Sun Sep 18, 2011 2:26 pm
Firstly, I'd like to say that I got the speed wrong - it's MUCH closer to c than I stated before, only off by about 10<sup>-28</sup> m/s.
Now, to respond to Tech's statement about energy release:
(EDIT: although the following is "pretty", it's also wrong. As the edit in my earlier post states, the round will not experience gravitational collapse, and to treat this problem in a purely special-relativistic sense is fallacious. The airsoft round would be scattered on impact regardless of its velocity, releasing all its energy at the surface.)
If the round was still in the form of atomic (or electron-degenerate) matter, it would probably be scattered on impact and release essentially all its kinetic energy as high frequency EM radiation.
As we get to higher mass density though... We get into areas that nobody fully understands yet. If singularities are a physical reality (or at least the actual diameter is low enough to make the following roughly accurate), as opposed to simply a mathematical artifact, then the following would be the case:
The singularity (which masses 110 billion tonnes) has an "actual" diameter of 0, so it does not "collide" with any of the matter that it passes through. It has a Schwarzschild radius of 1.63 * 10<sup>-13</sup> m. It is moving relative to the matter it passes through at almost exactly lightspeed, so only the mass within that radius would be captured by it as it passed through. This gives a core with a cross sectional area of 4.25 * 10<sup>-25</sup> m<sup>2</sup> which would, using Earth's average density, have a mass of about 1.5 * 10<sup>-10</sup> grams.
Now, using momentum conservation, I get...
Well, I must admit that I was expecting a lower number. Not counting the effects of the mass being constantly added as the particle moves (i.e., modeling it as an inelastic collision, this is still accurate to at least within an order of magnitude), I get an energy loss of 10<sup>24</sup> J during the transit through the Earth. That's 238 MT/m of its path through the Earth (assuming it went right through the centre). So, while it wouldn't destroy the target, it would certainly make for quite an impressive show. Energy release equivalent to a 20km bolide at 10km/s. Most of that energy release wouldn't affect the Earth's surface, but you'd still be looking at an extinction level event (although certainly a recoverable one).
In conclusion, singularities are very inefficient projectiles, but the one in question here would still punch a transient hole a few hundred metres (possibly several kilometres) across right through the Earth (and the entrance and exit holes would be craters probably over ten kilometres across). So now we reach the old answer yet again, in a more thoughtful manner - accelerate something fast enough, and it will destroy any target. It just becomes a very inefficient process after the target can no longer scatter the projectile.
EDIT: if anyone feels like wasting an hour or so with an arbitrary-precision calculator to verify my results or improve anything, I've been using a Lorentz factor of exactly 556 * 10<sup>15</sup>, and a 0.2g airsoft round.
Last edited by
DYI on Tue Dec 13, 2011 10:57 am, edited 2 times in total.
Spudfiles' resident expert on all things that sail through the air at improbable speeds, trailing an incandescent wake of ionized air, dissociated polymers and metal oxides.
