# A Study of Cislunar-Based Small Satellite Constellations with Sustainable Autonomy
## 5 Visual Simulations and Analysis (Constellation Scenarios)
### Earth-Based Constellation Simulation
#### 5.1.2 Monte Carlo Conjunction Tracking Analysis (Earth's Side of Cislunar Space)  
Conjunction tracking is the next major element in the analysis onboard that needs to be aligned with the proposed method and be autonomous until the mission objectives are attained. This need to be done onboard, which will be presented in the later sections of this paper. Figures 7 and 8 below show the detailed analysis of the tracking conjunction using Monte Carlo. The word 'conjunction' is specifically mentioned in this paper due to the reason that two or more events are to be addressed in space at the same point in time. The debris and other missions operating and propagating together in multiple orientations, will make the situation risky some times when they all pass nearby each other and the chances of the collisions increase. Hence, the conjunction analysis is inevitable to ensure that the mission is safe and seamlessly operating specifically when it is a constellation of small satellite operating as one system.  
The observations are provided in the Tables 2 and 3 below.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Probability of Collision (Pc) & 0.022097 \\ Probability of Collision (Pc)- & 0.018540 \\ with Monte Carlo & 58 ms \\ The difference in TcAs & \(-\)9.4902\% \\ Difference in Pc & 112 \\ No. of potential hits & 0.147045 Km \\ Closest Avg. Range & 1.331830 Km \\ \end{tabular}
\end{table}
Table 2: Observations from Case-1 (Earth).  
Figure 6: The parametric analysis of Earth’s small satellite constellation (Cislunar) [16]. (**a**) Along, Cross, and Radial separations Sat-to-Sat (Km); (**b**) Along Arc Track, In-track, and Range variations (Km); (**c**) Satellites portraying the Radial projections (Km); (**d**) RAAN-Azimuth-Elevation variations (Deg.); (**e**) Azimuth angle variation with aligned satellites; (**f**) Elevation angle variation with the aligned satellite.  
Figure 7: The debris (points) distribution over the constellation (Earth scenario). (**a**) Tracked debris in the safer zone with mission in progress [16]; (**b**) Constellation variation under intense debris movement; (**c**) Mission operations in medium-risk zone of Debris.  
The observations are in the real-time scenarios of Earth-based small satellite constellations. The space environment considerations are also made and are incorporated in the analysis that needs to be autonomous in every instance of the constellation operations.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Probability of Collision (Pc) & 0.022097 \\ Probability of Collision (Pc)-with Monte Carlo & 0.019147 \\ The difference in TCAs & 61 ms \\ Difference in Pc & \(-7.6800\%\) \\ No. of potential hits & 204 \\ Closest Avg. Range & 0.147045 Km \\ Closest Avg. Range- & 1.315941 Km \\ with Monte Carlo & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Observations from Case-2 (Earth).  
Figure 8: Autonomous collision assessment-Earth scenario (Monte Carlo) [16]. (**a**) Probability of collision (Pc-6000 random states); (**b**) State variations of missed collisions (6000 Distance-Km); (**c**) Probability of collision (Pc-10,000 random states); (**d**) State variations of missed collisions (10,000 Distance-Km).