Planetary Differentiation: Iron Rain & Core Formation

Protoplanet Setup

Iron droplet radius 5.0 mm

Magma-ocean viscosity η 20 Pa·s

Surface gravity g 9.8 m/s²

Playback speed 1.0×

Legend

Molten iron droplets Growing metallic core Silicate mantle (magma ocean)

Live Readouts

Settling velocity

— cm/s

Core radius

0.0%

Differentiated (iron settled)

0.0%

How it works

A young rocky planet can be hot enough throughout to melt: a global magma ocean. Dense molten iron does not mix with lighter silicate melt — it separates into droplets and sinks, an event called planetary differentiation, which is how every terrestrial planet built its metallic core.

Each droplet is small enough, and the melt viscous enough, that inertia is negligible (Reynolds number ≪ 1). It falls at the Stokes' law terminal velocity, where viscous drag exactly balances the net gravity + buoyancy force:

v = (2/9) · Δρ · g · r² / η

Δρ = ρ(iron) − ρ(silicate) ≈ 3700 kg/m³
r  = droplet radius
g  = surface gravity
η  = mantle (magma ocean) viscosity

Velocity grows with the square of droplet radius — doubling grain size quadruples the sinking speed — and falls linearly with viscosity. Every droplet that reaches the core boundary merges in, conserving its volume; the core radius therefore grows as R_core = ∛(3·V_core / 4π).

Grain radius — sets droplet size r in the formula above (mm-scale droplets, as inferred from iron-rain models of Earth's early magma ocean).
Viscosity η — a fully molten magma ocean is ~1–100 Pa·s (close to water); a crystal-laden mush is far more viscous and slows settling drastically.
Surface gravity g — from Mercury-like (3.7 m/s²) to a super-Earth (24 m/s²); stronger gravity drives faster core formation.
Playback speed — a real magma-ocean core forms in years to millennia; this only rescales the animation clock, not the physics — velocity always obeys the formula above.

Real-world relevance: this "iron rain" mechanism is the leading model for how Earth, Mercury and Mars formed their cores within the first ~10–100 million years after accretion, long before the mantle ever solidified.

Model time: 0 yr (illustrative)

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