A starship cruising at a fraction β = v/c of light speed sweeps up interstellar dust grains at a rate set by the local number density n and its frontal shield area A. Each grain hits with relativistic kinetic energy, and every hit ablates a little of the shield until it is worn through:
γ = 1 / √(1 − β²) Lorentz factor
E_impact = (γ − 1) · m · c² relativistic kinetic energy per grain
n = ρ_dust / m number density from grain mass
rate = n · v · A impacts per second on the shield
dM/dt = η · rate · E_impact / E_vap shield mass eroded per second
t_fail = M_shield / (dM/dt) time until the shield is gone
- Cruise speed — higher β raises both the relativistic γ-factor and the sweep rate, so impact energy climbs faster than linearly with speed.
- Regional dust density — the local interstellar medium is patchy; this scales a typical mass density of ρdust ≈ 10⁻²⁶ kg/m³ up or down for denser or sparser regions along the route.
- Dust grain radius — sets grain mass m = (4/3)π r³ ρgrain (ρgrain ≈ 2000 kg/m³). Bigger grains are far rarer but hit with vastly more energy — this is the real trade-off Breakthrough-Starshot-style probe designers face.
- Shield areal density — mass per m² of the leading Whipple-style shield; thicker shields survive longer but add mass that must itself be accelerated.
- η (coupling efficiency) and Evap ≈ 8×10⁶ J/kg (specific vaporization energy of an aluminum-class shield) are held fixed to keep the model legible; η = 0.3 here.
The visualisation compresses time so the shield-health bar depletes at the physically computed erosion rate — about one real second per million mission years — so tuning the sliders toward denser dust or larger grains visibly shortens the ship's life, exactly as the underlying equations predict. This side-on 2D view streams dust grains past a fixed ship silhouette and flashes an impact spark on the shield each time the computed impact rate ticks over — the same physics as the 3D version, redrawn flat.