Live readouts
Live graph
Curves are model output for the reference history. Dates before ~540 Ma, greenhouse and oxygen levels are approximate, and continent shapes/positions are schematic - see "The science".
Date a rock from this epoch
The sample crystallised at the age on the timeline. Pick a clock, add lead loss, press "Measure": the lab sees only isotope ratios (with ~1 % noise) and must recover the age.
0 %
Concordia: the curve of (207Pb*/235U, 206Pb*/238U) for closed-system crystals of every age. Lead loss slides a sample toward the origin; the chord meets the curve at the true age.
Radioactive decay lab
Blue = parent atoms, orange = daughters. Each atom has an independent random decay time; the count follows N = N0 2-t/T½ within shot noise √(Np(1-p)).
Numerical checks run
The science
Faint young Sun
L(t) = L₀ / (1 + 0.4 (1 - t / t₀)), t₀ = 4.54 Gyr
Hydrogen burning raises the Sun's mean molecular weight, so the core contracts and the Sun brightens ~1 % per 100 Myr: 71 % of today's output when Earth formed (Gough 1981). With today's greenhouse the early oceans would freeze, yet there are 3.5 Ga pillow lavas and sediments - the faint young Sun paradox. Here it is "solved" by a stronger greenhouse (CO₂, CH₄, H₂O) and a darker, cloud-poor, land-poor planet; the exact mix is still debated.
Equilibrium temperature, greenhouse and the ice-albedo switch
Teq = [ S (1 - A) / 4σ ]1/4
With S = 1361 W/m² and A = 0.30 this gives 255 K; the real mean is 288 K, the difference (33 K) is the greenhouse effect. The model that drives the globe is a zero-dimensional energy balance:
C dT/dt = S(1 - A(T))/4 - [ εσT⁴ - ΔF ], ΔF = 5.35 ln(CCO2/280) W/m²
A(T) = Aw + (Aice - Aw) / (1 + e(T - 270)/5), Aice = 0.62
ε is fixed so that today (280 ppm, A = 0.30) gives 288 K. Because ice is bright, a colder planet reflects more sunlight and cools further: for some range of S there are
two stable climates (warm and snowball) separated by an unstable one, and the planet flips at the folds (saddle-node bifurcations). The freeze threshold is the minimum of
Sneeded(T) = 4 (εσT⁴ - ΔF) / (1 - A(T)) over the warm branch. The lab integrates the ODE with RK4 and compares with this analytic value.
A 0-D model has no latitude, ocean heat transport or clouds. Real snowball onset in 1-D/3-D models needs the ice line to reach ~30° latitude; the parameters here are tuned (not fitted) so that today is stable, the Cryogenian is marginal and a CO₂ build-up of ~0.1 bar thaws a snowball. "CO₂-equivalent" is an effective forcing, not a proxy record.
Snowball Earth
Glacial deposits at tropical palaeolatitudes (~717-660 and ~650-635 Ma, and ~2.4-2.2 Ga) support global or near-global ice. Volcanoes keep emitting CO₂ but silicate weathering stops under ice, so CO₂ accumulates until the greenhouse melts the ice within a few Myr, leaving cap carbonates. Whether the ocean froze completely ("hard") or kept an open equatorial belt ("slushball") is debated.
Radiometric clocks
N(t) = N₀ 2-t/T½ = N₀ e-λt, λ = ln2 / T½
t = (1/λ) ln(1 + D*/P)
concordia: 206Pb*/238U = eλ238 t - 1, 207Pb*/235U = eλ235 t - 1
Half-lives used: U-238 4.468 Gyr, U-235 0.7038 Gyr, K-40 1.248 Gyr (10.72 % to Ar-40), Rb-87 49.23 Gyr, C-14 5730 yr. Two independent uranium clocks that agree (concordant) validate each other; lead loss moves points along a chord to the origin. Simplifications: no common-lead correction, no isochron, no decay-constant uncertainty, no calibration curve for C-14.
Tidal braking, the Moon and the day
Tides drag on Earth's spin and push the Moon outward; total angular momentum is (almost) conserved:
I ωE + μ √(G (M+m) a) = const, I = 0.3307 M R²
The day length curve is anchored on measured data (coral and clam growth lines, tidal rhythmites, cyclostratigraphy: 23.6 h at 70 Ma, 21.9 h at 400 Ma, ~21 h at 600 Ma, 18.7 h at 1.4 Ga, ~5 h just after the giant impact); the Moon's distance is then derived from the formula above, giving 60.3 Rₑ today, ~3 Rₑ (near the Roche limit) at 4.51 Ga and a present recession of ~3.8 cm/yr, matching Lunar Laser Ranging. Ignores solar tides, the changing obliquity and core coupling; the ~1.0-2.0 Ga "stall" near 19 h (atmospheric thermal tide resonance) is only approximated. Lunar tide force ∝ a-3.
Plate motion and palaeogeography
Present continents are rigid blobs rotated about Euler poles. Pangaea (~320-200 Ma) and a Rodinia-like supercontinent (~1.1-0.9 Ga) were assembled by an automatic jig-saw fit (maximising shelf contact, penalising overlap) of schematic continent outlines; Nuna/Kenorland layouts and the India dash are interpolations. This is not a published reconstruction - it shows the principle: plates move at ~2-10 cm/yr (the model reports its own speeds). Continental area grows with time (crust growth models differ: 25 % by 2.5 Ga is one choice) by raising a threshold on the continent fields so cratons survive first.
Oxygen and life
O₂ stays below ~10-5 of today's level until ~2.45 Ga, jumps in the Great Oxidation Event (banded iron formations stop forming), is low again through the "boring billion", rises after the Neoproterozoic snowballs, and peaks near 30 % in the Carboniferous (Berner-type models). The curve is a smoothed consensus; error bars are large before 540 Ma. Ocean colour turns from iron-rich green to blue as O₂ rises. Plants reach land ~470 Ma; the land turns from rock-brown to green.
How accurate are the dates?
- 4.54 Ga Earth, 4.40 Ga zircon, 2.4 Ga GOE, Cryogenian 720-635 Ma, 538.8 Ma Cambrian base, 252 Ma, 66 Ma: firm (U-Pb, ±<1 %).
- Moon formation 4.35-4.51 Ga: debated. Late heavy bombardment: debated or even absent. Earliest life: 3.5-4.1 Ga depending on evidence.
- Greenhouse, oxygen, land area before ~540 Ma: model-dependent, order-of-magnitude.
- Continent shapes and positions: schematic. Do not use for geology homework!
Credits and method
Assets (continent fields, cloud/crack/detail maps, Moon, props, specimens) were built headless in Blender 5.2 (Cycles-baked textures, Draco GLB); the globe shader, physics and charts are Three.js r160 + WebGL + plain JavaScript, vendored locally. Educational model; not affiliated with any institution.