# Equation to get the size of a crater created by a meteor strike?

Im trying to find the equation to the the size of the resulting crater created by meteor strike when I have the mass, volume, diameter, density, velocity and kinetic energy of the meteor

Can anyone help?

• Welcome to worldbuilding! Sounds an exciting world you're buildi... destroying! :P Googling "asteroid impact calculator" gives some calculators, but I imagine you know about them already, which is why you asked for the equation itself, as linked in Basher's comment. For more detailed info, you may be better off asking on the physics or astronomy stack exchanges. For all three stack exchanges, the "astrophysics" tag might also be useful to attract those people who know the topic best. – Dewi Morgan Dec 6 '18 at 22:54
• Thanks guys, yes you’re right, I’ve seen the calculators but I’d like to try it myself. I’ll try the stacks you mentioned. – user58119 Dec 6 '18 at 22:59
• I was gonna mark this as off topic, but checked over the definitions and it seems to fit the definition of a worldbuilding question to me :) – Dewi Morgan Dec 6 '18 at 23:00
• Without digging out my physics book I would start here, >en.wikipedia.org/wiki/Inelastic_collision<, and also find your earth impact density before trying to solve. Most of the measurements you have given offset each other. So look them up one by one. Most crater impact equations are rather complicated so you need to understand the basics first. – Robus Dec 7 '18 at 4:20

Equation to determine Crater Size: $$D=0.07 \cdot C_f \cdot (g_e/g)^{1/6} \cdot (W \cdot p_a/p_t)^{1/3.4}$$

Where:

D = Crater Diameter

$$C_f$$ = Crater Collapse Factor ( this is equal to 1.3 for craters >4km on Earth)

$$g_e$$ = Gravitational Acceleration at the surface of Earth

g = Acceleration at the surface of the body on which the crater is formed

W = Kinetic Energy of the impacting body (in kilotons TNT equivalent)

$$p_a$$ = Density of the impactor (ranging from 1.8 $$g/cm^3$$ for a comet to 7.3 $$g/cm^3$$ for an iron meteorite).

$$p_t$$ = Density of the target rock

Note: Typical impact velocities for asteroids are around 20 km/s and approximately 60 km/s for comets.

• How does this work? I’m not sure it is accurate. I mainly question what is involved in the (cf) crater collapse factor. I can’t find any accurate information about it. Other than from a previous se post. Where it sites a book to be bought on google and has no info on the equation. – Robus Dec 7 '18 at 4:34
• @Robus, if a crater is too large it will collapse on itself, reducing its diameter as a result. That's why some on line calculators give a transient crater diameter and a final crater diameter. Cf accounts for that. – L.Dutch - Reinstate Monica Dec 7 '18 at 4:45

Here's a super convenient coincidence, we're in the Impactors/Impacts unit in my planetary science class, and one assignment requires us to use this website to simulate impacts according to parameters and record the resulting data calculated for us by the website. Enjoy!