Each object orbits at the angular rate set by Kepler's third law, T ∝ r3/2, so the outer GEO shell visibly crawls while LEO objects race around. The population itself follows a mean-field cascade equation — the same kind used to describe real orbital-debris growth: the collision-fragment production rate scales with the square of the object density (more objects ⇒ quadratically more close encounters), while natural atmospheric decay and active removal both pull the count back down:
risk = density² / (1 + mitigation)
dN/dt = N · (k · risk − 1/life_shell)
When the bracketed net rate is positive, population grows without bound — a runaway Kessler cascade. When it is negative, decay and mitigation win and the shell settles to a low, stable count. Because natural decay time (life_shell) is ~8 years in LEO but ~1000 years in GEO, the exact same density and mitigation settings that keep LEO controlled can push GEO into runaway growth — geostationary debris essentially never falls out of orbit on its own.
- Dots — a capped visual sample of the tracked population, orbiting at the shell's true angular rate.
- Sparkline — population N(t) over simulated time; a rising curve that bends upward is the cascade signature.
- Flashes — probabilistic collision events, drawn more often as risk rises.