## 3 Results and Discussion
### Coverage Characteristic Analysis  
Coverage characteristics are an important evaluation indicator for Earth observation. In order to simulate the coverage characteristics of the Earth's surface of the MS-BiSAR, we used the observation geometric model for further analysis. The observability of a region on Earth is determined by the position of the transmitter, the receiver, and the observation target. Only surface areas that are observable by both the transmitter and the receiver can be considered as areas covered by the MS-BiSAR. Since the radar echo of the terrain becomes very weak with a large incidence angle, it can result in a low signal-to-noise ratio (SNR) of the image and may also be obstructed by the topography of the terrain. As a result, the incidence angle is usually set within a certain range. As for BiSAR, the incidence angles of the transmitter and the receiver are not the same. Thus, this research defined the coverage area of bistatic SAR for Earth observation based on the incidence angle of the transmitter and the receiver and set the threshold (\(\theta_{im}\) and \(\theta_{im}\)) for the incidence angle to 60\({}^{\circ}\). Then, we calculated whether the location of the given point on the Earth's surface is observable. We defined the coordinates of the Moon-based observatory \(O_{M}(X_{M},Y_{M},Z_{M})\), the satellite \(O_{s}(X_{s},Y_{s},Z_{s})\), the target on the Earth \(T(X_{T},Y_{T},Z_{T})\), and the barycenter of the Earth \(O_{s}(0,0,0)\). The incidence angle of the transmitter \(\alpha\) and the receiver \(\beta\) are as follows:  
\[\alpha=arccos\left(\frac{(X_{M}-X_{T})X_{T}+(Y_{M}-Y_{T})Y_{T}+(Z_{M}-Z_{T})Z_ {T}}{\sqrt{\left((X_{M}-X_{T})^{2}+(Y_{M}-Y_{T})^{2}+(Z_{M}-Z_{T})^{2}\right) \left(X_{T}^{2}+Y_{T}^{2}+Z_{T}^{2}\right)}}\right) \tag{5}\]  
\[\beta=arccos\left(\frac{(X_{S}-X_{T})X_{T}+(Y_{S}-Y_{T})Y_{T}+(Z_{S}-Z_{T})Z_ {T}}{\sqrt{\left((X_{S}-X_{T})^{2}+(Y_{S}-Y_{T})^{2}+(Z_{S}-Z_{T})^{2}\right) \left(X_{T}^{2}+Y_{T}^{2}+Z_{T}^{2}\right)}}\right) \tag{6}\]  
When \(0<\alpha<\pi/3\) and \(0<\beta<\pi/3\), the target on the Earth is observable. In order to calculate the accumulated coverage time of each area on the Earth, the Earth's surface needs to be meshed first with an appropriate sampling grid. In this paper, we used a Fibonacci grid instead of altitude-longitude grid to achieve a more uniform sphere partitioning, and effectively reduce the calculation time and numerical errors [27]. Then, the Fibonacci grid was used to set 10,001 sampling points on the Earth's surface (each point represents an area of about 50,000 m\({}^{2}\)) and calculate the accumulated observable time of GEO, IGSO, HEO, and GEO constellation bistatic configurations in 2022 with the time step of 10 min. As can be seen from Figure 10, all three MS configurations can achieve large coverage of the Earth, but the characteristics of coverage vary depending on the orbit of the satellite. For the GEO receiver configuration, it has good long-term coverage of middle and low latitudes within the longitude range of more than 100 degrees. For the IGSO receiver configuration, since its subsatellite point is not fixed, its accumulated observable coverage is larger than GEO, especially in middle and high latitudes. The coverage area of both configurations above is nearly equatorially symmetric. For the HEO receiver configuration, because most of its subsatellite points are concentrated in the middle and high latitudes, it has better coverage for high latitudes than the GEO and IGSO receiver configurations, so the HEO configuration will be more suitable for the continuous monitoring of polar regions. However, none of the three configurations above can achieve global coverage. The configuration of IGSO constellations can achieve good coverage of most of the Earth's surface, and if the number of satellites in the constellation is increased, the coverage of Earth observation could be improved. Due to the unique properties of each orbit, the observation geometry will differ after the formation of MS-BiSAR.