# The Interaction between the LEO Satellite Constellation and the Space Debris Environment
## 3 Risk Analysis of Constellation Collision
### Starlink Constellation Collision Risk  
SpaceX has given the planning parameters of about 38,000 satellites expected to be deployed in Phase iii and iv, but the final deployment mode still needs to be adjusted according to the actual use after the completion of the networking of Phase i and Phase ii. Therefore, in this paper, only the Phase i satellites have already been in orbit and the Phase ii satellites to be launched are used in the overall analysis of the Starlink constellation, with a total of 4452 satellites. It can be seen from Table 1 that phase ii satellites are deployed in four orbital layers. The height of the first orbital layer is 540 km and the inclination is 53.2\({}^{\circ}\). There are 1584 satellites in total. The height of the second orbital layer is 570 km and the inclination is 70\({}^{\circ}\) with 720 satellites. The main orbital parameters of the third orbital layer and the fourth orbital layer are the same, the altitude is 560 km, the inclination is 97.6\({}^{\circ}\), a total of 520 satellites. Similarly, the complete mission cycle of the satellite is divided into three stages to evaluate the space object flux and collision risk in the orbit of a single  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Class** & **Flux (1/m\({}^{2}\)/a)** & **N** & \(P_{\geq 1}\) **(\%)** & \(N_{1628}\) & \(P_{\geq 1,1628}\) **(\%)** \\ \hline \(d\geq 1\) cm & 2.21 \(\times 10^{-5}\) & 4.28 \(\times 10^{-4}\) & 0.04 & 6.96 \(\times 10^{-1}\) & 50.15 \\ \(d\geq 6\) cm & 2.20 \(\times 10^{-6}\) & 4.34 \(\times 10^{-5}\) & 0.01 & 7.07 \(\times 10^{-2}\) & 6.83 \\ \(d\geq 10\) cm & 1.37 \(\times 10^{-6}\) & 2.73 \(\times 10^{-5}\) & \textless{}0.01 & 4.45 \(\times 10^{-2}\) & 4.35 \\ \(d\geq 1\) m & 5.35 \(\times 10^{-7}\) & 1.44 \(\times 10^{-5}\) & \textless{}0.01 & 2.34 \(\times 10^{-2}\) & 2.32 \\ \hline \end{tabular}
\end{table}
Table 4: Fluxes, numbers of impacts and probability for one or more collisions for constellation objects during Phase 3.  
Figure 4: Flux and satellites altitude over time during Phase 3 with objects \(\geq\)6 cm.  
satellite, and to calculate the overall collision probability of the satellite in the orbital layer. The flux variation of the objects above 6 cm encountered by satellites with different orbital layers in the Starlink constellation during the mission cycle is shown in Figure 5, and the single and overall collision probabilities of satellites with different orbital layers are shown in Table 5.  
In the working stage of the satellite, when satellites have a similar orbit, the object flux in the orbit with a 97.6\({}^{\circ}\) inclination is about twice as much as that at the inclination of 53\({}^{\circ}\), and the collision risk of the satellite in the orbit with high inclination is higher. When satellites have a similar inclination, the initial flux of the space object at the 540 km is slightly larger than that of the 550 km, but due to the influence of atmospheric resistance, the fading speed of the object with low orbit is faster, and the average flux at the 550 km is larger during the overall working time in orbit, so the risk of satellite collision is higher. As can be seen from Table 5, the collision probability of a single satellite increases with the promotion of the orbital inclination, but because of more satellites in the orbital layer near the low inclination, the corresponding overall collision probability is higher. In the whole mission cycle of the satellite life, the collision risk is the highest in the in-orbit operation phase, so we need to pay more attention to the design of collision avoidance and in-orbit satellite monitoring.