No single engine spans cloud collapse to the Moon-forming impact. This entry chains eleven peer-reviewed reduced models — one per physical regime — on a shared narrative timeline, with two stages (terrestrial accretion, the Nice instability) driven by live REBOUND N-body. Each stage declares where its model is trustworthy and where it breaks.
Planet formation is not one physics problem. It is a relay of at least four — self-gravitating hydrodynamics (cloud collapse), viscous/wind-driven disk evolution, two-fluid dust–gas dynamics (drift and the streaming instability), and gravitational N-body (embryo growth, migration, the giant-planet instability, the Moon-forming impact) — run over five orders of magnitude in time, from the ~0.5 Myr free-fall of a core to the ~100 Myr assembly of Earth. No code integrates the whole relay self-consistently; published "formation" results are always stitched from regime-specific calculations. This entry makes that stitching explicit. Each of the eleven stages declares the reduced model it stands on, the epoch it occupies relative to CAI formation, and the boundary at which it must hand off to a fuller treatment.
Four model classes appear, the same taxonomy the Models series uses elsewhere, plus live N-body where it is cheap enough to run honestly: analytic closed-form self-similar or perturbative solutions; snapshot parameterized tracks from published grids; N-body live REBOUND integration. The two genuinely N-body stages — terrestrial accretion and the Nice instability — are integrated with REBOUND (Rein & Liu 2012) using mercurius and whfast (Rein & Tamayo 2015); they are deliberately reduced runs (fewer bodies, shorter baselines than a publication study) and are labeled as such in their validity cells. They demonstrate the dynamical mode — giant impacts, resonance-crossing migration — not a converged outcome.
Absolute times are keyed to CAI condensation, t0 = 4567.3 Myr (Connelly+ 2012). Stages 1–8 all complete inside the gas-disk lifetime (~3–10 Myr) and overlap heavily; stages 9–11 run for tens of Myr afterward. The timeline scrubber spaces the stages evenly for legibility — read each stage's true epoch from the table and the live panel.
| # | Stage | Anchor model | Class | Epoch (since CAIs) | Char. timescale |
|---|---|---|---|---|---|
| 1 | Cloud / core collapse → disk | Shu 1977; Terebey-Shu-Cassen 1984 | analytic | −0.1 → 0.5 Myr | tff ≈ 0.5 Myr |
| 2 | Viscous disk evolution | Lynden-Bell & Pringle 1974; SS73 | analytic | 0.1 → 3 Myr | tν ~ 0.1–1 Myr (10 AU) |
| 3 | Dust settling + radial drift | Weidenschilling 1977 | analytic | 0.1 → 1 Myr | St=1 drift ≲ 100 yr |
| 4 | Streaming-instability planetesimals | Youdin & Goodman 2005; Johansen+ 2007 | snapshot | 0.2 → 1 Myr | ~orbital, on clumping |
| 5 | Pebble + oligarchic embryo growth | Lambrechts & Johansen 2012; Kokubo & Ida 1998 | snapshot | 0.3 → 3 Myr | 10⁵–10⁶ yr (pebble) |
| 6 | Giant-planet core accretion | Pollack+ 1996 | snapshot | 0.5 → 4 Myr | Mcrit ≈ 10 M⊕ |
| 7 | Grand Tack migration | Walsh+ 2011 | analytic | 0.1 → 5 Myr | during gas disk |
| 8 | Photoevaporative disk dispersal | Clarke+ 2001; Owen+ 2012 | analytic | 3 → 10 Myr | clearing ~10⁵ yr |
| 9 | Terrestrial giant-impact accretion | Chambers 2001; Raymond+ 2009 | N-body | 10 → 100 Myr | ~30–100 Myr |
| 10 | Giant-planet (Nice) instability | Tsiganis/Gomes/Morbidelli/Levison 2005 | N-body | ~10–100 Myr* | 2:1 resonance crossing |
| 11 | Moon-forming giant impact | Canup & Asphaug 2001; Canup 2012 | snapshot | ~30–100 Myr | single event |
* Stage 10 timing is shown in the modern early-instability placement (Nesvorný+ / Clement+ 2018), not the classic ~700 Myr Late-Heavy-Bombardment timing. See the stage-10 validity cell.
The series rule is that every reduced model states where it fails, beside the figure it produces. Here that means eleven boundary statements — one per stage. The two recurring, field-level revisions to flag: Pollack's ~8 Myr core-accretion timescale (shortened to <1 Myr once pebble accretion is included) and the ~700 Myr Nice instability (now placed early, within ~100 Myr).
Self-similar collapse of a singular isothermal sphere; Ṁ = 0.975 cs³/G constant in time; material lands at rc ∝ t³.
Lynden-Bell & Pringle self-similar spreading with Σ ∝ R⁻¹ and an α stand-in for turbulent viscosity.
Drift peaks at Stokes number St≈1; vdrift,max ≈ η vK ≈ 50 m/s at 1 AU — the meter-size barrier.
Strong clumping needs St~0.01–1 and metallicity Z ≳ 0.02; collapses to ~100 km planetesimals (top-heavy IMF).
Pebble accretion grows cores in ~10⁵–10⁶ yr; oligarchs spaced ~5–10 mutual Hill radii; pebble isolation mass ~10–20 M⊕.
Critical core ~10 M⊕; three phases; crossover ~16 M⊕ then runaway gas.
Jupiter migrates to ~1.5 AU then tacks outward at Saturn's 3:2 capture, truncating the inner disk → small Mars + belt dichotomy.
Two-timescale "UV switch": slow viscous draining, then inner-hole clearing in ~10⁵ yr once Ṁ drops to the photoevaporation rate. Lifetime ~3–10 Myr.
Real REBOUND mercurius with merging collisions. Reduced run: 16 embryos (~4 M⊕), 0.7–1.7 AU, 0.6 Myr, Jupiter perturber, modestly inflated collision radii (standard accretion-N-body technique).
Real REBOUND whfast. Giants compact inside the J–S 2:1; a 35 M⊕ planetesimal disk drives divergent migration toward resonance crossing.
Canonical Mars-mass (~0.1 M⊕) oblique impact leaves a ~1.5–2 lunar-mass, mantle-dominated disk.
Bottom line. Stages 1–8 are analytic/snapshot reductions valid for the morphology and timescales of each regime but blind to the magnetized, wind-driven, ring-structured detail that ALMA and modern MHD now demand. Stages 9–10 are honest but reduced N-body — correct in dynamical mechanism, not in converged outcome. Stage 11 is the one with an openly unsolved core (the isotopic identity problem). The animation is a teaching scaffold across the whole relay; each handoff is where you would reach for a dedicated code.