# Modeling and Simulation of Sky Survey
## 4 Design of the Model Solving Algorithm
### Overall Arrangement Algorithm
3:for\(i=St\) to \(Et\)by Interval do
4:\(//\) Interval: Minimum time interval;
5:if\(i\in Oc\)then
6: Continue;
7:else
8:for\(j=1\) to M do
9:\(\delta=\theta(Eph_{i},s_{j})\) by Equations (5) and (6) //Sky area for zenith angle observation;
10:if\(\delta\leq\Delta\)then
11: Calculate the angles \(\alpha\) and \(\beta\) by using Equations (5) and (6). 12:if\(\alpha\geq\epsilon_{1}\) & \(\beta\geq\epsilon_{2}\)then
13:\(//\)Record the location of the sky area: \(PosVisible\in[1,2,\ldots,M]\);
14:\(SkyArea(PosVisible)=SkyArea(PosVisible)+1\);
15:else
16: Continue;
17:endif
18:endif
19:endfor
20:endif//Calculate the observation frequency of the sky zone;
21:endfor
22:\(Frequency(j)=\frac{SkyArea(j)}{\sum_{i=1}^{M}SkyArea(j)}\);
23:\(v(j)=\frac{1}{Frequency(j)}\); //Calculate sky area weights;
24:if\(Frequency(j)\leq\tau_{2}\)then
25:\(DifSky(j)=1\); // Recording difficult observation areas;
26:endif
27:return\(DifSky,v\)
```  
**Algorithm 5** The Algorithm 5  
```
1:INPUT\(A=\{Eph,Sun,Moon\}\); \(S=\{s_{j},j=1,2,\ldots,M\}\);
2:OUTPUT\(\;\)Difficult to observe sky areas \(DifSky\); Sky area weights \(v\). 4:for\(i=St\) to \(Et\)by Interval do
5:\(//\) Interval: Minimum time interval;
6:if\(i\in Oc\)then
7: Continue;
8:\(//\) Interval: Minimum time interval;
9:if\(i\in Oc\)then
10: Continue;
11:\(//\)Record the location of the sky area: \(PosVisible\in[1,2,\ldots,M]\);
12:\(SkyArea(PosVisible)=SkyArea(PosVisible)+1\);
13:else
14: Continue;
15:endif
16:endfor
27:endif//Calculate the observation frequency of the sky zone;
28:endif
29:\(Frequency(j)=\frac{SkyArea(j)}{\sum_{i=1}^{M}SkyArea(j)}\);
30:\(v(j)=\frac{1}{Frequency(j)}\); //Calculate sky area weights;
31:if\(Frequency(j)\leq\tau_{2}\)then
32:\(DifSky(j)=1\); // Recording difficult observation areas;



==WARNING: Truncated because of repetitions==



+++

## 5 Experiments and Analyses

This section starts by providing an introduction to the basics of satellite design, including the selection of the orbit parameters, the survey area, and the selection of the algorithm parameters. Then, the sequence planned by the sky survey algorithm is statistically analyzed, including efficiency statistics, difficult sky area statistics, CMG rotation angle statistics, and coverage efficiency statistics. Finally, the observations of different parameters are compared and analyzed. ### Basic Information

The time horizon of scheduling is from 1 January 2021 00:00 to 1 January 2030 (universal time coordinated). The experiments are performed by using an Intel (R) Core (TM) i7-7720U 2.30 GHz CPU with 16 GB RAM under the Windows 10 operating system. The experiments and analyses will be discussed in this section. Orbital Parameters: The spacecraft orbits in near-Earth orbit at an altitude of approximately 350-450 km (400 km desirable) with an orbital inclination of 42\({}^{\circ}\)\(\sim\)43\({}^{\circ}\) (42.5\({}^{\circ}\) desirable). As part of \(J_{2}\) perturbation, orbital propagation is taken into consideration, which has an effect on the RAAN by natural process in Equation (10). \[\dot{\Omega}_{d}=-\frac{3}{2}J_{2}\sqrt{\mu}R_{T}^{2}a_{d}^{-\frac{7}{2}}\cos I _{d} \tag{10}\]

where \(\dot{\Omega}_{d}\) is the RAAN change rate of OTV on drift orbit, \(J_{2}=1.086610^{-3}\) is the first zonal term of Earth, \(\mu=3.98600410^{14}\) (m\({}^{3}\)/s\({}^{2}\)) is the standard gravitational parameter, and \(R_{T}=6378137(m)\) is the Earth equatorial radius. \(a_{d}\) is the semi-major axis of drift orbit, and \(I_{d}\) is the inclination of drift orbit, \((SemimajorAxis:a,Eccentricity:e,Inclination:i,Argument\ of\ Perigee:\Omega,RAAN,Trueanomaly:\omega,)=(6771.14\) km, 0, 42.5 deg, 0, 0, 0). In this paper, it is assumed that the orbital model under \(J2\) perturbation is adequate for the long-term sky survey planning problem [42]. Focal Plane Basical Condition: The size of each CCD is 0.22\({}^{\circ}\)\(\times\) 0.2\({}^{\circ}\). The sky survey requires full coverage of each band, and for more detailed information, refer to [28].