Sunday, September 20, 2015

Armageddon

The year is 3015. It is the 20th of September

I was worried this week's movie would hit close to home, with a title like "Armageddon" but it turns out I had nothing to worry about. The flaws in that movie are too numerous to count, the biggest of which (not that they could have known), is that an asteroid is not the way the world ends. So, in the end the movie was actually rather enjoyable, as long as you didn't try and take it too seriously.

Rather than analyze the physics of this movie (as it is absolutely awful), we dug up some old plans for actual asteroid defense back before the Collapse. I found one that is rather interesting. Evidently the plan revolved around launching a shuttle or nuke, or basically something capable of impacting with a lot of energy, straight for the asteroid. When you think about it, the danger zone, time and place, for an asteroid strike is actually really small. The earth is about 12,750 km in diameter, and orbits at a rate of about 30 km/s. Do the math, and it takes the earth 425 seconds to move it's own width in it's orbit, or about 7 minutes. So regardless of the size, speed, and mass of the asteroid, it only has a narrow window of actually hitting the earth, instead of just being a near miss. The idea of launching a massive projectile at the asteroid is to impart enough energy into it and hit it with enough momentum to slow the asteroid down so it misses it's window.

Obviously, we need to know about the asteroid pretty soon in order to be able to slow it down enough to miss the earth. Take the asteroid in Armageddon for instance. With 18 days warning, we would have to slow that asteroid down by about 3 m/s. Given 18 years on the other hand, and you only have to slow it down by .008 m/s, give or take. And the further ahead we notice it, the less we need to slow it down. (Speeding it up would also work, but I will focus on slowing it down, just as preference)

Now, even 3 m/s doesn't sound like much, That is about as fast as humans walk. However, we have to look at that in terms of this massive object hurtling through space. Doing the calculations for the Armageddon asteroid, it gets a little depressing. Just to get an idea of how much energy we need to impart into the asteroid, we can view slowing it down as a conservation of energy equation. The initial kinetic energy has to equal the final kinetic energy minus the Work done to slow it down by the impact. We can write this (after moving some terms around) as: KE(i) - KE(f) = E(a), where E(a) is the energy of the impactor (the shuttle, nuke, etc.). The problem is, the more massive the object is, and the faster it's velocity is, the larger those numbers are. With the example from Armageddon, decreasing the asteroid's speed by even 3 m/s gives us 2.71 x 10^26 Joules, or 6.5 x 10^10 megatons of energy. That is an enormous amount of energy, and it is safe to say that we would not have been stopping the Armageddon asteroid given 18 days warning using this method.

Even given 18 years warning, and only needing to reduce the speed by .008 m/s, we still would need 5.45 x 10^23 Joules of energy. Thing's aren't looking so good for this defense plan. But there is hope. Take one of the largest nukes ever developed and tested, the Tsar Bomba, built by the Russian's during the first Cold War. It measured in at 100 megatons, or 4.184 x 10^15 Joules of energy. Using the same velocity calculations as the Armageddon asteroid, what is the size of asteroid that 100 megaton's would reduce the velocity by the required .008 m/s? Using the earlier formula, KE(i)-KE(f) = E(a), we can rewrite it to solve for the mass as: m(a) = 2(E(a))/v(i)^2 - v(f)^2
Plugging in our values, we get a mass of: 4.25 x 10^15 kg. Anything that size or smaller, we could slow down enough with a single large nuke. Lucky for us, I am fairly sure most asteroids are not as massive as the "large as Texas" and "compressed iron ferrite" (don't even get me started) asteroid from Armageddon. And as long as the asteroid is not much larger than the calculated mass, it may even be possible to slow it down the necessary amount with multiple nukes, or multiple impacts. In the end, this plan could work against most asteroids. But if something as big as the Armageddon asteroid is coming our way, we would be hard pressed to stop it.

Especially now that all our early detection equipment is unmanned or inoperable.... Oh well. Next week we get to see a 21st century super hero movie. I am looking forward to it, though I worry they won't be able to compare to our modern Captian Batman and his sidekick SuperHulk.

1 comment:

  1. Very nice analysis. I would have preferred to see you reference some documentation from NASA that they are actually considering this plan, but overall, this is a nice recapitulation of the physics.

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