Probability of collision for a newly generated debris cloud
Abstract
The growing amount of space debris, which mostly results from fragmentation events, has increased the hazard of in-orbit collision with operational satellites. The high spatial density of the debris cloud immediately after the fragmentation event increases the collision risk. Moreover, the high orbital speed of the fragments, which could partially or completely damage a satellite in case of collision, necessitates the development of an effective method to quickly quantify the risk posed by a newly formed debris cloud and estimate the impact probability. The filtering techniques which usually assess the hazard of the fragmentation events by analysing the risk of each fragment individually then filter out non-hazardous fragments could be time consuming. Furthermore, the traditional approach – which represents the discrete population of the debris cloud by a continuous debris density, then estimates the impact probability using a Poisson distribution – is questionable for not accurately representing the population of the newly formed debris cloud. Therefore, this work focuses on developing two novel approaches to quickly and accurately assess the hazard of a newly formed debris cloud with a discrete population all at once, then estimate the impact probability. T'his is enabled by first using the astronomical measure MOID combined with the automatic domain splitting-based differential algebra technique to quickly quantify the hazard of the population of the debris cloud all at once, and an advanced Monte Carlo simulation combined with a sequence of pre-filtering techniques to quickly and accurately estimate the impact probability. Second, a tool is developed based on the boundary value problem, namely the Lambert targeting problem (LTP), and a semi-analytical approach to quickly quantify the risk of the population of the newly formed debris cloud and accurately estimate the impact probability. The developed approaches are validated against Monte Carlo simulation, and they are found to be much faster and accurate enough in terms of assessing the collision risk. However, in terms of the computation time, the performance of the developed tool based on LTP outperformed the stochastic approach. This is due to the application of novel analytical and semi-analytical improvements in the calculation of the impact probability in this approach.
Description
The thesis has focused on developing more than one approach to swiftly and efficiently quantify the hazard posed to satellites by a debris cloud in its early stage, then estimate the impact probability, taking into account the discrete population of the debris cloud. The purpose of developing the two approaches is as follows: first, the necessity of having a tool that can tackle the problems associated with the conjunction detection methods, which required performing the conjunction computations for each fragment individually. Exploiting such methods to assess the hazard that a population of thousands of objects of a debris cloud pose to a satellite is time-consuming. This time tends to increase significantly if these methods necessitate complex computation or are relying on an iterative scheme. Secondly, most of the current approaches that concern estimating the impact probability of a debris cloud in its early stage adopt the concept of the kinetic theory of gas. This concept, which assumes that the gas molecules are moving along a straight line in a random direction and uniform density, does not resemble the actual motion of the debris fragments, which are highly correlated by the gravitational force. Hence, in each of the developed approaches a new tool is built, with each tool consisting of two stages: the first one to determine the severity of the hazard posed by the debris cloud to a satellite, and the second one to estimate the impact probability considering the actual environment of the debris cloud.
Keywords
Space debris - Probability of collision- debris cloud