# Research on the Efficient Space Debris Observation Method Based on Optical Satellite Constellations
## 2 Constellation Design  
### Model Establishment  
The constellation spatial coverage model was established by comprehensively considering the point coverage numerical simulation model, the optical sensor coverage calculation, ground shadow model, the visual function, and the constellation comprehensive coverage performance evaluation index [16]. The point coverage numerical simulation technology was used to divide the target airspace into multiple blocks according to specific criteria. According to the constellation coverage of all the blocks, the space and time coverage performance of the constellation to the target airspace was analyzed. In order to avoid the infrared radiation interference of the Earth and its atmosphere, the optical sensors on the satellite could only face the cold background of the universe to detect space objects above the edge of the Earth. The influence of the Earth's shadow on the observation of space debris also needs to be considered. The coverage of the constellation to the target airspace was measured in time and space to evaluate the comprehensive coverage performance of the constellation. 1. Point coverage numerical simulation model  
The numerical simulation technique of the point coverage is also known as the spatial meshing method [17], as shown in Figure 1. The target airspace is divided into grid points according to specific criteria, and the coverage of the target airspace in time and space is analyzed according to the coverage of all the airspace grid points by the constellation. The problem surrounding constellation coverage in general Earth observation is that it mainly considers the two-dimensional coverage of the earth's surface. Due to the need to monitor space debris, two-dimensional grid point sampling needs to be extended to three-dimensional, and low-orbit space-based optical satellite constellations need to consider three-dimensional coverage within a certain altitude range above the Earth's surface where the sampled airspace is roughly a spherical shell. To establish a three-dimensional grid point sampling criterion, the height variables and the sample latitude, longitude, and altitude at the intervals need to be added. 1. Optical sensor coverage calculation  
In order to avoid infrared radiation interference from the Earth and its atmosphere, the optical sensor of the satellite can only be oriented towards the cosmic cold background of space to detect objects above the edge of the Earth [18], as shown in Figure 2.  
In Figure 2, O is the center of the earth and S is the space-borne optical sensor. The solid circle represents the sphere model of the Earth, and the dotted circle represents the edge of the Earth's atmosphere. The sensor covers a sector beyond the tangent line of the satellite to the Earth's atmosphere. Figure 1: Schematic diagram of the point coverage grid method. Figure 2: Coverage area of the space-based optical sensor. The covering conditions of a space-based optical sensor for specific space debris in a specific altitude are shown in Formula (1). \[\left\{ \begin{array}{l}\varphi>\beta\\ 0<d_{st}<L_{\max}\end{array} \right. \tag{1}\]  
where \(\varphi\) is the angle between the space object and the Earth's center relative to the satellite, \(\beta\) is the angle between the earth's atmosphere boundary and the Earth's center relative to the satellite, \(d_{st}\) is the distances between the satellites and the space object, and \(L_{\max}\) is the maximal detection range of the satellite-borne optical sensor. (3) Earth shadow model  
When space-based optical sensors observe space objects, the space objects need to be illuminated by the Sun. When the space object is in the shadowed area, the optical sensor cannot observe it, so the influence of the shadow on the observation of the space object needs to be considered.