Jaewoo Kim, Korea Advanced Institute of Science and Technology; Minchan Song, Korea Advanced Institute of Science and Technology; Jaemyung Ahn, Korea Advanced Institute of Science and Technology; Jinsung Lee, Kyung Hee University; Jiwoong Yu, Korea Astronomy and Space Science Institute; Hosik Kam, Korea Astronomy and Space Science Institute; Jung Hyun Jo, Korea Astronomy and Space Science Institute; Eun-Jung Choi, Korea Astronomy and Space Science Institute; Jin Choi, Korea Astronomy and Space Science Institute
https://doi.org/10.64861/JTJE2996
Keywords: space debris, space domain awareness, space environment modeling, space situational awareness, space traffic management, space environment model
Abstract:
Advances in launch transportation (lift capacity, reusability, and ridesharing) and declining space manufacturing costs have lowered barriers to space access, accelerating growth in Low Earth orbit (LEO) activity. While LEO provides attractive operational advantages, increasing traffic density creates more conjunction opportunities and can increase collision risk. High-energy collisions can generate long-lived debris and further degrade the environment. Consistent with this trend, ESA’s statistics for the Earth-orbiting population, updated on 25 June 2026, report roughly 54,000 regularly tracked objects larger than 10 cm, including about 9,300 active payloads, approximately 1.2 million objects between 1 and 10 cm, and about 140 million objects between 1 mm and 1 cm. As these populations grow, concerns about self-sustaining debris growth, often discussed in the context of the Kessler syndrome, become more salient for operators and policymakers.
This risk landscape elevates the importance of space situational awareness (SSA) and space domain awareness (SDA). In addition to maintaining catalogs and supporting near-term conjunction assessment, SSA/SDA can benefit from credible long-term projections that can be generated quickly enough to support scenario analysis. Such projections can be used to examine how launch rates, constellation deployment patterns, and mitigation assumptions may shape future collision exposure and debris growth. Accordingly, diverse space-environment modeling tools have emerged, ranging from dedicated fragmentation models to integrated long-term evolution frameworks. This continuing demand motivates computationally tractable methods that complement, rather than replace, higher-fidelity simulations.
Within this landscape, source-sink evolution models, also known as particle-in-a-box models, have been developed with different state definitions and evolutionary dynamics for long-term projection and scenario analysis. In this approach, objects are categorized by collision characteristics and the orbital domain is discretized. Depending on the model, collision participants may be represented using only a few classes (e.g., active satellites, derelicts, and debris) or with finer granularity (e.g., debris clouds from individual fragmentation events and satellites grouped by constellation). In the spatial dimension, the orbital region may be divided into spherical shells of equal altitude or into bins defined by additional orbital parameters, including inclination and eccentricity. Because modeling fidelity and computational burden vary with these choices, model granularity should be selected according to the intended analysis. Simpler models are useful for rapid aggregate and equilibrium studies, whereas higher-fidelity models can represent more detailed environment evolution.
A common reduced-order formulation discretizes the environment into one-dimensional altitude shells with a small number of object classes. This approach retains low computational cost and supports rapid analysis of aggregate population evolution. However, representing the environment only through altitude shells can obscure effects associated with the anisotropic distribution of the current LEO population. Sun-synchronous orbits, for example, follow coupled altitude-inclination conditions and concentrate traffic in particular inclination bands. Large constellations also occupy selected inclination corridors according to their coverage and mission requirements. Consequently, inclination aggregation may suppress sensitivity to encounter geometry and to the nonuniform distribution of sources within an altitude shell.
To examine this issue, this paper develops an inclination-aware extension of an existing 1D source-sink model by formulating a 2D altitude-inclination population-evolution model for LEO. The objective is to retain the speed and transparency of ODE-based projection while representing a dominant anisotropy of the LEO traffic distribution. The orbital domain is discretized into altitude and inclination bins under a circular-orbit approximation, and separate states are maintained for active satellites, derelicts, and debris. For each class and altitude-inclination bin, the coupled ordinary differential equations include: (i) launch and deployment sources; (ii) lifecycle transitions from active to derelict states; (iii) atmospheric-drag transport of derelicts and debris between adjacent altitude shells while retaining the inclination index; and (iv) collision interactions between all inclination-bin pairs within the same altitude shell. Collision rates are evaluated using a particle-in-a-box framework that combines shell-wise number density, effective cross section, and finite-bin moments of inclination-dependent relative speed. These reduced-order kernels describe relative-speed geometry under an unresolved right-ascension-of-the-ascending-node assumption; they are not interpreted as full intrinsic collision probabilities. Catastrophic and non-catastrophic fragment yields are retained from the 1D formulation. For bookkeeping, generated fragments are assigned to the inclination bin of the first-listed population in each collision pair rather than being physically redistributed from reconstructed post-impact orbits.
Using the 2D source-sink model, we compare long-term population evolution from the 1D and 2D formulations under consistently matched assumptions. Controlled cases are used to examine whether the 2D equations recover altitude-only behavior when inclination carries no additional information, while representative nonuniform inclination distributions are considered to assess the sensitivity of projected outcomes to inclination resolution. The analysis may also examine alternative reduced-order collision-kernel assumptions and source levels as part of the model-sensitivity study. Any equilibrium or limiting behavior identified numerically will be interpreted as conditional on the selected model, closure, and scenario rather than as a direct physical orbital-capacity threshold. From an SSA/SDA standpoint, the resulting framework supports rapid sensitivity and scenario analysis while making the consequences of inclination aggregation explicit. It is intended as a computationally tractable complement to, rather than a substitute for, detailed orbit-resolved environment models.
Funding Information) This research was supported by the Korea Astronomy and Space Science Institute under the Development of an Integrated Space Risk Response System (Project No. 2710103796) supervised by the Korea AeroSpace Administration.
Date of Conference: September 15-18, 2026
Track: Space Debris