# Methodology for CubeSat Debris Collision Avoidance Based on Its Active ADCS System
## 3 Materials and Methods
### ADCS System
These pairs of maneuvers yield similar effects but with opposing outcomes. When we increase the drag area, it leads to a reduction in the semi-major axis and the period of the osculating orbit over time, compared to the values when the orientation remains unchanged. Conversely, when we decrease the drag area, it results in a larger semi-major axis and period than what would be expected without the maneuver. Consequently, after a period \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**CubeSat Format** & **Drag Face** & **Drag Area (m2m2)** & **Mass (kg)** & **Drag Area/Mass (m2/kg)** & **Case Study** \\ \hline \multirow{2}{*}{2U} & 1U & 0.01 & & 0.005 & B \\  & 2U & 0.02 & 2 & 0.010 & A \\ \hline \multirow{2}{*}{3U} & 1U & 0.01 & & 0.003 & C \\  & 3U & 0.03 & & 0.010 & A \\ \hline \multirow{2}{*}{6U} & 2U & 0.02 & & 0.003 & C \\  & 3U & 0.03 & 6 & 0.005 & B \\  & 6U & 0.06 & & 0.010 & A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Case studies for 2U, 3U, and 6U CubeSats. of time, the satellite will be situated lower or higher than initially anticipated, giving rise to what we term the Vertical Distance Difference (VDD). Furthermore, these maneuvers also impact the overall distance traveled by the satellites. Surprisingly, an increase in the drag area leads to an acceleration in velocity, owing to the reduced period of the osculating orbit. Consequently, the satellite covers a greater distance than expected without the maneuver. Conversely, decreasing the drag area has the opposite effect, causing a reduction in velocity and, consequently, a shorter traveled distance. This phenomenon is referred to as the Horizontal Distance Difference (HDD). In summary, the possible maneuvers are consolidated in Table 4, where we have three distinct maneuvers to analyze: AB, AC, and BC. In this table, the initial and final position states are shown, corresponding to a maneuver named after the combinations of both states (i.e., initial A position and final B position results in AB maneuver that can be applied to 2U and 6U CubeSats). Also, interchangeability between AB and BA maneuvers (i.e.) was considered because they would have the same effect but in opposite directions. These maneuvers exhibit intricate interactions between drag area, orbital parameters, and satellite trajectories, contributing to a comprehensive understanding of satellite behavior in collision avoidance scenarios. The calculation of drag is conducted by utilizing the parameters incorporated within the STK Lifetime tool. This calculation encompasses both atmospheric and solar radiation drags. However, for the specific scope of this study, we focus solely on adjusting atmospheric drag parameters, while maintaining default data for solar flux pressure. To establish a baseline for drag coefficient, a value of 2.2 is set, aligning with the typical default value for conventional satellites. While this value may appear somewhat elevated for CubeSats, it is within the same order of magnitude. The computation of atmospheric density is derived from the U.S. 1976 Standard Atmosphere model [24], ensuring accuracy and reliability. To account for the diverse scenarios under examination, modifications are applied to the drag area and mass, as outlined in Table 3. These modifications serve as the foundation for the computation of drag force, including the effects of atmospheric drag force acceleration (1), which are then incorporated into the governing equations. This meticulous adjustment of parameters allows us to comprehensively analyze how variations in drag area and mass influence satellite behavior in different scenarios, contributing valuable insights to our study. \[a_{drug}=\frac{1}{2}\rho V^{2}C_{D}\frac{S}{m} \tag{1}\]  
The drag integration process is executed through the Lifetime tool, employing a meticulous approach involving nine-point Gaussian quadratures per orbit. To enhance precision, we set the value of \"\(n\)\" to 6.