Kishan TiwariPlanetary materials
Tools

Do the arithmetic yourself.

Three calculators I use in my own work, made public. Change the numbers, watch the curve move, take the data away as a spreadsheet. Everything runs in your browser, nothing is uploaded, and each model names the paper it comes from.

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01 · Conduction

Shock-melt vein cooling

A vein of half-width a, molten at Tm, quenching into host rock at Th. Whether a high-pressure phase survives comes down to this curve: nucleation and growth need time above a threshold, and a thin vein does not give it to them.

Parameters

µm
K
K
W/m·K
kg/m³
J/kg·K
s
K
Presets

Result

Exact solution for a slab initial condition in an infinite medium: T(x,t) = Th + ½(Tm−Th)[erf((a−x)/2√(αt)) + erf((a+x)/2√(αt))], α = k/ρcp. Carslaw & Jaeger (1959), Conduction of Heat in Solids, §2.3.

02 · Hugoniot

Peak shock pressure

Planar impact approximation with a linear shock–particle Hugoniot, Us = C0 + S·up, solved by impedance match so the impactor and target need not be the same material. The pressure is then mapped onto the Stöffler shock stages.

Parameters

km/s

Impactor

Target

Result

Melosh (1989), Impact Cratering: A Geologic Process, ch. 4. Shock-stage boundaries for ordinary chondrites after Stöffler, Keil & Scott (1991) and Stöffler, Hamann & Metzler (2018). Hugoniot constants are room-temperature literature values; they shift with porosity and pre-heating.

03 · π-scaling

Crater scaling

How big a hole a given impactor makes, in the gravity regime, in competent rock. The Lonar preset reproduces the real crater's 1.88 km in Deccan basalt for a plausible impactor, which is the most you should ask of a scaling law.

Parameters

m
km/s
°
kg/m³
kg/m³
m/s²
Presets

Result

Dtc = 1.161 (ρi/ρt)1/3 L0.78 v0.44 g−0.22 (sin θ)1/3 Simple craters finalise near 1.25 Dtc; above the ~3.2 km simple-to-complex transition on Earth they collapse wider. Schmidt & Housen (1987); Melosh (1989) §7.8.

Caveats

What these will and won't tell you

Every one of these is a first-order estimate. Treat them as a way to check whether a number is plausible, not as a substitute for a model.

Vein cooling

Assumes constant thermal properties, no latent heat of crystallisation, and a host that is infinite and initially uniform. Latent heat holds the vein hotter for longer than this curve shows, so quench times here are lower bounds.

Shock pressure

The planar impact approximation holds only near the impact point, in the first moments. It ignores porosity, which raises shock heating sharply, and pre-shock temperature. Real peak pressures decay steeply away from the contact.

Crater scaling

Gravity-regime scaling for competent rock. It is wrong in the strength regime (small craters, strong targets), wrong for very oblique impacts below about 15°, and does not model atmospheric break-up of the impactor.