## 3 Threshold FOV of the Satellite Based on the Improved Observation Mode
Therefore, the width of the sensor sweep across the GEO strip in one cycle is only related to the sensor's AOFOV. Due to the small FOV, it is difficult for the sensor to scan such a wide range of GEO bands in one orbital period. If we ensure that the sensor can revisit the GEO target within a few days, we must ensure that the GEO strip areas scanned by the sensor each day do not completely overlap, and we must ensure that the observing satellites do not operate an integer number of turns per day. Otherwise, in natural rendezvous mode, the observation sensor would see the same batch of targets every day. \[N=\frac{T_{g}}{T}, \tag{5}\]  
where \(N\) is expressed as daily laps of the observation satellite, \(T_{g}\) is expressed as the rotation period of the Earth, and \(T\) is expressed as the orbital period of the observation satellite. The orbital period can be represented by the orbital altitude of the observing satellite. \[T=2\pi\sqrt{\frac{\left(R_{e}+h\right)^{3}}{\mu}}, \tag{6}\]  
where \(R_{e}\) is the average radius of the Earth, \(h\) is the orbit altitude, and \(\mu\) is the Earth's gravitational constant. Assuming that the observation satellite can complete the revisit of the GEO target within \(P\) days, the following conditions must be met:  
\[\frac{360\text{deg}}{2\text{AOFOV}}=P\times N, \tag{7}\]  
Since \(N\) cannot be an integer, we define the following representation of \(N\):  
\[N=K+m/M, \tag{8}\]  
where \(K\) is the integer part of \(N\), and \(m/M\) is the fractional part of \(N\). Furthermore, \(m\) is a key parameter that determines the order of scanning bands on the GEO belt with the value range of 1, 2... \(M-1\), and \(m\) and \(M\) are relatively primes. The satellite can circle the Earth \(KM+m\) times in \(M\) days, resulting in an integer number of scanning bands. Therefore, \(M\) is called the revisit period of the GEO belt. Condition: \((KM+m)D\geq 360\text{deg}\) needs to be met if the satellite is to revisit the GEO band. Where \(D\) is the scanning width of the GEO belt by the observation satellite in each orbital period, and its value is twice AOFOV. The minimum revisit period of the observation satellite is expressed as \(M_{\text{min}}\). \[M_{\text{min}}=\left[\frac{360\text{deg}}{KD}-\frac{m}{K}\right]+1, \tag{9}\]  
According to Equations (5) and (6), the corresponding relationship between the number of laps per day and the orbit height of the observation satellite is shown in Figure 4:0  
The altitude constraint for a DDSSO is \([580\ \mathrm{km},1200\ \mathrm{km}]\), and the period constraint is \([96.27\ \mathrm{min},109.42\ \mathrm{min}]\). According to Table 1, we can obtain the value range of \(N\) as \((13,15)\), and according to Equation (8), we can obtain the value of \(K\) as \(13\) and \(14\). Then, we can obtain the orbital inclination from the constraint of the observed satellite. Figure 4:1  
The integer part of the daily operation circle of the observation satellite is determined, that is, \(K\)= \(14\). The corresponding relationship between the revisit period of the observation satellite and the sensor's scanning width can be summarized (see Table 2). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Daily Laps**} & **13** & **14** & **15** & **16** \\ \hline orbital altitude (km) & 1262.09 & 893.79 & 566.89 & 274.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correspondence between daily laps and orbital altitude of satellites.