# Modeling and Simulation of Sky Survey
## 4 Design of the Model Solving Algorithm
### Overall Arrangement Algorithm
As can be seen in Figure 6b, the number of rotation angles with more than eight rotation angles is significantly higher than the surrounding rotation angles in the statistics of rotation angles

Figure 3: Diagram of sky zone division. The diagram on the left shows the sky zone division range, \([-80^{\circ},-25^{\circ}]\), and \([25^{\circ},80^{\circ}]\). On the right side, the dimensions of each small sky zone are shown, as well as the numbering schematic of each sky zone, which is divided into \(N=17,712\) small sky zones. Ecliptic system of coordinates is used in this paper. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline _Parameter_ & \(\epsilon_{1}\) & \(\epsilon_{2}\) & \(\gamma_{1}\) & \(\gamma_{2}\) & \(\Delta\) \\ \hline _Value_ & 50\({}^{\circ}\) & 40\({}^{\circ}\) & 0.6 & 0.25 & 30\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter values used in the experiment. below 10 degrees. Figure 6c shows the statistical results for intervals of 10 degrees. As can be seen, the most rotation angles are between 10 and 20 degrees, followed by the angles between 1 and 10 degrees. This indicates that the rotation angles in the ten-year mission planning are still in small rotation angles overall. Figure 4: The results of the time efficiency statistics of the satellite sunshine zone. Horizontal axis is the ratio of the time of the day when the satellite is in the sunshine zone to the time of the whole day. Vertical axis is the statistics of the number of days. The total number of days in 10 years is 3655 days. The red bars indicate the enlargement of the fraction of time efficiency less than 0.6. Figure 5: The result of difficult sky area statistics. Rate represents the statistical results for different quantile intervals, with smaller values representing more difficult observations and larger weighting factors. It is planed to take 10 years to complete the 15,000 deg\({}^{2}\) survey, and the staged design algorithm used in this paper is able to complete the task three years ahead of schedule. The survey area in the seventh year is 15,215 deg\({}^{2}\). Figure 7 shows the growth of the survey area for different statistical intervals. From Figure 7a, it can be seen that the efficiency of the daily statistical coverage, with the red curve gradually increasing, rises more slowly in the beginning stage, which is due to the fact that the camera needs to reach 30 observations to be considered as completing a valid observation. As can be seen in Figure 8, the blue squares represent the sky areas where observations are conducted but do not reach 15 times, and this part of the sky area accounts for 82.38% of the sky area observed in the first year, while the part that completes 30 observations accounts for 14.38%, further indicating that the first year mainly conducts broad observations. During the increase of the survey area, there are many time periods when the area is not increased, and this time period represents the orbitally constrained part of the survey telescope, where the survey telescope cannot make observations, such as in the South Atlantic Anomaly region, in orbit maintenance, and when docking with the space station. The duration of this part is 120 days, which is 3.79% of the observation time. This indicates that it takes most of the time to do observations. Figure 7b shows the results of the growth of the coverage area according to the monthly statistics. As can be seen from the figure, the maximum of more than 300 deg\({}^{2}\) of sky area is observed each month, and the highest observation efficiency is in the middle position, which indicates that most of the sky area in the beginning stage does not reach the number of observations, and the observation efficiency is higher in the middle stage. On the other hand, there are less unobserved sky areas in the later stage, and it takes more time to wait for the observation window to finish the observation.