to deploy a satellite constellation designed for IoT communication, following the model of modern orbiters [28]. These satellites would enable the retransmission of communications using an ISL in S-band, as shown in Figure 2. The maximum communication distance between an IoT node on the Martian surface and the satellite at its farthest point on the Martian horizon can be estimated from this orbit. Using trigonometric calculations based on the radius of Mars indicated in Table 4, the maximum LoRa communication distance between an IoT node and a satellite orbiting at 500 km is 1909 km. Figure 8 illustrates the relationship between the maximum transmission power and the maximum distance to the frequencies of interest. For 868 MHz, the maximum reception power at a 500 km distance from the IoT node is estimated to be \(-109\) dBm, while at 1909 km, it is \(-117\) dBm. For 433 MHz, the estimated maximum received power is \(-106\) dBm at a 500 km distance, while at 1909 km, it is \(-120\) dBm. Therefore, in all cases of interest, the power received in the satellite is higher than the sensitivity of \(-137\) dBm. These results suggest that communications using LoRa technologies under the proposed conditions are feasible. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Carrier frequency & 868/433 MHz & \
\begin{tabular}{c} Antenna gains \\ (reception) \\ \end{tabular} & 22.6 dBi \\ \hline Transmit power & 14 dBm & Orbit height & 500 km \\ \hline Receiver sensitivity & \(-137\) dBm & Mars radius & 3390 km \\ \hline Antenna gains & 2.15 dBi &
\begin{tabular}{c} IoT node maximum \\ distance \\ \end{tabular} & 1909 km \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Key simulation parameters. The message capacity of LoRa satellites in the proposed architecture depends on the number of messages that can be received during each orbital period around Mars. This is determined by calculating the orbital period of the satellites using [PERSON]'s Third Law, resulting in a value of 122.7 min for a complete revolution around the planet. This calculation is essential to estimate the number of messages that can be processed by the satellite based on the data rate of each SF from theoretical IoT nodes. Table 5 displays the capacity analysis using SF values for standard LoRa messages (message size of 25 bytes and a bandwidth of 125 kHz [53]). The packet values also include duration, which determines the time it takes for the message to be transmitted or received based on the SF and the message size. Figure 9 shows the theoretical maximum number of messages per SF for a satellite in Mars orbit. However, this is only an estimate as it does not consider interference, collisions, the actual hardware capacity of the satellite, or other factors that could affect message reception. Although an SF7 allows for more messages, SF12 is typically used for satellite communications as it is more robust and increases the probability of reception in orbiting satellites [54]. Therefore, the maximum theoretical number of messages a satellite could receive is 10,794 from IoT nodes per orbital period. This is much lower than other studies for IoT constellations in LEOs, which can handle up to 60,000 messages from IoT nodes per hour [55]. Figure 8: Maximum power related to distance using LoRa 433 MHz (in blue) and LoRa 868 MHz (in red). \begin{table}
\begin{tabular}{c c c} \hline
**SF** & **Data Rate (kbps)** & **Packet Duration (ms)** \\ \hline
7 & 5.47 & 36 \\ \hline
8 & 3.13 & 64 \\ \hline
9 & 1.76 & 113 \\ \hline
10 & 0.98 & 204 \\ \hline
11 & 0.54 & 365 \\ \hline
12 & 0.29 & 682 \\ \hline \end{tabular}
\end{table} 
Table 5: Spreading factor values for 25-byte messages at 125 KHz. A critical analysis component was the computation of visibility access using STK's advanced models for Light Time Delay and Apparent Position.