# Hybrid-Compliant System for Soft Capture of Uncooperative Space Debris
## 2 Space Debris Capture
### Debris Data  
Space environment statistics is a new space debris topic addressing debris tracking. Due to the technological limitations of the surveillance networks, small-size debris is currently not trackable. In December 2022, more than 32,500 objects were regularly tracked by space surveillance networks. In contrast, more than 130 million objects starting from 1 mm in size are estimated to be in space orbit, based on statistical models [2]. The growing space debris issue in LEO creates the need for knowledge about those objects to design adequate debris removal systems. As ESA made available the catalogue of the tracked objects via the single-source DISCOS (Database and Information System Characterising Objects in Space) dataset [41], which is updated every few months, it is possible to analyze the LEO debris population. DISCOS plays a daily role in some of the ESA activities, such as collision avoidance, re-entry analyses, and for contingency support.  
By analyzing the DISCOS dataset, a debris population of almost 20,000 objects with nearly 300 different shapes was found in LEO. For each object, the available features are their mass, shape (with size characteristics, when available), and information about their orbits (apogee, perigee). All these objects could potentially threaten any space mission. However, we prioritize the shapes more commonly found in LEO (found more than a hundred times) for designing our capturing mechanism. Additionally, as the focus is on small satellite removal, the targeted debris' size and mass are non-negligible factors. To that extent, we narrowed down the catalogue of objects in LEO to those lower than or equal to 100 kg.  
The total number of objects found in LEO with the mentioned parameters was 4162. Among the 107 different specific shapes left, Sphere, Box, Box + 2 Pan (box shape with two solar panels), Cyl (cylinder), Cone, and Box + 2 Ant (box shape with two antennas) are the most present shapes in LEO. Together, they represent 84.24% of the total amount of small objects in LEO. Table 1 summarizes the main shapes of small objects found in LEO with their mass \(\leq\) 100 kg at the time of writing this paper.  
On the other hand, Figure 2 shows the distribution of objects in LEO (mass \(\leq\) 100 kg) grouped by their shape. Each dot represents a catalogued object relative to its apogee. The shape feature is ordered in descending order, where the sphere shape is the most present, and the Box + 2 Ant satellite shape is the least present.  
The data analysis shows that, despite the wide variety of shapes, one generic shape is predominant in LEO: the Box shape (with or without solar panels or antennas). If our capturing mechanism targets all the different Box-shaped objects with mass \(\leq\) 100 kg that exists in LEO (Box, Box + 2 Pan, Box + 2 Ant), it will have a clear impact on the debris problem at LEO. Indeed, the Box-shaped objects represent 41.59% of the total amount of small catalogued objects in LEO. Thus, actively catching Box-shaped debris helps answer the problem. Nano-satellites and mega-constellations are the future of LEO exploitation and will quickly saturate LEO. It is then essential to remove those satellites, even before  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Shape** & **Amount** & **\% of LEO Small Debris Total** \\ \hline Sphere & 1044 & 25.08 \\ Box & 949 & 22.80 \\ Box + 2 Pan & 669 & 16.07 \\ Cyl & 457 & 10.98 \\ Cone & 274 & 6.58 \\ Box + 2 Ant & 113 & 2.72 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main debris shapes found In LEO (mass \(\leq\) 100 kg).  
the 25 years of maximum stay in LEO proposed by Inter-Agency Space Debris Committee (IADC) guidelines [42].  
The hybrid-compliant (the combination of passive and active) system proposed in this paper targets Box-shaped debris of various masses, not exceeding the 100 kg threshold. Other shapes can be considered in further work.