The leading model for the Moon's origin is the giant-impact hypothesis: a Mars-sized protoplanet ("Theia") struck the young Earth, throwing a disk of vaporized and molten rock into orbit. What happens next to that disk splits into two regimes at the Roche limit:
Roche limit (rigid body):
d = 2.44 · R⊕ · (ρ⊕ / ρ_sat)^(1/3)
Kepler's third law (orbital angular speed at radius r):
ω(r) = √(G·M⊕ / r³)
Inside d, Earth's tidal gradient across a clump exceeds its own self-gravity, so debris there is continually sheared apart — it orbits fast but never accretes, remaining a thin ring (shown in cyan). Outside d, self-gravity wins: two nearby clumps can bind together. As a clump grows, its gravitational reach grows with it — gravitational focusing — so the biggest bodies capture disproportionately more mass, a runaway-growth feedback loop real accretion models rely on to explain why one Moon (not thousands of moonlets) is left after debris disks clear.
- Time speed — simulated days advanced per real second; each particle's orbital phase integrates ω(r)·dt exactly, so inner debris visibly laps outer debris (Kepler's third law in action).
- Satellite bulk density — sets ρ_sat in the Roche formula above; a fluffier, icier body (low density) has a Roche limit further out than a dense rocky one, so the ring/accretion boundary you see moves live.
- Disk mass — scales total debris mass relative to the Moon's real mass (7.34×10²² kg); more mass per particle means bigger capture radii and faster runaway growth.
- Outer debris particles — how many discrete clumps the outer disk starts as (finer resolution, slower to fully merge).
Simplifications: the disk is flattened to a plane, particle-particle gravity is replaced by an effective capture radius (mass^(1/3)-scaled, standard in toy accretion models) rather than full N-body integration, and the timescale is compressed for visualization — real models estimate most of the Moon's mass re-accretes within roughly a month to a few centuries, depending on how far out the debris starts.