Orbital Debris Collision Rate, Kessler Cascade and Satellite Density Lab Blender 5.2

A shell model of low Earth orbit (300-1500 km): launches, drag, disposal, collisions and fragments, with Keplerian orbits drawn on the GPU.

Scenario

Controls

Live readouts

Objects per altitude shell

Stacked bars: active / derelict / fragments (square-root scale). The strip below the bars shows the cascade ratio R of each 50 km shell (green < 0.5, amber < 1, red ≥ 1). Tap a bar to inspect that shell.

History

Population by class (log scale) against model years.

Experiment: where does the cascade run away?

A single shell, identical objects, no avoidance, no disposal. The cascade equation dN/dt = L - N/τ + kN² has a stable and an unstable fixed point; they merge at the critical launch rate L_c = 1/(4kτ²). The test integrates the ODE numerically and finds the runaway threshold by bisection.

N(t) in units of N_c = 1/(2kτ) against t/τ. Curves that cross the unstable fixed point N₊ run away.

Phase line dN/dt against N for the chosen launch rate: roots are the fixed points.

Close-up and collision demo

Collision demo (press the Collision view): choose two objects, the impact speed comes from the orbit shell. Time is slowed by the factor shown; fragment counts come from the NASA standard breakup model, sizes and speeds are sampled from its distributions.

Object 1 Object 2

Numerical checks

The science