Probability of Collision of satellites and space debris for short-term encounters: Rederivation and fast-to-compute upper and lower bounds

[In the Journal]

Authors:

• FCT-UNL, Portugal, rjn.ferreira@campus.fct.unl.pt
• FCT-UNL, Portugal, claudia.soares@fct.unl.pt
• Neuraspace, Portugal, marta.guimaraes@neuraspace.com 

The accelerated increase in space debris in the low earth orbit (LEO) is a growing concern. Given the high speeds that these millions of fragments can reach, even the fragments that are a few millimetres in size, can cause fractures in a satellite’s hull or put a serious crack in the window of a space shuttle. The conventional method proposed by Akella and Alfriend in 2000 remains widely used to estimate the probability of collision in short-term encounters. This study introduces a novel derivation based on first principles that naturally allow for tight and fast upper and lower bounds for the probability of collision.

Read the paper to know how we:

• Derive from first principles the expression for the probability of collision
• Introduce accurate and fast-to-compute upper and lower bounds of the probability of collision
• Study the computational complexity of our method when compared with the naive one
• Validate our approach on a real dataset of Conjunction Data Messages (CDM)