Every object orbits Earth on its own circular track at an altitude-dependent angular speed set by Kepler's third law — lower orbits move faster. When two objects' tracks share an altitude band and their angular positions coincide, they collide at orbital velocity (7+ km/s in reality) and shatter into several smaller fragments, each launched onto its own nearby track. More fragments mean more tracks, which means more chances of the next collision — the Kessler syndrome feedback loop.
ω(r) = √(μ / r³) (Kepler's third law, μ = GM_Earth)
collision → N fragments, N = fragmentation ×
risk ∝ (objects² × density) / shell_volume
- Launch rate — new satellites/rocket stages added to the field per second; more launches seed more starting objects.
- Fragmentation — how many smaller pieces a single collision produces; realistic collisions can spawn hundreds, so higher values push the cascade harder.
- ADR removal rate — objects captured and deorbited per second by active debris removal; raising it can outrun fragment production and stop a cascade before it runs away.
- Cascade risk — an index combining object count and local density; once it climbs steeply, collisions start outproducing removals and the field is in runaway Kessler growth.
Real-world relevance: this is exactly the argument behind international debris-mitigation rules — without active removal and passive deorbiting, busy low-Earth-orbit shells could become too cluttered with debris to use safely.