Friday, February 22, 2008

No more poison fuel!

As you may have heard, the Aegis-class USS Lake Erie fired one missile at the "dying spy satellite" and scored a direct hit. That is pretty sharp gun-slinging. The squawking from the Chinese and the Russians only underscores how much of an achievement it was. I suppose that the Chinese have more cause to be chagrined as they already destroyed a satellite much higher up last year.

I was a bit bemused by the public statement of the spokesman for an outfit called the Missile Defense Advocacy Alliance:
The factual reality of using deployed missile defenses to destroy a falling satellite or a ballistic missile or even a meteor from space that would risk human life is an achievement for mankind. Missile Defense will continue to become more and more universal throughout the world and it will become more reliable and effective, so as to one day in the near future, we as a world can eliminate and mitigate risk from any and all harmful objects coming from space that would threaten mankind.

Our missile defense capability would, indeed, have to improve dramatically for us to "eliminate and mitigate risk from any and all harmful objects". For example, meteors are generally a bit on the small side; certainly not bus-sized. Even if they are bus-sized, they're awfully hard to spot a long way off.

Those near-earth asteroids that have caused a stir by coming "close" to earth have rarely passed within the orbital distance of the moon. There's currently only one, 99942 Apophis, that is of significant size with even a marginal chance of striking the earth. This baby is about 250 meters across and weighs about 2.1 x 1010 kilograms. [Ed. - Since The Town Crank is determined to be metrically and avoirdupois-ally correct, that's about 820 feet and 46 billion pounds, or about 23 million tons.]

What does that mean in terms of destructive power if it ever hit the earth? Calculating the straight kinetic energy using a velocity of 30.7 kilometers per second (69,000 mph), we get:

½ x 2.1x1010 kilograms x (30,700 meters per second)2
= 9.9 x 1018 Joules

The killer is that squared velocity term.

That number of Joules translates to 2,360 million tons of TNT...or in nuclear weapons parlance, 2,360 megatons. That's if the full orbital speed of the asteroid was brought to bear. According to the Wikepedia site, NASA has estimated a lower figure based on the fact that Apophis is orbiting in more or less the same direction as the earth is. Thus, any impact would be a glancing blow or a strike from behind. Still, the speed at impact would be 12.6 kilometers per second (28,000 mph). That's still almost 400 megatons of TNT if the full weight of the asteroid makes it to earth at that speed.

For comparison, the meteor that dug out the 1200 meter wide (3900 feet) Baringer crater in Arizona has been estimated at 3-10 megatons.

Don't you just love huge numbers? By the way, the calculations for this post were assisted by the excellent unit converter available at

Anyway, Apophis looks like it's going to pass within about 36,000 miles of earth in 2029. That's spittin' distance!

The question remains, no matter how accurate an SM-3 missile fired from an Aegis-class vessel can be, what's going to push aside a 23 million ton mass far enough to miss the earth? 23 million tons is about 2400 times the displacement of the USS Lake Erie itself...and the Lake Erie's top speed, while classified, is on the order of 32.5 knots or 37 mph. If the USS Lake Erie were thrown at the ground at 37 mph (equivalent to a drop of around 60 feet [correction: 47 feet – Ed.]), the energy released would be about 0.29 tons of TNT and it would have several large dents in it.

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