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. This 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.