A simplified engineering algorithm for collision risk assessment and classification of LEO satellites

Abstract

Collision risk in low Earth orbit is now a sustainability constraint, not only a mission-level concern. Current standards (ECSS, NASA) classify risk in discrete per-mission categories and yield no continuous index that can be aggregated across missions or fed into broader sustainability assessments. This paper develops an engineering algorithm in which the expected number of collisions is estimated from the kinetic theory of the debris flux and combined with a severity term to give a continuous, dimensionally consistent risk index. An individual index, weighted by replacement cost, captures the expected loss to the operator; a collective index with homogeneous per-target severity captures the burden imposed on the operational population at the mission altitude band, independent of the mission's own value. Applied with a May 2026 Celestrak snapshot to three cases (ENVISAT, Sentinel-6, Starlink V2 Mini), the collective index exceeds the individual one by over two orders of magnitude for the constellation element: operator-centred assessment understates the collective cost of large constellations. A random sample of 100 LEO satellites, swept over 100 seeds, confirms the asymmetry as structural, and it survives the swap to a mass-based severity weight, which widens rather than closes the constellation gap. The construction is checked against a snapshot proxy of the ECOB family (rank correlation 0.91 on 103 objects) and against published ECOB values for MetOp-A and Sentinel-2, matched within a factor of two. A parametric analysis gives an explicit replacement-cost threshold per altitude band, about one to five million USD across the operational LEO bands, below which any satellite is structurally underestimated by operator-centred frameworks. The index is released as an open MATLAB toolchain and is intended as the orbital component of a multi-domain sustainability assessment.