# Modeling and Simulation of Sky Survey
## 1 Introduction  
Sky surveying has given a huge boost to the development of astronomy [1; 2], and there are many internationally renowned surveys, such as Supernovae observations [3; 4; 5; 6], Sloan Digital Sky Survey [7; 8; 9], Legacy Survey of Space and Time (LSST) [10; 11; 12], Hubble Space Telescope (HST) [13; 14; 15], Euclid [16; 17; 18], Wilkinson Microwave Anisotropy Probe (WMAP) [19; 20; 21], and Planck [22; 23], which have made a number of major scientific discoveries in astronomy, such as the discovery of the accelerating expansion of the universe [3]. Table 1 shows a comparison of the specification parameters of CSST, LSST, Euclid, and WFIRST [24; 25; 26] with information from [PERSON] [27].  
In 2024, China will launch the China Space Station Telescope (CSST) [27; 28]. It will be launched at the Wenchang launch site using the ChangZheng 5B launch vehicle. A wide and deep optical survey will be carried out to complete a 15,000 deg\({}^{2}\) sky area, including deep multicolor imaging observations, very deep multicolor imaging observations, slitless spectroscopic observations, and deep slitless spectrography observations [8; 27].  
The mission planning is a very complex problem, and there are many factors affecting the mission strategy, including the orbital motion of satellites; the influence of the Sun, Moon, and Earth light on the observations; the need to meet the energy supply requirements of the vehicle's solar panel in the sunlit region; and the influence of the Earth South Atlantic Anomaly (SAA) region on the equipment during the ground orbit operation. The complexconstraints and wide sky area factors bring great challenges to the existing optimization algorithms to solve the sky survey observation models.  
The survey observation of large space astronomy telescopes is a complex task [29], and advanced planning and operation control technology is the basis for the efficient completion of the task. The space astronomy observation telescope will be constrained by various factors in the process of a sky survey observation. In order to improve the observation efficiency, overall mission planning and optimal allocation of resources are required for the observation sequence of different target sky areas. The entire optimization of the life-cycle observation plan while in orbit operation will be performed to enhance efficiency and maximize the value of scientific applications. Figure 1 shows the planning diagram of the sky survey observation mission.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **CSST** & **LSST** & **Euclid** & **WFIRST** \\ \hline Caliber & \(\geq\)2 & 8.4 & 1.2 & 1.3 \\ Wavelength Range & 200–1000 & 320–1050 & 550–920 & 1000–2000 & 760–2000 \\ Effective Field of View & \(\geq\)1 & 10 & 0.56 & 0.55 & 0.85 \\ Image Quality & \(\leq\)0.15 & 0.7 & 0.2 & 0.6 & 0.3 \\ Relative Skywatching Speed & \(\geq\)3.1 & 7.3 & 1 & NaN & 0.7 \\ Sky Survey Area & 15,000 & 20,000 & 15,000 & NaN & 14,000 \\ Band Number & 6 & 6 & 1 & 3 & 4 \\ Availability of Spectrum & Yes & No & No & Yes & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of LSST, WFIRST, Euclid, and the suggested wide and deep survey on board the CSST [27].  
Figure 1: Diagram of the sky survey mission planning. The survey telescope needs to satisfy certain observing constraints during on-orbit observations, such as the angle constraints between the sunlight (\(\alpha\)), lunar light (\(\beta\)), and the observation pointing, etc., shown in the figure. Different colors in the sky zone represent different levels of importance (degree of value) of the observed sky zone. For example, there are extremely deep sky zones, seamless spectral sky zones, etc. The telescope can only be rotated parallel to the orbital plane normal (\(Z^{\prime}\) axis) during the search for the observing sky area. The red square is the area currently under observation. The telescope can only observe one sky area at a time and needs to keep observing for a fixed period of time to complete a single observation.