# Effect of a small mass at 'near light speed' in atmosphere? February 14, 2011 3:27 PM   Subscribe

Science of Science Fiction - What happens when a small mass at 'near light speed' enters the atmosphere?

So a (very) dorky discussion with some friends led to the following argument and I'd like to know who's "more correct".

Assume a man portable device (rifle sized) that is capable of accelerating a small mass to a "sizable percentage of lightspeed"*. The percentage wasn't defined, but assume 5-25%. The mass is assumed to be an average bullet or slug about the size of a marble made of some common material. What would happen once this mass left the device and entered sea-level atmosphere on earth at that speed?

Party one believes any mass hitting air at that speed would basically encounter a dense solid, so there would be a very sizable explosion once activated.

Party two believes the energy imparted would punch/push right through the air mass (much like a comet or meteorite) and aside from a sonic boom, would not cause the operator of this device much concern.

So what does the hive say?
posted by anti social order to Science & Nature (13 answers total) 1 user marked this as a favorite

Passage through the atmosphere would be so brief that little of its immense kinetic energy would be dissipated there. The column of air under the projectile would be compacted, creating a shock wave, but this would be rather small I think. My hunch is that 99% of the kinetic energy would reach the ocean/ground.
posted by neuron at 3:34 PM on February 14, 2011

Party one is more or less correct. Comets and meteorites don't "punch right through." They burn up, and whatever hits the ground is what's left over.

Even 5% of lightspeed is really, really fucking fast.
posted by Cool Papa Bell at 3:37 PM on February 14, 2011

5% of light speed is 9,300 miles per second.
posted by dfriedman at 3:39 PM on February 14, 2011

I plugged in much of what you wrote into here.

At .25 light speed coming at a 90 degree angle, with a density of iron = 1. This projectile is so small that it burns up during atmospheric traverse, 2. The Richter Scale Magnitude for this impact is less than zero; 3. The air blast at this location would not be noticed.

posted by edgeways at 3:44 PM on February 14, 2011 [1 favorite]

Isaac Asimov wrote a murder mystery that concerns something like this.
posted by Blazecock Pileon at 3:53 PM on February 14, 2011

Using this bullet energy calculator, a 62-grain bullet (standard NATO round) traveling at 0.05c (49,178,550 fps) would generate kinetic energy of 332,886,771,820.07 foot-pounds, or around 4.5 x 1011 joules, or some 450 gigajoules, about the energy achieved by exploding 75 barrels of oil, or roughly 1% of the yield of the Hiroshima bomb. For comparison, even Hiroshima would be a small fraction of the energy released by the presumed Tunguska bolide.

I'm personally of the opinion that it would reach the ground, though, assuming it struck the atmosphere with the correct rifle round attitude. The atmosphere extends at most some 200 miles and it would pass through that in about a millisecond.

See also "the rods from God" [a relativistic kill vehicle]. Alas, this is not just a back-of-the-envelope exercise for some people, the type of people who have somewhat unlimited federal funding. Somebody probably knows which advanced ceramic is best for this application.
posted by dhartung at 4:03 PM on February 14, 2011

Since you said "enters the atmosphere," I'm assuming we're talking about a projectile impacting the earth from space.

0.25c is 75,000,000 m/s. The specific kinetic energy of an object at that speed is 2.81x1015 J/kg. (Neglecting relativistic effects, so this is a slight underestimate.) If we assume a 5 gram bullet, its kinetic energy is about 14 trillion joules. According to Wikipedia, that's on the order of about 30,000 bolts of lightning.

Another way to look at it: suppose the bullet disintegrates completely before hitting the ground. We can put a very loose lower bound on the rate of energy release by assuming it loses energy uniformly. The bullet would traverse 100km of atmosphere in about a millisecond, so that's 14 quadrillon watts of power.

Divide that by the surface area of a sphere, radius 10 km, and at that distance the heat output would momentarily be about 10,000 times brighter than the sun. At 1 km, it would be a million times brighter than the sun. The incandescent gas trail would probably reach billions or trillions of Kelvin before it had time to cool.

This is all under the assumption that the bullet vaporizes before it hits the ground. If not, you still get the same amount of energy released, but it all goes into the ground instead. 2.8 petajoules is about the energy released in a magnitude 7.1 earthquake.

So my money's on catastrophic side effects.
posted by teraflop at 4:25 PM on February 14, 2011

Strike that last part about the earthquake, I mistakenly calculated it for a 1-kilogram object. 5 grams would be more like magnitude 5.5.
posted by teraflop at 4:36 PM on February 14, 2011

Assume a man portable device (rifle sized) that is capable of accelerating a small mass to a "sizable percentage of lightspeed"*. The percentage wasn't defined, but assume 5-25%. The mass is assumed to be an average bullet or slug about the size of a marble made of some common material.

Once you assume the existence of a man-portable device capable of imparting that much energy to a projectile without destroying itself and its operator, you may as well chuck all the rest of the physics out the window as well.
posted by flabdablet at 5:16 PM on February 14, 2011 [1 favorite]

"Man portable" is irrelevant to the question, as far as I'm concerned. The bullet doesn't care how it got moving to super-speed. The answer won't change if it was an imaginary rifle or something the size of a planet. All that matters is its current state & characteristics.
posted by scalefree at 6:06 PM on February 14, 2011

Once you assume the existence of a man-portable device capable of imparting that much energy to a projectile without destroying itself and its operator, you may as well chuck all the rest of the physics out the window as well.

Nu-uh! Maybe the device is... um... a portable wormhole generator, and there's some other facility where the slug is being accelerated to speed, and pulling the trigger just opens a portal to that facility to release the slug!
posted by Menthol at 6:17 PM on February 14, 2011 [1 favorite]

I think the OP is asking about a projectile down here at sea level, not something coming in from above the atmosphere.

I'm going with party 1. A relativistic gun would probably kill anyone nearby, including the gunman.
posted by General Tonic at 6:38 PM on February 14, 2011

it seems more likely you're asking about a person with a gun that can fire a bullet with near-light speed muzzle velocity, and that this gun is fired on a beach, target unspecified.

Yes, that's correct. Sorry for the confusion.

a portable wormhole generator, and there's some other facility where the slug is being accelerated to speed, and pulling the trigger just opens a portal to that facility to release the slug!

RETCON! hah yeah, the discussion was about hand-held sci-fi weapons that shoot slugs at hyperspeeds.
posted by anti social order at 6:33 AM on February 15, 2011

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