Ratio of projectile to ejecta mass, shoot the moon.

[Spinnor]

Say we shoot the surface of the moon with various sized steel balls of size a cm and larger, say up to a km in size. Say the balls hit the surface of the moon moving at 20,000 mph. Is there a simple formula for the mass of the ejecta as a function of the mass of the projectile? Will the formula depend on whether the projectile hits dust or rock or a combination of the two?

Thanks for any help!

 

[Spinnor]

After a bit of Googling, wow, what a find,

http://keith.aa.washington.edu/craterdata/scaling/index.htm

From, Crater Database and Scaling Tools,

http://keith.aa.washington.edu/craterdata/

The math behind the calculator,

http://keith.aa.washington.edu/craterdata/scaling/theory.pdf

 

[Drakkith]

Wow, nice find!

 

[Spinnor]

Used the above calculator, seemed buggy for multiple calculations, and got the following result. For a steel projectile striking the moon at 10,000 mph perpendicularly, the mass of the projectile, M, was roughly proportional to the volume, V, of ejecta for sizes from 1 cm to 10 m,

M ≈ V

above that size

M^α ≈ V

Where α is less then 1.

Is the above an example of scale invariance? If I draw a picture of the projectile next to the volume of ejecta I can change the scale but not have to redraw the picture, one picture works for a range of projectile masses and ejecta volume?