This is a genuine 2D counterpart of the 3D orbiting-belt scene, not a flattened camera view of it: the same 22-bin collisional cascade model runs underneath, but instead of scattering instanced icosahedra on a ring, this view plots the population directly in its natural coordinate — a live log-log size-distribution histogram, N(D) versus diameter D, which is exactly the plot researchers use to read off the Dohnanyi slope in the first place.
Impact energy per unit target mass:
Q = ½ (D_imp / D_target)³ v²
Catastrophic disruption threshold (strength + gravity regimes):
Q*_D(D) = Q_s·D^(-0.38) + Q_g·ρ·D^(1.36)
Collision rate (Wetherill):
k = P_i · Σ N_j · π(R_target+R_j)² [yr⁻¹]
N(t+dt) = N(t)·e^(-k·dt)
A target is catastrophically disrupted once an impactor exceeds the size that makes Q ≥ Q*D. Destroyed mass is redistributed into smaller bins following the Dohnanyi equilibrium slope (fragment number ∝ D⁻³·⁵) — animated here as bright particles flowing from a shrinking bar down into the bars it feeds, or streaming off the top of the chart when it escapes below the smallest tracked bin as dust. A dashed reference line at slope −3.5 lets you watch the live histogram bend to meet it as the cascade proceeds.
- Impact velocity — raises Q for a given impactor size, so smaller impactors become capable of catastrophic disruption.
- Material strength — scales Q*D directly, toughening or weakening every body at once.
- Time acceleration — the intrinsic collision probability used (~10⁻²¹ km⁻² yr⁻¹, order-of-magnitude representative of the classical Kuiper Belt per Kenyon & Bromley 2004 / Pan & Sari 2005) makes real evolution a multi-gigayear process, so this slider compresses it into an observable session.
Simplification: impactor populations are treated as an inexhaustible bombarding reservoir rather than being mutually depleted — standard in single-population cascade models and reasonable because a steep size distribution's small-body reservoir vastly outnumbers any single-body loss.