## 2 Determination of the Satellite Observation Mode
Figure 1: (**a**) Orbital plane with orbital inclination; (**b**) Evolution Law of Orbital Inclination. According to the sinusoidal distribution characteristics of GEO targets, in order to make the observation satellite effectively cover the GEO belt, we improved the passive observation mode [21]. This observation mode is based on the passive observation mode, with the vernal equinox, summer solstice, autumnal equinox, and winter solstice as time nodes, and the pointing of the satellite sensor is adjusted periodically. When the satellite observes the target, the latitude pointed at by the sensor remains the same throughout the day. According to the changing characteristics of the GEO belt, the sensor's pointing is finely adjusted once per day. Compared with the traditional passive observation mode, this observation mode is more effective for the observation of the GEO belt. And due to the influence of the moment generated on the GEO target orbital surface by the gravity of the sun and the moon and the perturbation of the Earth's oblateness, the PP area gradually becomes inconspicuous. Compared with the PP area observation mode in the active observation mode, this observation mode not only makes it easier to adjust the pointing of the camera, but also can observe the entire GEO belt. Since the observation satellite runs in a DDSSO, the celestial coordinate system with the Earth's center as the origin has two characteristics (see Figure 3). One is long-term characteristics. The orbital surface processes one circle a year, and the coordinate axis also moves with the year as a cycle. Another is short-term characteristics. Due to the small precession angle of the SSO in the short term, the coordinate system can be regarded as an inertial coordinate system. By analyzing the observation characteristics of the satellite, we obtain the pointing trajectory equation of the sensor on the celestial sphere [21]. \[\left(x+\varphi\right)^{2}+\left[z-\left(\gamma+\delta\right)\right]^{2}=R^{2}, \tag{4}\]  
where \(\gamma\) is expressed as the pitch angle, and \(\varphi\) is expressed as the yaw angle. At the same time, the position of the sensor pointing to deep space should also consider the inclination limit of the orbit. The inclination of an SSO is defined as \(i\), and the \(\delta\) of the orbital center is \(i-90^{\circ}\). When the passive observation mode is used to observe the GEO belt, the observation area is a circle with the coordinate \((-\varphi,\ \gamma+\delta)\) as the center and \(R\) as the radius [21]. The size of the observation area is fixed, but the location is variable. When the latitude of the observation area is fixed, there is a \"seasonal decline problem\" in the observation as the GEO distribution changes. To solve this problem, we improved the passive observation mode. Under this observation mode, the orientation of the sensor is adjusted with the change of the GEO target distribution, and the center of the observation area is controlled to the center of the GEO zone corresponding to the observation moment. Therefore, the GEO belt can be well covered in the daily observation area throughout the year. Figure 2: (**a**) The relationship between RAAN and inclination. (**b**) Theoretical distribution of GEO objects beyond control. Figure 4 shows the trajectories of all GEO targets on 21 March 2021, Beijing time. Comparing the changes in the observation area before and after the improvement, we conclude that by improving the satellite observation model, an observation model that is more suitable for the current GEO target distribution can be obtained. In this observation mode, we can control the selection of the FOV while ensuring the coverage of the satellite.