A Reproduction Number for Orbital Debris

Kessler’s debris cascade is an epidemic of collisions: a catastrophic collision creates fragments that cause further catastrophic collisions. We describe it with the tools of epidemiology: a next-generation operator over altitude shells, its reproduction number R, the reproductive value of each orbit and the target reproduction number for control. We then ask which conclusions a public catalogue supports. The clearest concerns where the cascade lives. In every one of twelve model variants, the shells below 600 km hold 71–73% of catalogued objects but less than 0.4% of the elasticity of R to the targets in each shell. At least 97% of it lies at 700– 1,500 km, where fragments persist for decades to centuries. Removing 2,000 objects where collisions are most frequent lowers R by at most 0.02%; removing them by reproductive value lowers it by 40–83%. Three other conclusions depend on choices that public data do not settle. The value of R depends on how long fragments are allowed to reproduce (0.90 at 5 years, 7.08 at 200 years) and on fragment physics (0.49–7.25 at 200 years). Whether one altitude band can control the cascade depends on collision avoidance. And because breakup yields vary as transmission does in superspreading, R alone does not decide whether one collision starts a lasting cascade. A separate mass-resolved model that scores catalogued objects one by one finds that the objects most worth removing over 50 years are not the heaviest.