Di Wu, Embry Riddle Aeronautical University
Keywords: Space Sustainability, Quantification, Space Safety, Critical Density, Fragmentation Footprint
Abstract:
Space systems are essentially safety-critical, cyber-physical systems (CPS) that rely on layered control structures, feature extensive supply networks, and function under uncertain conditions. Existing design and test methodologies are inadequate for providing the needed level of clarity in safety assurances. Precisely measuring the risks of space systems remains problematic, and the regulations needed for mitigating these risks are limited. Decisions made at each step in space safety are no longer dominated solely by mission feasibility considerations; they must be made in a context-sensitive manner and address explainability. At the planning stage, the need for and purpose of a space project must be examined. Safety, sustainability, and the preservation of resources must all be carefully considered in the design, operation, management, and rehabilitation phases of space systems. Efforts to eliminate long-term devastating costs, e.g., Kessler Syndrome, while preserving the needed functionality in the delivery of space system infrastructure, have led to the development of numerical models for mission designs and space environments. A key aspect in assessing the true impact of a space system, over its influence on the entire space system, is its safety performance. A balancing question is how much a space system’s deployment has tipped the balance toward a red alarm, and how much socio-economic benefit the long-term space system gains or loses at deployment. Safety performance has begun to take its place alongside operational performance (level of service), environmental performance, and financial performance.
Verification methods developed in formal methods have proven practical in domains including software model checking, autonomous driving environments, and air traffic and railway control systems. The computational problems related to automatically checking the safety of CPS are notoriously difficult. CPS normally rely on approximate solutions from simplified models. The challenge in connecting approximate solutions from simplified models with space systems containing tens of thousands of modules requires careful evaluation and investigation on a case-by-case basis. Kessler’s leading work provides a favorable framework to simplify complex CPS space systems into a manageable environment. The concept of critical density, derived from such simplification, was hailed in the initial stages of space sustainability as a wake-up call for the possible scenario of an exponentially growing number of collisions and debris, leading to an eventually useless and unbreakable space environment. The concept of critical density was powerful in setting boundaries for formally evaluating the danger level of space systems as a whole, and it could potentially be combined with evaluation and planning tools to validate the usefulness of space missions and their potential.
Many models have been developed to address the long-term sustainability of space systems, often validated and compared with existing model performance to build confidence in their accuracy. They serve various purposes, from guiding sustainable space economy policies and analyzing orbital conditions over time to supporting specific missions and capabilities. These frameworks also enable data-driven scenarios and parameter tuning, reinforcing simpler theories and methods used to evaluate space systems. However, there has been limited effort to apply insights from high-fidelity models to the simplified criteria developed by theoretical approaches. As a result, merging these complex simulations and data-driven results with simpler models remains a major challenge, requiring a more integrated view of space systems.
To address these challenges and questions, both theoretical development and numerical experiments are required to further improve space safety analysis. The first element involves reevaluating the simplified model’s critical density concept and expanding from a single-shell to a multi-shell condition, clarifying the alarm threshold from the theoretical perspective. Moreover, the missing link in explaining what constitutes the inherent “fragmentation footprint”—a novel concept akin to a carbon footprint but at a space object fragmentation level—must be reevaluated. This concept would provide the first clarified derivation result for multi-shell systems that can be employed in understanding space sustainability and space safety around Earth. The last contribution involves applying data-driven scenario building to fill the missing parameters in the theoretical development, following the same approach as combining traditional reachability analysis with sensitivity analysis of the complex or unknown parts of the system. Sensitivity analysis gives bounds on how much the states or outputs of a module change with small changes in the input parameters. Sensitivity analysis for space systems with fully known models has previously been used to evaluate their compliance with long-term sustainability requirements, particularly by identifying where a system might fail to meet those objectives. The aspect of analyzing autonomous space systems as part of evaluating the current status of space systems has not yet been fully explored, given the previously missing theoretical part of building an explainable framework for multi-shell space systems. This framework would be the first to combine empirical numerical models with analytically developed novel theories, creating a framework of space safety analysis that would provide policy insights on mission designs and help identify potential solutions for the scope of operations and for building space systems beyond policy design and intervention.
Date of Conference: September 16-19, 2025
Track: Space Debris