A Stochastic Model for Predicting Charged Orbital Debris Probability Densities by Utilizing Earth's Electromagnetic Field to Guide Active Debris Remediation Efforts

Clouds of sub-centimeter debris are generated during space operations in Earth orbit and pose a threat to current and future missions but are undetectable and untracked by radar ground stations. Orbiting objects become charged by space plasma and experience a Lorentz force due to Earth's magnetic and electric fields. Our research has successfully simulated this perturbation on a three-dimensional cloud of debris and we determined that the variation in debris charging is the driving mechanism behind secular variation in orbital energy and inclination angle, which has implications in debris lifespan and orbit evolution predictions. We propose a thorough analysis of this orbital perturbation using chaotic dynamics will identify regions of orbital stability and lead to the development of a predictive statistical tool for space mission planners to isolate orbital regimes to focus Active Debris Remediation (ADR) efforts and conduct spacecraft conjunction assessment and collision avoidance with debris. The resulting predictive tool would help design engineers identify where to prioritize debris remediation, calculate debris lifetimes following known fragmentation or collision events, and determine the probability of collision with debris along planned spacecraft trajectories. We propose three critical tasks to build the necessary framework to accomplish this objective. First, we will derive analytical expressions for the time evolution of variation in the orbital elements of charged sub-centimeter Earth-orbiting debris due to Earth's electromagnetic field. Next, we will analyze these solutions using chaotic dynamics to identify the conditions that promote orbital stability caused by the Lorentz force perturbation. Finally, we will apply the transport equation from the kinetic theory of gases to develop a stochastic orbital propagation model that utilizes a Kalman Filter to evolve the debris cloud probability distribution function to validate the conditions for orbital stability and to provide statistical outputs compatible with NASA debris remediation and collision avoidance operations.

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