Time-Dependent Satellite Explosion Probabilities for Long-Term Orbital Debris Environment Modeling

On-orbit accidental explosions are a significant contributor to the growth of the orbital debris population. Certain types of satellites have been seen to exhibit different behaviors and timelines of explosions. Recent assessments of on-orbit explosions for three categories of satellites-Russian Sistema Obespecheniya Zapuska (SOZ, Proton 4th-stage attitude and ullage motors) units, spacecraft, and rocket bodies-suggest that on-orbit explosions can be modeled using a continuous, time-dependent probability of explosion. This paper discusses the methodology for developing a time-dependent probability of explosion as a function of the satellite's orbital lifetime based on historical explosions. The SOZ units are found to be best modeled by a modified Gaussian probability distribution, with the peak probability of explosion occurring around 10.4 years on-orbit. Spacecraft and rocket bodies both exhibit exponentially decaying explosion probabilities, with rocket bodies showing fast-, medium-, and slow-time modes of decay. Total cumulative probabilities of explosion are approximately 57% for SOZ units, 4% for spacecraft, and 2% for rocket bodies. Examples of implementation in a simulation of the orbital debris environment using NASA's long-term evolutionary model are given, showing that the overall explosion behavior over two centuries is significantly different from that using a previously implemented constant-probability-type-dependent explosion rate model and provides a better representation of the historical explosion record.