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Parameters
Model checks
The science
Energy and crater size
The kinetic energy is E = ½ m v2 with m = ρi π L3 / 6; one megaton of TNT is 4.184×1015 J. The transient crater diameter follows the pi-group scaling of Collins, Melosh and Marcus (2005) for a non-porous target: Dtc = 1.161 (ρi/ρt)1/3 L0.78 v0.44 g-0.22 sin1/3θ. A simple bowl crater ends up about 1.25 times wider after the rim slumps; above a transition diameter of about 3.2 km on Earth (inversely proportional to g) the crater is complex and Df = 1.17 Dtc1.13 / Dc0.13. The ejecta blanket thickness falls off as r-3 (McGetchin et al., 1973).
What it shows
The scaling is a fit to experiments and numerical models, so the output is an estimate good to a factor of order 1.5. The check compares it with Barringer Meteor Crater, Arizona.
Honest simplifications: atmospheric entry and break-up are not modelled (small stony bodies burst in the air), porosity and layered targets are ignored, depth values use fixed depth-to-diameter rules and the ejecta profile is idealised. Educational model only.
What to try
- Pick Meteor Crater (Arizona): the model gives a crater of about 1.3 km, close to the real 1.19 km.
- Raise the impact speed: the crater grows only as v0.44 while the energy grows as v2.
- Choose Same rock on the Moon: lower gravity makes a larger crater, by g-0.22.
- Lower the impact angle: grazing impacts dig smaller craters (sin1/3θ).