<title>Poisson validity for orbital debris: II. Combinatorics and simulation</title>

Abstract

The International Space Station (ISS) will be at risk from orbital debris and micrometeorite impact (i.e., an impact that penetrates a critical component, possibly leading to loss of life). In support of ISS, last year the authors examined a fundamental assumption upon which the modeling of risk is based; namely, the assertion that the orbital collision problem can be modeled using a Poisson distribution. The assumption was found to be appropriate based upon the Poisson's general use as an approximation for the binomial distribution and the fact that is it proper to physically model exposure to the orbital debris flux environment using the binomial. This paper examines another fundamental issue in the expression of risk posed to space structures: the methodology by which individual incremental collision probabilities are combined to express an overall collision probability. The specific situation of ISS in this regard is that the determination of the level of safety for ISS is made via a single overall expression of critical component penetration risk. This paper details the combinatorial mathematical methods for calculating and expressing individual component (or incremental) penetration risks, utilizing component risk probabilities to produce an overall station penetration risk probability, and calculating an expected probability of loss from estimates for the loss of life given a penetration. Additionally, the paper will examine whether the statistical Poissonian answer to the orbital collision problem can be favorably compared to the results of a Monte Carlo simulation.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.