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Calculate crater diameter

An asteroid with a diameter of 500km has an impact strength of 4000J/kg. What is the largest sized crater diameter which can be formed without melting the asteroid? The asteroid has a density of 3.5 g/cm^3 and the impact velocity is 5km/sec


I have a few formulas:


The asteroid will not melt if: kinetic energy < mass* impact strength

and, crater diameter is proportional to W^(1/3)


I have no information about the body being impacted so I don't know if I can use the formula for crater diameter as it requires information about the material strength of the body being impacted for an accurate answer.

I approximated the asteroid as a sphere (as I was given a diameter) and calculated the mass and the kinetic energy which I got to be : 2.875*10^27 Joules. However, the mass* impact strength is four orders of magnitude less.


I guess I'm not entirely sure how to approach this problem. Any suggestions?
 

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