On the Risk of Kessler Syndrome: A Statistical Modeling Framework for Orbital Debris Growth

We present a statistical framework for modeling the evolution of orbital debris and the risk of the runaway debris growth, commonly known as the Kessler Syndrome. The framework builds upon traditional Particle in the Box (PIB) models with sources and sinks for the relevant orbital debris processes. In contrast to PIB models that typically provide a single trajectory for the evolution of the system, we stochastically sample a range of trajectories representing possible evolutionary paths, given the underlying source-sink rates. This statistical framework allows us to provide a measure for risk of exponential runaway growth, \(P_\textrm{Exp}\) $P_{\text{Exp}}$ , defined as the fraction of trajectories that have produced runaway growth. The parameter is shown to be sensitive to debris generation in collisions, satellite de-orbit rules and debris injection events (e.g., anti-satellite tests). For a certain set of parameters, we also show that there exists an unstable equilibrium absent in the traditional deterministic models.