Kinetic weapons - establishing an upper limit when dealing with grey goo

Question

This answer to my last question suggested, rightly, that there are targets dangerous, and large scale, enough that there is neither overkill nor spillover damage when it comes to attacking a planetary target. This is usually a variation on grey goo, sometimes organic and sometimes technological but almost always able to survive in space as well as on an otherwise habitable world.

We're pretty sure that if something hits some planets hard enough pieces come off and go into interplanetary space. Mars is relatively small and airless and I'm interested in a habitable, Earth-like, world; we're also pretty sure that the Chicxulub blast did put out ejecta that got at least as far as the moon. That blast was caused by an object estimated at 60km across well above the size generally depicted for kinetic weapons carried on or used by star ships.

So the question is, assuming a hardened pathogen (one that can survive both the impact itself and an extended trip through space), what is the upper limit on the magnitude of a single impact during a kinetic orbital bombardment to ensure that such material is not spread beyond the world being bombarded, is impactor speed or size more of a factor or is it purely a matter of the total magnitude of the blast produced?

I'm assuming that any ejecta that reach escape velocity, just over 11kms^-1, are going to be a potential vector.

Answer 1

Data by Berthoud et al, 1997 [Meteoritics & Planetary Science, vol. 32, n. 4 supp. p. 13] as well as by Oberbeck and Morrison (1976) seem to indicate that the maximum speed of massive ejecta might approximately range from 50% to 75% that of the initial impactor depending on impacted structure and angle of attack.

Additionally, this velocity is imparted at impact, therefore at sea level; the ejecta then need to overcome atmospheric resistance, i.e. keep escape velocity when at an altitude of roughly 10 km. This would indicate a "safe" limit for Earth of around 17-19 km/s.

This means that is way easier for Martian tephra or ejecta to reach Earth than it is for Earth (or any habitable planet, with a reasonable gravity and atmosphere) to reach Mars, or anywhere else.

Indeed, Chicxulub ejecta reaching the Moon is at the far right of the probability graph for the estimated velocity of the Chicxulub impactor (20 km/s).

Also, unless they have some sort of in-flight shaping capability, the smaller an object the greater proportionally its atmospheric resistance (the section goes down as the square of the radius, the kinetic energy is dependant on mass which goes with volume, as the third power of the radius). So grey goo could only escape if embedded in larger, aerodynamic ejecta. Utility dust and "dry goo" would only go as far as the actual atmospheric displacement - it would surely reach the stratosphere riding on the fireball, but once there it would have zero velocity and fall back after a while.

So, a very large and dense penetrator with speed below escape velocity ought to be both effective and safe. You will probably never have absolute security because secondary phenomena (explosions, etc.) might still supply higher velocities.

For your grey goo suppression needs, I suggest tuned lasers or gigantic Joule resonators, or chemical or radioactive warfare approaches.

On the other hand, if the grey goo is capable of self-assembling in flight and has sufficient energy or fuel storage capability, it could actually exploit the impactor - reach the stratosphere as a dust cloud, then condense in a needle-like aerodynamic structure, and start ejecting part of the structure's own mass to achieve reaction propulsion.