# Methodology for CubeSat Debris Collision Avoidance Based on Its Active ADCS System
## 3 Materials and Methods
### ADCS System  
This study explores the potential for establishing a methodology aimed at minimizing the likelihood of a collision involving a CubeSat lacking a propulsion system, solely relying on its active ADCS. The fundamental concept revolves around the idea that altering the satellite's orientation can influence its cross-sectional area, thereby either increasing or decreasing the drag force it experiences. This adjustment in orientation is intended to occur within the time frame spanning from the initial alert period (7 days prior to the Time of Closest Approach (TCA)) to the recommended limit for maneuvers (2 days before TCA). This action will change the orbital elements of the satellite, modifying the TCA conditions in the following alerts. To assess the potential implementation of such a methodology in CubeSats, various formats (including 2U, 3U, and 6U) are subjected to analysis. The insert orbit of Lume-1 serves as the mission scenario. Two additional altitudes are considered in this investigation: one positioned 40 km lower and another situated 80 km lower, analyzing the influence  
Figure 5: Lume 1 2U-satellite [23]. of altitude in the performance. The Lifetime tool within the STK software package is employed to model orbit propagation, considering factors such as cross-sectional area, mass, and the satellite's initial position. The primary objective of this part of the methodology is to ascertain the discrepancy in horizontal and vertical satellite positions within a Local Vertical/Local Horizontal (LVLH) reference frame at the TCA. This disparity is then compared against the threshold miss distances prescribed by CDMs to assess the potential utility of employing an ADCS maneuver. Three different satellites are defined for comparison. SAT-H (semi-major axis of Lume-1 in the orbit insertion: semi-major axis of 6878 km), SAT-M (40 km lower than SAT-H: semi-major axis of 6836 km), and SAT-L (80 km lower than SAT-H, semi-major axis of 6798 km). The drag force computation relies significantly on the cross-sectional area in the direction of velocity, also known as the drag area. This cross-sectional area varies according to the orientation of the satellite, which can be controlled by the ADCS. Specifically, 2U and 3U CubeSats can adopt two different orientations, resulting in either a 1-unit or 2-unit face area for 2U CubeSats and a 1-unit or 3-unit face area for 3U CubeSats. In contrast, 6U CubeSats offer three possible orientation options, resulting in drag areas of 2-unit face area, 3-unit face area, or 6-unit face area. It is worth noting that CubeSats adhere to a constrained mass budget, allowing for an estimated mass of 1 kg per unit. Consequently, a 2U CubeSat will have a mass of 2 kg, a 3U CubeSat will weigh 3 kg, and a 6U CubeSat will carry a mass of 6 kg (Table 3). Three different states, equivalent in drag force, A, B and C, can be defined considering the drag area-mass ratio. As an illustrative example, when calculating drag effects, a 6U satellite oriented with its 2-unit face aligned in the direction of velocity produces an equivalent impact to that of a 2U satellite oriented with its 1-unit face directed toward the velocity vector. This equivalence arises because the drag area-to-mass ratio remains constant in both cases. Collision avoidance needs maneuvering, which means that the employment of the ADCS for this purpose must be expressed in terms of specific maneuvers. In the context of the satellites under examination, three distinct maneuvers are identified: for 2U satellites, a maneuver involves altering the orientation from the 1-unit face to the 2-unit face or vice versa; in the case of 3U satellites, a maneuver consists of transitioning the orientation from the 1-unit face to the 3-unit face or vice versa; and for 6U satellites, maneuvers can encompass changing the orientation from the 2-unit face to the 3-unit face or vice versa, from the 2-unit face to the 6-unit face or vice versa, and from the 3-unit face to the 6-unit face or vice versa.