Kuiper Belt Collisional Cascade

Collision Parameters

Impact velocity 1.0 km/s Typical relative speeds between classical Kuiper Belt objects today.

Material strength 1.0× Scales the disruption threshold Q*_D — weaker, porous ice vs. more consolidated bodies.

Time acceleration 200 Myr/s Simulated megayears advanced per real second.

Belt State

Elapsed time

0 Myr

Size-slope q (N∝D⁻q)

—

Mass remaining

100.0%

Cumulative disruptions

How it works

The population is tracked in 22 logarithmic size bins from 20 cm to 300 km diameter. Each bin's collisional fate follows the classic self-similar cascade framework (Dohnanyi 1969; Wetherill 1967):

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. Q*_D is V-shaped: small bodies resist breakup by material strength (threshold falls as they shrink further), large bodies resist breakup by self-gravity (threshold rises with size) — the weakest bodies sit around the km scale, exactly where real strength-scaling laws for icy bodies place the minimum.

Destroyed mass is redistributed into smaller bins following the Dohnanyi equilibrium slope (fragment number ∝ D⁻³·⁵), which is why an initially shallow distribution (fewer small bodies than equilibrium) visibly steepens toward q≈3.5 as collisions proceed. Mass that would fragment below the smallest tracked bin instead leaves the model as dust — the real fate of collisional debris, removed by radiation pressure and Poynting–Robertson drag.

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.

Small fragments / debris Large surviving bodies Catastrophic disruption flash

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