Thursday, September 08, 2011

Realistic Relativistic Spacecraft and Impact Events

As everyone knows by now, impacts from space have occasionally devastated much of life on earth, most recently and famously in the K-T boundary impact event, 65 million years ago, that appears to have killed off most dinosaurs. Typically, impactors from space that come from within the solar system arrive at 20-50 km/s. And the specific impactor that shmushed the dinosaurs' world was probably a hard/dense rock (not ice), say 3000 kg/m^3, 10-14 km in diameter. That's remarkable: something doesn't need to be 'the size of Texas' (a la Michael Bay's Armageddon (1998)) or to be travelling at anything like relativistic speeds (say > .1C = 30,000 km/s) is required to obliterate much of life on Earth.

But what if an impactor is out at one of these extremes? Well, supposing that 'something the size of TX' means a 10^4 (a 100x100) scaling up of mass from the actual K-T event impactor then K-T-level impact energy results from only 1/100 the v, i.e., only .2-.5 km/s = 200-500 m/s, the speed of current fighter planes.

And what about a space-ship moving at relativistic velocities, i.e., the sort of thing that travel to the stars 'without warp drive' will require? Won't it look like a very dangerous projectiles to any other life-forms who spot it, as it were, in-coming?

Suppose as a kind of base-line that the sort of space-ship that could conceivably sustain technological life for 20+ years would be at least the size/mass of the largest current aircraft carriers, which are about 100,000 long tons = ~ 10 million kg. For simplicity, ignoring relativistic effects, how fast does does an aircraft-carrier-scale ship have to be going to have the kinetic energy of the K-T impactor?

Current estimates of the K-T impactor energy are 400-420 x 10^21 J. Solving for v we get that the aircraft carrier would have to be traveling at ~ 90,000 km/s ~ .3C to do K-T-type damage. If we take relativistic effects on kinetic energy into account, the sufficient-for-a-K-T-disaster v computes out to ~ .29C.

On the one hand, then, why build a Death Star when you can devastate a planet just by ramming something the size of the Starship Enterprise or Space Battleship Yamato into it (at anything like their normal speeds)? On the other hand, the sorts of moderately large spaceships humans might use to get to the stars over a generation (e.g., accelerating continuously at 1 g for the first half of the trip then decelerating at the same rate for the second half) are going to look like menaces to intelligences at the other end. If the decceleration goes wrong, e.g., fuel runs out early or some such thing, then those ships will 'come in hot', at a non-trivial fraction of C, and will threaten to destroy civilizations and possibly life more generally at their destination. Look out.

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