# Methodology for CubeSat Debris Collision Avoidance Based on Its Active ADCS System
## 2 State of the Art
### Space Debris
In the LEO, objects at the same altitude move in different directions at a speed of about 7.5 km per second. However, during a conjunction event, two objects can move close to each other, and their relative velocity can reach as high as 14 km per second. If the conjunction happens at an angle of approximately 45 degrees, the relative velocity is about 10 km per second, which is ten times faster than a rifle bullet's speed. Even small objects can cause tremendous damage due to the kinetic energy at these speeds, with the potential damage transmitted being proportional to the debris object's mass. Based on the potential damage, space debris is categorized according to size and mass. Table 2 shows five categories of space debris based on their diameter: 1 mm, 3 mm, 1 cm, 5 cm, and 10 cm. It is shown the effect that a collision in each category produces in terms of kinetic energy and its equivalent in kg of TNT, comparing the energy with impacts of objects of daily life (i.e., a sphere of diameter 1 mm and a mass of 0.0014 g would have the same effect as the impact of a baseball ball). From bigger to smaller, the first category includes objects that are 10 cm or larger, which can cause explosive damage if they collide with a spacecraft. Debris smaller than 10 cm can still be tracked by the SSN, depending on the object's composition and shape, but reliable tracking is limited to objects larger than 5 cm. The second category comprises debris between 1 and 10 cm, which cannot be tracked but can destroy a satellite or rocket body upon impact. The third category includes objects larger than 1 cm, which can completely fragment upon impact and add tens of thousands of new space debris fragments to the population. The fourth category contains debris between 3 mm and 1 cm, which cannot be tracked but can cause damage to critical components of a spacecraft, potentially ending its mission. The last category is made up of debris smaller than 3 mm, which cause localized damage but can still affect critical components such as solar arrays and optical systems. Protective measures can be taken to prevent this type of damage [8]. Even collisions with very small objects (a few centimeters in size) at orbital speed can cause tremendous damage with catastrophic consequences. Each explosion or collision with space junk produces additional debris, which can lead to a cascade of more collisions. Space debris is a growing concern as the number of satellites and other objects in orbit increases, and the debris can potentially collide with other objects and create more debris, creating a chain reaction known as the \"Kessler Syndrome\". In 1978, [PERSON] and [PERSON] published the paper \"Collision Frequency of Artificial Satellites: The Creation \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Rank**} & **International** & \multirow{2}{*}{**Common Name**} & **Year of** & **Altitude of** & **Cataloged** & **Debris in** & **Assessed** \\  & **Designator** & & **Breakup** & **Breakup** & **Debris** & **Orbit** & **Cause of** \\ \hline
1 & 1999-25 & Fengyun-1C71 & 2007 & 850 & 3428 & 2880 & intentional \\  & & & & & & & collision \\
2 & 1993-36 & Cosmos 2251 & 2009 & 790 & 1668 & 1141 & accidental \\  & & STEP-1 Rocket & 1996 & 625 & 754 & 84 & accidental \\  & & Body & & & & & explosion \\
4 & 1997-51 & Iridium 33 & 2009 & 790 & 628 & 364 & explosion \\
5 & 2006-26 & Cosmos 2421 & 2008 & 410 & 509 & 0 & unknown \\
6 & 1986-19 & SPOT-1 Rocket & 1986 & 805 & 498 & 32 & accidental \\  & & Body & & & & explosion \\  & & OV2-1/LCS 2 & 1965 & 740 & 473 & 33 & accidental \\  & & Rocket Body & & & & explosion \\
8 & 1999-57 & CBERS 1/SAC1 & & & & & accidental \\  & & Rocket Body & & & & explosion \\
9 & 1970-25 & Nimbus 4 Rocket & 1970 & 1075 & 376 & 235 & accidental \\  & & Body & & & & explosion \\
10 & 2001-49 & TES Rocket Body & 2001 & 670 & 372 & 80 & accidental \\  & & & & & explosion \\ \hline \hline \end{tabular}
\end{table}