Planetary Formation: From Dust Grain to Rocky World

Starting material: a disc of gas and dust

A star forms from a collapsing cloud of gas and dust, and conservation of angular momentum flattens the leftover material that did not fall into the star into a spinning protoplanetary disc — roughly 99% hydrogen and helium gas, 1% dust grains of rock, metal and ice. Building a planet from this disc is a problem of scale: it starts with micron-sized grains and ends, tens of millions of years later, with bodies thousands of kilometres across — twelve orders of magnitude in size, and the physics that dominates growth changes completely along the way.

Stage one: sticking, from grains to pebbles

At micron to centimetre scale, grains grow by simple collisions sticking together through electrostatic and van der Waals forces, in the same way dust bunnies form under a bed. This stage is comparatively fast and well understood, but it runs into a serious problem once grains reach roughly meter size.

The meter-size barrier

Gas in the disc orbits slightly slower than solid grains do, because pressure support partially counteracts the star's gravity on the gas but not on the solids. That relative headwind drags on meter-sized bodies hard enough to sap their orbital energy and spiral them into the star in as little as a few hundred orbits — faster than sticking collisions can grow them past that size. This is the unsolved "meter-size barrier," and the leading resolution is the streaming instability: pebbles concentrate into dense clumps by aerodynamic feedback with the gas, and once a clump is dense enough, its own self-gravity takes over and collapses it directly into a kilometre-scale planetesimal, skipping the dangerous size range almost entirely.

Runaway and oligarchic growth

Once planetesimals exist, gravity itself drives growth, and it does so unevenly. A slightly larger body has a proportionally larger gravitational reach (its "gravitational focusing" cross-section grows faster than its physical size), so it accretes neighbouring material faster than smaller bodies nearby — a positive feedback called runaway growth that can turn a modest head-start into a thousand-fold mass advantage in a short time.

gravitational focusing factor ≈ 1 + (v_esc / v_rel)²

  v_esc = escape velocity of the growing body (grows with mass)
  v_rel = relative velocity of nearby debris

as a body grows, v_esc rises, focusing rises, growth accelerates
— until the body is massive enough to stir up (v_rel) of its
neighbours, which throttles the runaway into "oligarchic" growth

Runaway growth cannot continue forever: as a body grows, it gravitationally stirs the orbits of nearby planetesimals, raising their relative velocities and reducing the focusing advantage that fuelled the runaway. This self-limiting transition is oligarchic growth — several similarly sized "planetary embryos," roughly Moon to Mars sized, emerge spaced out across the disc, each having cleared and dominated its own local feeding zone, growing in parallel rather than one runaway winner taking everything.

Giant impacts and the frost line

The final stage is chaotic and gravitationally driven: embryo orbits cross and embryos collide directly, in giant impacts that assemble the last Earth-mass planets over tens of millions of years — Earth's own Moon is widely thought to have formed from debris ejected by one such collision, between the proto-Earth and a Mars-sized body nicknamed Theia. Meanwhile, location in the disc decided which planets became rocky and which became giants: beyond the frost line, where the disc was cold enough for water, ammonia and methane to freeze solid, there was several times more solid material available, letting cores there grow past roughly 10 Earth masses quickly enough to gravitationally capture enormous hydrogen-helium envelopes before the surrounding gas disc dissipated — producing Jupiter and Saturn. Inside the frost line, only rock and metal condensed, capping core growth at a size too small to trigger that runaway gas capture, which is why Earth, Venus, Mars and Mercury stayed small and rocky.

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