What happens if you hit a planet with a small rock (or other projectile)
moving VERY fast?  say at 100 km/s, or even at relativistic speeds?
There have been some discussions about this on r.a.s.s in the past, but
as I can't find them on DejaNews, I'll summarise from memory and my own
knowledge of physics (such as it is).

I expect that, like a bullet fired into a sandbag, the projectile would
decelerate very quickly as its momentum transferred to the material it
was trying to push out of its way.  Most of its energy would also
transfer to that material, causing a sizable explosion and crater.
Meteorites that have hit the Earth, at speeds above 10 km/s though
probably not as high as 100, have done that, and the craters are wide
rather than deep.  I extrapolate that a somewhat bigger, somewhat
faster meteorite would dig a bigger crater but would still not drill
very far into the planet.

To get a vague idea of the likely penetration, calculate how far the
projectile has to travel before the mass it has pushed out of the way
is equal to its own mass: this will decelerate it by a factor of perhaps 2,
depending, I think, on how streamlined it is (because this affects the
speed at which the obstructing mass will have to move in order to get
out of the way).  For a roughly spherical asteroid made of ordinary rock,
the answer would be about equal to its own diameter; a long, thin projectile
made of a dense material would penetrate further for the same total mass.
However, no material of which I'm aware is strong enough to hold its shape
when it hits a rock at speeds of tens of km/s: the projectile would not
stay long and thin for very long.

I'm less sure of what would happen to a relativistic projectile, but I
think the overall picture would be much the same as far as penetration
is concerned.  However, the energy released, and the resulting crater,
would be larger.  Much larger.  The only real-world comparison I can
make is with cosmic rays, some of which arrive at high relativistic
speeds.  They more or less invariably hit an atom in the upper
atmosphere, and what arrives at the surface is a "shower" of many less
energetic particles spread over a considerable area.

Some folks like to suggest that if you control enough energy to
accelerate an asteroid to a relativistic speed, you can probably find
other ways of making the Earth an uncomfortable place to live.  In _The
Killing Star_ by Pellegrino and Zebrowski, the Earth is bombarded with
a large number of small relativistic projectiles, so that the planet is
not perforated, but the atmosphere is heated considerably.

If someone who knows more would care to correct any slips I've made,
or to re-write this piece for me, I'll be grateful.

	- Richard Treitel