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.

Planet of the Apes (1968) timeline image

In yesterday's post on special relativity and space-travel I mentioned Planet of the Apes's very optimistic time-line for humans to light out to the stars (without warp drive). Here's the key image from the film that establishes what's supposedly going on:

6 months ship time corresponds to ~700 years time on Earth. So how fast is the ship going? Granted the simplifying assp. that the ship's velocity is constant throughout its voyage, it's traveling ~0.999999745C.

Compare: the fastest particles ever produced in accelerators on Earth were at ~0.999999999976C, and the fastest particle ever detected was a cosmic ray proton at ~0.9999999999999999999999951C.

Going Somewhere Fast

Wanna see the universe? Don't care about having anyone you knew back on Earth still alive when and if you return (perhaps not about getting squished to a pulp either)? Then special relativity (SR) is your friend. If you get your spaceship moving close to the speed of light, C (to keep calculations simple, suppose essentially instantaneous accel. and deccel. to constant velocities) then you can travel to a star system x light years away from Earth in ~x years according to a clock on Earth.^[1]
From Earth's frame of reference nothing much turns on whether your ship's cruising velocity is .99C or .99999C (cf., particle collision velocities in Cern's LHC are projected to reach .99999999C): either way you're taking just a little over x years according to clocks on Earth to get to wherever it is you're going. To you on the ship, however, how close your velocity is to C matters immensely: at .99C you spend ~x/7 years in transit, whereas at .99999C you spend ~x/223 years. If your destination is in the Alpha Centauri system (where Avatar's Pandora supposedly lives), then either way your outbound flight takes 4.4 years according to clocks on Earth. At .99C, however, your ship flight-time is just over 6 months, whereas at .99999C, your flight lasts a week.

Here's a graph for some intermediate ship velocities, focusing on in-ship flight times of whole years.

Relying on time dilation effects to help you explore the universe doesn't allow for any of the normal science fiction possibilities of continued interaction with loved ones at home, etc.. All of those possibilities require various sorts of relativity-breaching physics. But even if there's no way around SR, if getting very close to C turns out to be technologically feasible and survivable, etc. then humans could still spread out through the galaxy, but all but the very shortest trips would be importantly 'one way'. From Earth's frame of reference a relativistic diaspora would tend to happen on supra-civilizational or even quasi-geological time-scales. For example, a five year flight out for you at .99999C traverses 1000 light years and sees 1000 years pass on Earth. That's some frontier experience you've bought yourself, pard'ner.^[2]
Very close to C travel by a massy body like a space-ship might depend upon a particular kind of technological and physical breakthrough: essentially on finding some way to 'hide' or 'encode' a lot of the ship's mass as patterns of e-m. radiation. The limit case for this hypothetical possibility would hide or encode all of the mass. Complete masslessness, i.e., complete, (at least) temporary transfiguration of the space-ship and all its contents into e-m. radiation would allow and require travel at C, i.e., as e-m. radiation/light of some kind. That transfigured, massless, informational carrier state would, of course, involve no reference frame/point of view/time factor whatsoever. Decoding/de-beaming/re-materializing a ship with sub-C mass and time in a reference frame as the terminal stage of a 'flight' would be some trick! While realizing this possibility would require huge physical and technological advances, the possibility itself is relatively clear. It represents the least upper bound, limit case for diaspora through the universe that's compatible with SR.

It's somewhat heartening that the mass-less, travel-at-C limit case, while not the 'hyperdrive' of sci-fi dreams nonetheless allows for quite wild arrangements: people in ships get light-like encoded and 'beamed' to new worlds thousands of light years away. Civilizations rise and fall back on Earth while those light-like signals travel to their destinations, all before the next eye-blink of de-beamed/re-materialized time occurs for the people in the ships subject to this process. Their lives restart/continue without missing a beat, notwithstanding that that next beat occurs thousands of light years away, and thousands of years into the future according to clocks on Earth:

'I was just...' - Zap! - 'saying, that would be one small step for a man, and holy mackerel it was! Here I am completing my sentence in 2999 with Altair 4 hanging below me and off to starboard...'

That's not Star Trek or Forbidden Planet, but it's a hell of a space western model. One-way voyages of discovery and settlement into the far away and future: every ship its own, effectively linguistically isolated civilization (effectively the model of 1967's Planet of the Apes).^[3]

Two usefully bleak discussions of the feasibility of non-faster-than-light interstellar travel and associated colonization possibilities:

• The High Frontier, Redux by Stross
• Starflight without Warp drive by Landis et al.

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^[1] While we effectively assume away accel. and deccel. to ease calculation, it's important that they're still 'really' there. If observers on the ship didn't accel./deccel. then both observers on Earth and observers on the ships would be moving inertially. Einstein's Principle of Relativity would then force all observations to be symmetrical, e.g., if one set of observers sees the others' clocks as running slowly, the other observers must see the first groups's clocks similarly slowed (i.e., since there would then be no frame-independent fact that the ship speeds away from the earth rather than the earth speeds away from the ship). Our cases require clock asymmetries, which implies that they essentially involve accel./deccel.. See John Norton's Einstein for Everyone course notes for patient, detailed explanations of the temptations and pseudo-paradoxes in this area. Wikipedia's time dilation page is excellent, but is too technical and gravitationally-oriented for non-specialists.

^[2] Jesus was supposedly 33 when he was crucified. If, instead of dying, Jesus

• hopped a .99999C flight home to a planet 1000 light years away
• spent several years there generally recuperating and chilling out with descendants of his family
• hopped a .99999C flight back to Earth

then a well-refreshed, 50-ish Jesus could be walking amongst us now.

^[3] Planet of the Apes was heroically optimistic about technological progress, supposing that a close-to-C, one-way expedition to the stars would blast off from Cape Kennedy in July 1972. That makes 2001's speculations about, e.g., large moon-bases and manned Jupiter missions by the end the 20th Century look incredibly sober and cautious! The fantasists of 1967 didn't come close to guessing the somewhat disheartening truth: that 1972 would see the last Apollo mission to the moon, and that 40+ years later, no further manned exploration of the solar system, let alone the universe beyond that, would have occurred.