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46 th COSPAR Scientific Assembly Public-Catalogue Collision Risk Screening in GEO Utilising Hollow Shell Approximation and Operator- Centred Proximity
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46 th COSPAR Scientific Assembly Public-Catalogue Collision Risk Screening in GEO Utilising Hollow Shell Approximation and Operator- Centred Proximity

COSPAR (Committee on Space Research) Scientific Assembly, 46 (Florence, Italy, 01/08/2026–09/08/2026)
04/08/2026

Abstract

Space Debris Astronautics Collision Avoidance Systems Space Mechanics

Public Two-Line Element (TLE) catalogues enable repeatable studies of the Geostationary Earth Orbit (GEO)

debris environment; however, their use in slot-level collision risk assessment is limited by simplified control volumes and the difficulty of linking congestion metrics directly to operators. Building on the longitude-resolved torus Cell Passage Event (CPE) framework, we present a TLE-driven pipeline that calibrates effective solar-radiation-pressure area-to-mass histories, propagates drifting objects with a high-fidelity numerical model, and replaces the idealised torus with two complementary, operator-relevant methods: (i) a hollow spherical shell aligned with formal GEO Protected Region (GEOPR) bounds and (ii) covariance-normalised proximity screening between drifting objects and maintained-slot references.

For the controlled comparison, we analyse a common 92-day propagation window using 10-minute torus sampling and 5-minute hollow-shell and covariance sampling, with local Lagrange interpolation for event refinement. In a separate paired causal validation across 214 objects, joint area–mass inference reduced the median next-interval three-dimensional position error from 4.54 km to 4.31 km, with improvement for 70.1% of objects. The longitude-resolved baseline uses 1.0◦ cells and a 50.0 km torus minor radius, yielding 4.21 × 104 CPEs across 312 drifters, with a median of 20 occupied longitude cells per detected drifter. Replacing the torus with the hollow-shell GEOPR volume records 2.62×105 passages across 720 drifting objects, with a median of 90 occupied cells per drifter. The hollow shell therefore records 6.23 times as many events and 130.8% more contributing objects. Despite this broader coverage, the longitude distributions retain a Spearman rank correlation of ρ = 0.788 and identify the principal concentrations associated with the geopotential gravitational wells near 75◦E and 105◦W. Across sensitivity windows of three to seven months, the hollow-to-torus event

ratio remains between 6.16 and 6.23, while longitude rank agreement ranges from ρ= 0.788 to 0.839, indicating that the principal spatial structure is persistent.

The second method replaces the previous fixed-radius proximity sphere with an uncertainty-normalised, operator-centred screen. Empirical diagonal Radial, Transverse and Normal (RTN) covariance proxies are estimated from held-out propagated TLE residuals for each drifter and from historical scatter about each maintained-slot reference. Samples satisfying Mahalanobis separation D ≤ 3 are retained, and consecutive retained samples are merged into a single encounter. The 92-day analysis retains 1.23 × 105 drifter–slot encounters involving 918 drifters, 442 maintained objects and 25,493 unique pairs across 234 occupied 1.0◦ longitude cells. Of these encounters, 3,645 (2.97%) have physical miss distances below 100 km and 82 fall below 10 km. The encounter burden is concentrated near approximately 85◦E and 140◦W, translating uncontrolled drift into an operator-centred prioritisation signal for higher-fidelity follow-up.

Across the operator-relevant methods, drifter contribution becomes more concentrated as the screening geometry broadens: the top 10% of drifters account for 14.3% of torus events, 28.2% of hollow-shell passages and 29.4% of covariance-normalised encounters. Alternative spatial, velocity and consequence-weighting kernels preserve the principal hollow-shell longitude ranking, with Spearman correlations of ρ= 0.982–0.985 relative to the hollow geometry control. This indicates that protected-region occupancy governs the global congestion pattern, while alternative risk kernels primarily refine local priorities. These results support a robust, reproducible GEO screening framework that identifies persistent longitudinal concentrations and a manageable watchlist of high-contribution drifters, motivating targeted monitoring, higher-cadence updates and uncertainty-aware reruns.

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