Clear Orbit Secure Future 2026

Appendix B Orbital debris projections – assumptions and methodology The orbital population model developed in collaboration with the Saudi Space Agency and LeoLabs estimates the likelihood and rate of orbital collision using the Poisson probability distribution23 and kinetic-theory analogy,24 where orbiting objects behave like particles in random motion. Where: PC: probability of collision for one target AC: collision cross-section VR: relative velocity SPD: spatial density = (objects per km3) N: number of objects V: volume of orbital shell This equation is applied separately to three debris- size classes used throughout the model: PC(HNT): 5 mm–1 cm (hazardous non-trackable) PC(LNT): >1–10 cm (lethal non-trackable) PC(Cat): >10 cm (catalogued/trackable)Where: CR: Poisson-derived collision rate for the cluster T: time interval, typically one year but in units of seconds (3.1536E7 sec) The ½ term in Eqn. 2 ensures that the potential encounters within a cluster are not double-counted. Where: Г: number of years until the first collision event C: confidence interval This equation is consistent with the Poisson probability distribution for rare events. These calculations were applied to three identified clusters in LEO around altitudes of 775 km, 840 km and 1,000 km, where dense constellations of derelicts and fragment clouds persist. The resulting probabilities of a first major collision by c. 2032 are 8%, 6% and 29% respectively. To represent additional long-term debris generation, the model also includes rocket-body explosions in 2029, 2033 and 2037, consistent with historical recurrence rates. B1 Mathematical formulation (orbital population model) Single-target collision probability: The basic Poisson form for the probability that a single satellite is struck by another object within a given interval of time is: Eqn.1 Cluster collision rate: To estimate the combined probability of collisions within a dense region of derelicts (“clusters”), the cumulative collision rate (CR) is used: CR =AC VR T VolN2 2()( ) Eqn.2Time to first collision To estimate when the first collision is expected, the model applies a gamma distribution,25 which relates the collision rate (CR) to a chosen confidence level: 1 CR( )Г = -ln(1 - C) Eqn.3 And the probability that a collision occurs within  years is: C = 1 - e-CR Г Eqn.4PC = 1 - e-(AC VR SPD T) Clear Orbit, Secure Future: A Call to Action on Space Debris 25