Tuesday, April 07, 2015

A Relativistic Impact Weapon

A Relativistic Impact

I first wrote about this on sciencefiction.com, but armed with information on highly-relativistic beam effects from the Large Hadron Collider (which I wrote about just a few posts ago)  it's timely to revisit.
"The logistic computer calculates that we have about a 62% chance of success, should we attempt to destroy the enemy base. Unfortunately, we would have only a 30% chance of survival - as some of the scenarios leading to success involve ramming the portal planet with the Anniversary at light speed." 
So speaks the unfortunate starship commander in The Forever War (Haldeman, 1974, p. 110).

An attack by highly relativistic impact weapons is a military planner's nightmare. The first problem is that the incoming weapon is highly superluminal: it appears to be travelling much faster than light. Suppose such a weapon was launched from interstellar space towards the earth at a velocity of 0.99995c (i.e. 99.995% of the speed of light). Its apparent velocity as observed from the earth is 20,000 times the speed of light (the speed-up factor is c/(c-v) which tends to infinity as the object's speed approaches that of light).

Suppose our military first spots this incoming object out at Jupiter's orbit, 35 light minutes away. How long do we have before impact? Less than one tenth of a second: there is simply no time to react.

What would be the effect on the Earth of such an impact? Some people have speculated that a relativistic impactor would simply tunnel all the way through the planet, perhaps not slowing down at all and not causing much damage. After all, light transit time through an Earth diameter of 12,800 km is just over 40 milliseconds. There’s not much time for lateral effects as the object barrels in.

But this conclusion is profoundly wrong.

Assume an adversary fires a one tonne object at the Earth at 0.99995c - the weight of a small car, or a cubic meter of ice. To work out the energy we use the relativistic energy formula E = γmc2, where γ = 1/√(1 - v2/c2) - in this case,  γ = 100. Most of that kinetic energy, (γmc2 - mc2) is going to get dumped into the Earth to create a stupendous explosion; there will also be colossal lateral radiation from the descending fireball. If we put the numbers in, the energy of the arriving impactor is around 2,000 Gigatons of TNT (compare with the 50 Megatons of the Russian Tsar Bomba, the largest nuclear weapon ever tested). This is broadly equivalent to a mile-wide asteroid hitting the earth at 30,000 mph; not bad for a single one meter cube.

Imagine watching the weapon as it hits the atmosphere with time slowed down a million times. In one microsecond light (and the weapon) travels only 300 metres. If the atmosphere is taken to be ~50 km deep, transit time to ground impact is just 170 microseconds (almost three minutes in our slow-motion view). But this is nuclear physics: microseconds are an eternity and the paradigm is particle accelerator.

Physicist Lawrence B, Crowell takes up the story in his analysis of the scenario:
"I think there would not be a hard collision of the object with the ground. It would pass through a column of air of comparable mass, so I suspect the energy of the object would be consumed before it hits the ground. This would be a sort of massive cosmic ray event. The interaction energy of atoms would be comparable to Tevatron energy (1/10 of that or so) and what would reach the ground would be a huge pulse of secondary particles that generate an enormous thermal-mechanical shock wave."
The LHC beam-dump engineering team modeled the LHC's proton beam hitting a solid copper tube. Half a microsecond after impact it had already penetrated 2 meters (around 7 feet)  into the copper tube with a core overpressure of 30 GigaPascals (300,000 atmospheres). The LHC protons are faster than our assumed impactor, but it seems clear that the atmosphere - hitting the impactor at 99.995% of the speed of light - would have completely penetrated the weapon in the first 1% of its atmospheric transit. After ten microseconds and three kilometers, the ice-block would be plasma. You may object that the top of the atmosphere is pretty sparse .. but then, so is the LHC proton beam.

Its very arrival would be spectacular enough - to conclude, here's an account from "The Killing Star" (Pellegrino and Zebrowski, 1995, pp. 23-24) of the arrival of a similarly-sized object arriving at just 92% of the speed of light.
"Then, looking east, she saw it coming - at least her eyes began to register it - but her optic nerves did not last long enough to transmit what the eyes had seen ... a flaming spear with every square foot of its surface radiating a trillion watts ... Virginia was more than three hundred kilometers away when the light burst towards her. Every nerve ending on her body began to record a strange pricking sensation - the sheer pressure of photons trying to push her backwards ..."
So there you have it. A weapon system very difficult to detect, arriving before defense systems could engage, and causing an extinction-level event. I present to you the Relativistic Kill Weapon (Wikipedia). Read more at Orion's Arm.

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