Collision risks for end-of-life satellite de-orbit trajectories

Abstract

Satellites that have reached their end-of-life pose a threat to the space environment. An object in orbit that no longer adds value to its user is called space debris. Collisions between objects in Low Earth Orbit (LEO) can have disastrous consequences and have the potential to create thousands of new debris objects, which in their turn can cause collisions. In order to limit the number of potential collisions it is vital to remove space debris from orbit. Removing space debris from orbit can be done via a so-called de-orbit maneuver. Satellites often have an integrated on-board propulsion system, used for stationkeeping. At the end-of-life, these systems can be used to apply a thrust force and guide the satellite into a de-orbit maneuver. This thesis investigates the effect of a controlled low-thrust de-orbit maneuver on the propellant usage, duration and collision risk of the trajectory. This maneuver is conducted for three different objects in LEO: Zenit-2, Tsyklon-3, and Kosmos-3m. These three objects represent a wide range of different debris scenarios that form a potential danger to the space environment. Two different epochs of the debris environment are investigated: October 23, 2013, and November 7, 2014. Each trajectory is shaped by a thrust magnitude and thrust control algorithm that turns the engine of the object either on or off at different time points. The values for the thrust magnitude and thrust activation times are determined by an optimization algorithm that tries to find trajectories with optimal (minimal) values for the propellant usage, trajectory duration and collision risk. The collision risk associated with a de-orbit trajectory is determined by representing the position error of each object as an error covariance matrix. By mapping the error covariance matrix of each object pair during a close conjunction onto a common plane of reference (the B-plane), the collision probability can be described in terms of a probability density function. Integrating this function over the occupied area of the two objects in the B-plane results in a collision probability associated with that close conjunction. The total collision probability associated with a de-orbit trajectory is then the result of the accumulation of the collision probabilities of all close conjunctions. The result of this analysis is a set of different de-orbit trajectories with varying values for the propellant usage, duration and collision probability. Trajectories with a high collision risk have collision probabilities ranging from $10^{-1}$ to $10^{-3}$. The low-risk trajectories have collision probabilities ranging from $10^{-6}$ to $10^{-16}$. A general trend is observed where trajectories with a short duration have relatively low collision probabilities. However, by observing the accumulation of the collision probability over time, it can be seen that the value of the total accumulated collision probability is largely determined by a low number of high-risk conjunctions. A sensitivity analysis is performed to assess the robustness of the obtained trajectories. It is found that a small variation in an initial state vector element results in a difference in the associated collision probability ranging from $10^{-3}$ to $10^{-6}$ for some cases, and $10^{-2}$ to $10^{-48}$ for other cases. This shows that the obtained result are not robust and are highly sensitive to variations in either the initial state vector or the state derivative (i.e. changes in the environment model). Additionally a high thrust is applied in order to further assess the statistical effects of multiple conjunctions on the accumulated collision probability. Again, the associated collision probability was determined by a low number of risk-risk conjunction events. These results lead to the conclusion that no robust method was found for a de-orbit trajectory that limits the collision probability. The accumulated collision probability is not smoothly determined by the number of encountered conjunctions but rather a limited number of high-risk conjunction events. Additionally, the collision probability is highly sensitive to small position offsets of either of two objects in a conjunction. Therefore, a prediction of a de-orbit trajectory that limits the collision probability is unreliable.