## 5 Example and Discussion  
In this section, this paper gives a satellite cluster simulation example to further demonstrate the topology control strategy used in the actual workflow. Additonally, some analysis about the simulation results are also discussed. In the discussion part, this paper involves two other usual topology control algorithms for comparison, MST and \(\text{FIYG}_{\pi/3}\). MST is a centralized algorithm to get a subset of the edges of a connected, edge-weighted undirected graph that connects all the nodes together. And it can be used to generate a spanning tree of minimum energy cost in MWSNs [21]. \(\text{FIYG}_{\pi/3}\) is a 3-dimensional Yao-based distributed algorithm, which uses identical cones with a top angle of \(\pi/3\) to partition the transmission ball and to connect nodes in each partition [24]. The generated network topology of \(\text{FIYG}_{\pi/3}\) has the properties of bounded degree and energy efficiency. This paper establishes a satellite cluster scenario with 16 satellites, including two EOS (Sat1, Sat2), two GSC (Sat15, Sat16), and 12 DRS (Sat3 -14). This paper supposes an EO mission that Sat1 and Sat2 send the observed image data to Sat 15 and Sat16. The satellite cluster scenario is tested with OMNET++ 5.0 [37] and the detailed simulation parameters are listed in Table 1.  
Let Sat1 be the reference center of the relative motion coordinate system. Then, the rest can be described as running at a range of (0, 30 km) with Sat1. The main parameters of Sat1 are listed in Table 2. Figure 5(a) shows part of the satellite runs with Sat1 in the cluster. Figure 5(b) shows the periodic variation of distance from Sat16 to Sat1, where \(R=12\) km is the maximum communication range. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline ISLs bandwidth & 10 Mb/s \\ ISLs queue type & FIFO \\ ISLs queue length & 100 Packets \\ Simulation duration & 5000 s \\ Size of packet & 512 Bytes \\ Terminal bitrate & 8 Mbps \\ Maximum communication range & 12 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of satellites in communication. Before providing the experimental results regarding the topology lifetime and packet loss rate, we first observe the actual topologies at time \(t=0\), for one simulated satellite cluster network using different topology control algorithms, including the proposed topology control strategy. Six figures are given here. 1. Figure 6(a) shows the network topology after applying RAT algorithm Step 1.1-1.3, where the solid links (blue) denote the essential inter-satellite links (EISLs) and the dashed links (green) are the redundant inter-satellite links (RISLs). It is the key topology for Sat1 sending data to Sat15 and 16. 2. Figure 6(b) shows the network topology after applying the RAT algorithm Step 1.4 and it adds the other key topology of Sat2 transmitting data to Sat15 and 16 in Figure 3(a). 3. Figure 6(c) is the final topology after applying the RAT algorithm, where the dot-dash links (red) are the additional inter-satellite links (AISLs). 4. Figure 6(d) shows the origin of the physical topology without topology control. All nodes communicate with the maximal transmission range. 5. Figure 6(e,f) represent the network topologies after using the \(\text{FIYG}_{2\pi/3}\) and MST algorithms. First, this paper discusses two kinds of results, topology changing times and average topology lifetime, which can both reflect the network stability. Once the network topology changes, it may lead to the recalculating of routing paths with a result of increasing the end-to-end transmission delay. Thus, the lower topology changing times means the more stable the data transmission condition. Moreover, the average topology lifetime directly influences the amount of transmitted data in one topology lifetime.