FTL drives: unsafe at any speed

2013-02-03

We got to talking about space warfare last night, and I realized something pretty weird: FTL drives effect massive shifts in velocity.

Almost every FTL spacecraft, in fiction, is capable of moving between planets in different star systems. The ship starts out roughly stationary relative to planet A, and winds up roughly stationary relative to planet B. How fast are A and B moving compared to one another? How fast do stars move?

Proxima Centauri has a radial velocity (relative to the solar system’s center-of-mass) of -21.7 +/- 1.8 km/s. Its proper motion vector is -3.77530 arcsec/year in right ascension, and 0.76933 arcsec/year in declination. At 4.243 light-years away, its proper motion relative to sol is 23.777 km/s. Its total relative velocity to sol is somewhere around 32.19 km/s, which is just a little faster than the velocity of the earth, rotating around the sun.

Jumping from Proxima Centauri to Sol means a ship’s faster-than-light drives can effect a delta-v in real space of at least 32 km/s per jump. These are tame velocities for stellar neighbors. If Earth is headed straight for Proxima Centauri at jump time, and the ship departs from a similar planet headed towards Sol, we can assume routine jumps impart up to 91 km/s velocity differentials.

If the Millennium Falcon has a mass of roughly 1.5 x 10^6 kg, its FTL drives are capable of imparting 6.211 x 10^15 J of kinetic energy to the ship per jump, which is roughly 2/3rds of the energy released in the impact forming Meteor Crater in Arizona. This means the Falcon could, with a single jump, put a hole in the earth roughly 1.2 kilometers across. We’re talking about an independent freighter captain operating a device which routinely yields the destructive power of a fusion warhead.

If a Mon Calamari cruiser has a mass of 15 million metric tons, a similar jump imparts 6.2 * 10^19 joules of kinetic energy to the hull, or roughly 14 gigatons of TNT. That’s more than 100 times more powerful than the Tsar Bomba.

The Battlestar Galactica is roughly ~1400 x 500 x 180 meters, or roughly 10^8 cubic meters. If we assume it’s ~90% air and the remainder has the density of iron, its mass is 1.4 * 10^8 kg air + 9.9 * 10^10 kg iron, or 9.8 * 10^10 kg. In the very first episode it makes 237 jumps, one every 33 minutes. If each jump can impart 32 km/s, its final velocity relative to origin could be 75,000 km/s, or 2.5% of c.

In this universe, a forty-year old spacecraft due for decommissioning is capable of acquiring 2.7 * 10^26 J of kinetic energy (assuming uniform Newtonian mechanics cuz I’m lazy). That’s 6.5 * 10^16 tons of TNT. Almost the energy output of the entire sun in one second. We’re talking 3.067 * 10^9 kilograms of mass converted to kinetic energy by e = mc^2 (a good chunk of the Battlestar itself, if you’re wondering).

Chicxulub crater is 180 kilometers across. The impact caused a megatsunami and boiled the atmosphere. We think it caused a mass extinction event. That took 4.2 * 10^23 J.

If you rammed a planet with the Galactica, we’re talking about an impact a thousand times more powerful.

Why bother with nukes? You can wipe out entire planets with a single ship apiece, without any concomitant radioactivity, and do it a billion times faster. There’s no need to infiltrate computer systems or engage in elaborate orbital battles. Just jump in-system at 2.5% the speed of light. If you miss the planet, it’s no big deal. Just jump back and give it a second go.

You don’t even have to waste the whole ship. Just jump in-system, let go of a suitable chunk of rock or metal, and jump into open space before hitting the atmosphere. The only practical limit is the ablative shielding required to survive relativistic velocities in the interstellar medium, but… I dunno, magnetic fields or something.

Quit playing around. Sci-fi superweapons are easy.

Adam Fields on 2013-02-03

Jumps always seem to go standstill to standstill. Does a ship in hyperspace lose all momentum before returning to regular space? Maybe you can’t hit a planet while in motion from hyperspace.

Aphyr on 2013-02-03

Momentum is only defined relative to a reference frame. If you accept special relativity’s postulate that inertial reference frames are indistinguishible, there’s no reason for a ship to match at any particular reference frame when it emerges from hyperspace.

“OK,” you say. “Our FTL drive behaves differently near gravity wells. At the end of a jump, when the ship returns to normal space, it sticks to the nearest heavy object. That’s what I mean by ‘lose all momentum’.”

General relativity is a local theory of spacetime, so any constraints we impose on this drive need to be phrased in terms of local spatial invariants. We could say that when a ship re-enters normal space, it does it in such a way that the instantaneous time differential of the local stress-energy tensor is zero, i.e. the force of gravity doesn’t change in direction or strength over time.

This still allows for spectacular relative velocities, because gravity falls off quadratically with distance. Sure, if you jump into earth orbit you’ll be stationary; but if you jump in to the system say, three days forward in earth’s orbit, all you have to do is wait and earth will smash in to you. Same deal, really.

“OK, so we constrain FTL exits such that our exit vectors put us in a stable orbit.” Worse. Now you’re allowed to pick extreme orbits. Extremely elliptical solutions to solar orbits can crash you into planets at fantastic speed.

“Circular orbits?” Not sure what physical reasoning would lead to this one, but Earth’s orbit has exceptionally low eccentricity so it would probably be safe. You could still orbit counterspinward to the earth and smash into it at 60-odd km/s.

“How about requiring that four-momentum be conserved between entry and egress from hyperspace?” Probably the most realistic constraint. Sol is moving at roughly 220 km/s relative to galactic core, so if you went to the opposite side of the galaxy you’d have to burn off roughly 440 km/s. That’s a lot of energy, but certainly not infeasible. It still gives you the opportunity to smash into things, though. For starters, earth could easily be flying towards a planet around a different star at 90 km/s, so once a year you’ve got a window to deliver a pretty impressive kinetic payload to your enemy. Regular freight travel would likely require months of orbital maneuvering to get into a favorable position for orbital sync.

It actually gets much worse than this. FTL drives which conserve four-momentum could allow you to violate conservation of energy. All you have to do is jump into their neighborhood of a big gravity well (e.g. a neutron star, supermassive black hole), allow it to pull you to fantastic speeds, then jump to your target before hitting the surface.

I can think of an interesting corollary to this technique, which relies on the fact that gravity wells actually change the energy of light heading into or out of the well, because space near large masses is stretched out more. If you have an FTL system which works like a four-momentum-conserving portal, you can shine a laser towards a black hole or other massive gravity well, have it acquire energy from spacetime compression, enter a portal, and come out at a higher energy than it started. Then you collect the energy with an antenna. You can extract free electricity from spacetime curvature.

It gets weird, because time flows slower deep inside gravity wells. FTL drives are also by definition time machines, and FTL drives which allow you to change your position in a gravity well allow for changing how fast time flows.

I’m pretty sure these sorts of systems are not valid solutions to the equations of general relativity. ;-)

FTL drives: unsafe at any speed

Post a Comment